Prjzépa Pou Evavdla

Kai Ozov Aôsxcpô Pou Axéçavôpo

Azov Ayanrjpévo Pou Izazépa

Zouzov Zov Kôapo

Biancale, R., Sundaramoorthy, P. P Stavros A Melachroinos

Ingénieur Géomètre

Topographe

Joëlle Nicolas

Stéphane Durand

Laurent Morel

Marie- Noëlle Bouin

J Cali

B De Saint-Jean

H Duquenne

J Verdun

J-P Barriot

M.-N Bouin

F Masson

M Vergnolle

M.-N Bouin

M.-N Bouin

Autority Country

VTcépo/q

Keywords:

2.3.2.4

The narrow-lane combination (LNi) 95 2.3.2.5 The ionospheric geometry-free combination (Lion) 95 2.3.2.6 Combinations for Ambiguity détermination 96 23.2.1 New GNSS signais, new combinations 97 2.3.3 GNSS orbit errors 2.3.4 4.3 Summary 5 Kinematic GNSS technique to measure océan surface dynamic topography, sea-state, and derived parameters 205 5.1 Background of the DRAKE GPS campaign 5.2 Data collection and editing 5.2.

Firstly I sincerely thank Richard Biancale for his supervision, guidance and friendship that he so generously offcred me through the last three years. I specially thank him for the trust that he demonstrated to me and which I will always honour.

Félix Perosanz and Sylvain Loyer also deserve spécial thanks for their time in

showing me the basic functionalities of GINS GNSS software. I thank Félix for sharing his knowledge on GNSS as being the pioneer of GPS implémentation in GINS software.

I would like to thank Muriel Llubes who so kindly explained to me the complexity of océan tide loading prédictions and for sharing her algorithms.

Especially I would like to thank Jean Michel Lemoine for his kindness and friendly advices on normal équations and people's moods and attitudes.

Sean Bruinsma is also thanked for his kind contribution in correcting my idiomatic English mistakes.

I will never forget as well the warming welcoming of Nicole Lestieu who did not stop offering us delicious house made marmalades for breakfast.

Before, giving my final acknowledgments I would like to thank as well ail my Greek family, Lena, "giagia", "thia" Kaiti and cousins for the unstoppable encouragement during this difficult road. I specially thank my grandmother "giagia" for her infinité wisdom, simplicity and patience that she taught me in life and who I always hâve in mind when I loose my patience. Many thanks go as well to the French part of my family and especially Jean-Michel and Monique Fromion, Jean and Brigitte Fromion, Anne and Thierry Leveque and many more who were always there to support us when needed.

Finally, and as said in the cover and repeated again, I would like to express my endless love to Marie for her patience and efforts that this period represented for her and our daughter. I promise her that long waiting hours and difficult moments belong in the past and that I am looking forward for our new adventures together ail three of us. from [START_REF] Niell | Interaction of Atmosphère modelling and GPS Analyses Strategy, Advances in GPS[END_REF] and (right) station height différences between VMF and NMF GPS solutions (Boehm et al. 2006); NMF : Niell mapping function [START_REF] Niell | Global mapping functions for the atmosphère delay at radio wavelengths[END_REF], GMF : Global Mapping Function (Boehm et al. 2006b), IMF : Isobaric Mapping Function [START_REF] Niell | Improved atmopsheric mapping functions for VLBI and GPS[END_REF], VMF : Vienna Mapping Function [START_REF] Schuh | VMF and IMF mapping functions based on data from ECMWF[END_REF] Fig. 2-20 : Scale rate caused by inconsistent satellite antenna offsets (Gendt et al. [START_REF] Crisci | GIOVE Mission Sensor Station receiver performance characterization: preliminary results[END_REF][START_REF] Piriz | The Galileo System Test Bed V2 for Orbit and Clock Modeling[END_REF] Table 1-5 : GLONASS carrier frequencies in L1 and L2 sub-bands for each channel K.

List of Figures

(Source GLONASS ICD) Dans une première partie de la thèse, je présente une recherche bibliographique sur les caractéristiques principales de quatre systèmes du positionnement global par satellites et qui constitueront le futur système global des systèmes de navigation. Les bénéfices et les complexités des futures combinaisons des multiples observables de phase et de code sont appréhendés.

Dans une deuxième partie de la thèse, je me concentre sur la définition des composantes géodésiques utilisées pour le positionnement par GNSS. Les modèles observationnels et les plus récentes évolutions en matière de précision et d'exactitude des GNSS qui ont occupé mes recherches pendant mon projet, sont simultanément présentés.

Les erreurs dues à des effets systématiques qui perturbent la précision sur la détermination des positions des stations sont estimées. Ces effets se trouvent soit au niveau du prétraitement des mesures, soit en provenance des délais exercés sur la propagation des signaux, soit dues aux déplacements de la croûte terrestre sur laquelle se positionnent les stations.

Dans une troisième partie de la thèse, je présente tout d'abord le logiciel scientifique GINS qui a constitué l'outil principal de mes études ainsi que les modifications que j'ai apportées. Je présente ensuite, les différents tests de validations que j'ai effectuées pour évaluer les modifications tells que : les comparaisons sur les positions des stations à des séries temporelles de haute fréquence avec des résultats en provenance des logiciels globalement connus dans la communauté géodésique ; les comparaisons d'orbite GINS GNSS par rapport aux orbites précises de l'IGS pour valider des nouveaux modèles de radiation de pression solaire implémentés pour les satellites GPS comme le modèle « Boxand-Wing » ; puis pour préparer les premiers pas vers l'exploitation scientifique de Galileo, l'évaluation sur la précision de l'orbite du premier satellite du système de navigation européen GIOVE-A.

Dans une quatrième partie, l'étude principale sur les paramètres de la surcharge océanique dans des régions côtières complexes, comme en Bretagne, est présentée. Les

Summary

The impact of GNSS in the realization of the International Terrestrial Reference Frame (ITRF) and the détermination of the Earth's Pôle motion was seized by the geodetic team of GRGS of the French Space Agency (CNES) throughout the Centres de Recherche et des Combinaisons (CRC) IERS project.

The measurement of surface deformations sensed by permanent GNSS stations is a subject that the CNES/GRGS team wanted to investigate thoroughly. As already noted in the IERS 2003 conventions, the impact of these deformations in today's scientific applications of geodesy of high précision cannot any longer be neglected. In parallel the needs of oceanography and altimetry for independent measurements of the sea level variations by validation and cross comparison, hâve made the use of GNSS receivers on floating tracers (buoys, ships) or permanent GPS stations collocated with tide gauge sites, more than necessary.

In the first part of this PhD I présent a bibliographie research on the main characteristics and différences of four global positioning Systems that will constitute the future Global Navigation Satellite System of Systems. The benefits and complexities of future combinations from a multiple of carrier phases and code observables are presented.

In the second part, I concentrate in the définition of the basic geodetic components of GNSS used in positioning. Observational models and the most recent issues of GNSS accuracy and précision and which hâve occupied my research during the last time are simultaneously presented for real cases. An updated error budget of the systematic effects perturbing the accuracy and précision of the détermination of position of the geodetic stations at the pre-processing level, from signal delay's and stations' displacements due to the movements of the Earth's crust are examined.

In the third part, the GINS' scientific software package the basic tool used in this

PhD study is presented. Updated modifications implemented for the needs of my research are overseen. Then, validations through inter-comparisons with other well-known in the geodetic community software and through comparisons to the précisé IGS sp3 orbits on the level of précisé orbit détermination for the GPS constellation are presented. Furthermore, a first-step implémentation for the intégration of the future Galileo GNSS System is evaluated.

In the fourth part, the main study of océan loading parameters in a complex Coastal area that of Brittany, in France is presented. The recently validated modifications in matters Where: xs (/) is the 3D coordinate vector of the point S at the time t\ xAE(/)is the 3D coordinate vector of the référencé point R at the time t. The observed distance between these points will help us détermine the coordinates of the one with respect to the other in time and in space. The exact and précisé knowledge of their coordinates at the mm and sub-mm level is mandatory in today's scientific applications of space geodesy. In ail cases, the exact détermination of the position State parameters is a problem of determining the 3D coordinates of a geodetic point on the surface of the Earth, which is subject to several types of displacements due to: • Effects of the Solid Earth Tides (permanent and time dépendent) ;

• Rotational deformation due to Polar Motion (Pôle tides) ;

• monument deformations (thermal expansions etc.).

In practice the methods used for determining the 3D positions of geodetic points, vary significantly in function with:

• the physical environment (atmospheric conditions, multi-path etc. );

• the positioning mode : static/kinematic, real-time/post-processed ;

• the method and the techniques used (SLR, GPS, DORIS, VLBI) ; • the altimétrie satellites like Topex/Poseidon, Jason, Envisat, ERS, GFO etc. ;

• the GRACE satellites used for the détermination of the gravity field ; The impact of GNSS on the way we détermine coordinates on the Earth's surface is considérable compared to other techniques.

Inside these recent évolutions in matters of high précision positioning, the GRGS team of CNES is developing over 30 years the scientific software GINS (Géodésie par Intégrations Numériques Simultanées). The main functions of this software are designated to problems of the adjustment and combination of data sets coming from ail techniques of space geodesy like GPS, DORIS, SLR, VLBI, SLR, LLR, altimetry etc.

GNSS hâve gained large popularity in the domain of geodetic sciences. The exploitation and use of their data sets offers significant advantages with respect to the other space geodesy techniques such as:

• high density of observations (every receiver can simultaneously observe up to 10 satellites from a single GNSS, and even more satellites in the case of Galileo, GLONASS and Compass) ;

• continuous tracking measurements for LEO satellites ;

• extreme précision, rapidity, and low cost ;

• easy to set up ;

The scientific "GNSS activity" of the CNES/GRGS team is regrouped around three axes:

1. POD of LEO satellites (TOPEX/POSEIDON, JASON-1, ENVISAT etc.) and the détermination of the gravity field from CHAMP, GRACE and GOCE ;

2. POD of MEO satellites (GPS, GIOVE-A, Galileo) and global Earth kinematic study.

GRGS participâtes in a pilot project coordinated by the IERS called Centres de • Bemese GPS software (Astronomical Institute and University of Berne, Switzerland) ;

• GAMIT/GLOBK (Massachusetts Institute of Technology/ USA) ;

• GIPSY/OASIS (Jet Propulsion Laboratory / USA) ;

c) The subject Since the beginning of its GNSS activities the team of GRGS/CNES had invested in the research and algorithmic/software development concepts designated to problems of POD and détermination of the gravity field modeling (GRIM and EIGEN gravity models sériés).

In parallel the impact of GNSS in the realization of the International Terrestrial Reference Frame (ITRF) and the détermination of the Earth's Pôle motion was seized by GRGS through the CRC project [START_REF] Biancale | Towards a new strategy for mutli-technique combined sériés of EOP and TRF[END_REF]).

The geodetic software package GINS used by GRGS and unique in France, initially was not adapted for the studies of positioning and the deformations of dense geodetic networks by GNSS. The measurement of surface deformations sensed by GNSS stations is a subject that the GRGS team wants to investigate thoroughly. As already noted in the IERS 2003 conventions (McCarthy and Petit 2004), the impact of these deformations in today's geodetic applications of high précision cannot be neglected any longer. The physical causes of these crustal deformations are numerous and their time scale varies considerably. In parallel the needs of oceanography and altimetry for independent measurements of the sea surface topography by validation and cross comparison, hâve made the use of GNSS receivers on floating tracers (buoys, ships) more than necessary.

So, under these conditions, and for the préparation of the future European GNSS positioning System Galileo, as well, one of my missions during my PhD, was to introduce ail the necessary modifications in the software and then perform high précision millimeter positioning of geodetic terrestrial and maritime GNSS networks designated to the study of geophysical deformations and the observations of the mean sea-level.

I hâve organized the development of this PhD project around 4 axes: 1) Initially, I had to adjust myself in the logic and the complex treatment of GPS data by the use of other scientific GPS software. For that I firstly used the GAMIT/GLOBK software package of MIT. Then for reasons of compréhension and acquisition of expérience with GPS processing I studied the long term motion of GPS stations in tectonically active (Crete) and non-active régions (S-W France) and the impact on the final coordinate time-series from different strategies combinations.

2) Secondly, I concentrated in problems of POD and notably that of the impact of solar radiation pressure parameters on the GPS satellites orbits and the use of SLR for the POD of the First GIOVE-A satellite including the implémentation of a box-and-wing solar radiation pressure model.

3) Thirdly, I dealt with the study of océan tide loading parameters and the validation of tide models by the use of a dedicated GNSS campaign, in a complex Coastal area, that of Brittany, in France. This part was divided into three steps. The first was dedicated to the GINS' software modifications:

• Ambiguity resolution;

• Troposphère modeling;

• Algorithmic modifications;

• New processing strategies.

The The fifth chapter is dedicated to the preliminary results of a GPS kinematic campaign applied to the study of the Antarctic Circumpolar Current.

Last but not least, the conclusions of my studies during this PhD and the perspectives for further research continuation are given in the sixth chapter.

1 The GNSS System of Systems

If Ulysses had a GNSS receiver in his disposai would hâve he found an easier way to Ithaca?

In this chapter a description of the characteristics of GPS, Galileo, GLONASS and

Compass-Beidou Systems is given. GPS is currently fully developed. Galileo is at its first steps of implémentation. In 2006 the first test-bed satellite of the constellation, GIOVE-A, has been launched. GLONASS is under a modemization phase. Compass, which will be the future Chinese global positioning System, is also under way and a first satellite has been placed in a MEO in April 2007. Problems, related to the interoperability and compatibility between GNSS Systems, are also presented.

The GNSSes of today

Today, Russia hopes to retum GLONASS to Full Operation Capability (FOC) with a completed constellation by 2009, and Galileo's FOC is expected now for 2012 [START_REF] Hein | Envisioning a Future GNSS System of Systems, Part 1[END_REF]. Compass-Beidou is already on the move with its successful launch on April, 14, 2007. A scénario of four global coverage satellite Systems seems to be very likely in the near future.

With this increasing number of GNSS matters of interoperability corne to the surface.

For example, Galileo has managed to deal with problems of interoperability with its predecessor GPS, in a more successful way than GLONASS. But what does the word interoperability and compatibility of GNSS mean? According to the new PNT policy (available at http://pnt.uov/policy/ ):

• Compatibility refers to the ability of U.S. and foreign space-based PNT services to be used separately or together without interfering with each other service or signais and without adversely affecting navigation warfare.

• Interoperability refers to the ability of civil U.S. and foreign space-based PNT services to be used together to provide better capabilities at the user level than would be achieved by relying solely on one service or signal.

The previously mentioned model to compute the level of interférence is set up in the 2004 EU-US agreement.

The general term of interoperability splits into : System interoperability -where different GNSS provide the same answer, within the specified accuracy of each individual System, and signal interoperability -in which different GNSS transmit signais allowing their successful combination inside a receiver or a combined solution.

1.1.1.1 Interoperability of GPS, Galileo and GLONASS

The présent signal interoperability between GPS and Galileo is unique with respect to the other two GNSS (GLONASS and Compass). In order to ensure combined use of the two Systems with the highest performance possible at the user level the following requirements were considered:

• Signals-in-Space (SIS). Different frequencies may introduce frequency biases. between GPS and ITRF amount to less than two centimeters. The présent goal for Galileo is to realize within less than three centimeters with respect to ITRF a Galileo Terrestrial Reference Frame (GTRF). This ensures independence of both GPS and Galileo Systems. For the GLONASS more information is given in § 1.1.4.5,

• Time reference frame. The Galileo System Time (GST), the GPS time and the GLONASS time will be different real-time realizations of the Universal Time Coordinated (UTC) / Atomic Time (TAI). The GPS -Galileo time offset will be easily determined and received at the user's level.

Moreover GLONASS is not signal interoperable with GPS and Galileo but mostly is System interoperable. More description on GST and GTRF is presented in § 1.1.3.4 and §1.135 Since the launch of the first IIR-M satellites, a second civil signal was introduced with improved services (L2C). This génération is about to reach the 24-satellite FOC around 2012 [START_REF] Hein | Envisioning a Future GNSS System of Systems, Part 1[END_REF]. For military purposes a modemized M-code will be placed on both L1 and L2.

The second civil signal L2C may enable higher civilian accuracy when combined with the existing civil GPS signal L1 (C/A). L2C overcomes some limitations of L1(C/A) such as:

• Higher effective power ;

• Improved data structure ;

• It will hâve reduced interférence and it will enable indoor use.

BlocklIF

The third civil signal L5 (Fig. 1-1) will be présent in the future IIF satellites. The FOC with 24 satellites is expected to be complété around 2015. The First launch of this génération is scheduled for 2008. The third civil signal L5 will hâve:

• New enhanced performance with higher power (higher than other GPS civil signais); The GPS Block III phase is still under design stage. It includes significant improvements both in the ground and space segment. This will most likely include:

• Assured and improved level of integrity;

• Improved availability of accuracy with integrity;

• Backward compatibility with existing receivers; o L1C and future options for new navigation messages, flexible power levels;

The first launch is previewed for around 2013 [START_REF] Hothem | GPS Modernisation Program Current Status and Plans, National Space-Based PNT Coordination Office[END_REF]. The new improved The L1C will hâve a pilot carrier, which, as in the case of Galileo's L1 band, helps for better code and carrier tracking.

A preview of the four GPS satellites générations is shown in the following Fig. Currently the operational capability of the GPS control segment counts a total of 14 globally distributed stations. During the improvement plan a total of 4 more control sites is envisaged (Fig. 123). The modemization of the Operational Control Segment (OCS) has as goals:

• Each Satellite Vehicle (SV) will be tracked at least by three or more monitor stations over 99% of the time;

• The User Range Error (URE) will be around 1.0 m; Nevertheless the vision of a European GNSS existed long before, since 1992. Benefits for Europe in a level of social and économie growth will be considérable. Galileo is not only another technological project but it is a key component to tomorrow's civil, commercial, scientific, industrial and defense strategie tasks of the EU and its 27 nations.

Galileo is designed to provide a highly accurate, global positioning service.

According to Galileo 's Signal-In-Space Interface Control Document (Galileo SIS-ICD) the System will be signal interoperable with GPS and, at least to some extent -excluding the real-time high-precision services of the Systems -with GLONASS.

The fully deployed Galileo Systems will consist of 30 Satellites (27 operational and 3 non-active spares). The System's orbit will be a quasi-circular MEO orbit of 29601.297 km semi-major axis and an inclination of the orbital planes of 56 degrees with reference to the Earth's équatorial plane.

The development phase

In December 1992, Galileo was just a glimmer in a few visionaries' eyes. That was the month that two European Commission (EC) directorates-general -those for transport and science, research and development -decided to fund a modest study of satellite navigation options for Europe. Since that epoch Galileo went through many seas and storms. Some of the past, présent and future steps in its rather "wild" coarse are exposed:

• the 5 services of the Galileo System were defined as well as the beginning of the deployment and exploitation phase;

• Beginning of the European Geostationary Navigation Overlay Service (EGNOS); well as 3 more experimental spacecraft;

• FOC with the complété constellation is projected for 2012 (Fig. 1234).

• On July 26 2007, the US and the EU announced their agreement to jointly adopt and provide an improved design for the respective GNSS signais. These will be implemented on the Galileo Open Service (L1F) and the GPS IIIA (L1C) new civil signais.

Fig Two of these carrier phases will be in common with GPS, the E5a and Ll. In Fig.

1-5 are illustrated the Galileo signais mapped onto the services. • Maintenance of the GTRF until the IOV phase ;

• Recommendations for the permanent service ;

• Delivery to the GRSP ;

• GTRF définition, réalisation, maintenance, link to the IERS and to the International Laser Ranging Service (ILRS).

A stable and précisé GTRF will serve as the basis for ail Galileo-related services and Galileo orbits. It will be an independent reference frame made by Galileo's own observations, at least after the completion of the FOC phase. Until then the GTRF will be materialised by observations of both GPS+Galileo. One of the quality spécifications is that the GTRF shall be compatible with the ITRF at 3cm (2a). That means that the relative accuracy of the GTRF solution (station positions) with respect to the solutions of ITRF or those of the International GNSS Service (IGS) core stations expressed in ITRF shouldn't be more than 3cm at a 95 % confidence level (Gendt et al. 2007). The coordinates and velocities necessary for the GTRF réalisation will be provided by a core network of 18

Galileo Sensor Stations (GSS) during the IOV phase and a total of 50 GSS including 5

Galileo Uplink Stations (ULS) after the kick off of the FOC phase [START_REF] Sôhne | GGSP: Réalisation of the Galileo Terrestrial Reference Frame[END_REF]. In the total number of GSS are included also stations with at-least 2 collocated techniques such as SLR and VLBI and optionally GLONASS and DORIS (Mandatory GPS) [START_REF] Sôhne | GGSP: Réalisation of the Galileo Terrestrial Reference Frame[END_REF]. The réalisation of the GTRF will be established by a free network adjustment [START_REF] Grafarend | Unbiased free net edjustement[END_REF]Schaffrin 1973, Heflin et al. 1992) in order to avoid errors in fixing the ITRF reference stations and to simultaneously détermine:

• Station positions and velocities ;

• Earth Orientation Parameters (EOPs) ;

• Orbit and Clocks.

The necessary alignment to ITRF will be accomplished via an IGS core network expressed in ITRF collocated to GSS and non co-located stations. As none of the space geodesy techniques is able to provide ail the necessary parameters for the TRF datum définition, SLR and VLBI stations co-located to GSS will provide independent quality check and connection to geocentre, scale and the inertial frame (earth rotation) [START_REF] Sôhne | GGSP: Réalisation of the Galileo Terrestrial Reference Frame[END_REF]).

Local and intra-technique ties must be determined with an extreme précision. Preliminary observations from around 10 GSS stations in combination with IGS stations hâve been collected during the IOV phase for the détermination and characterisation of GIOVE-A orbits and clocks (see § 3.2.2.2).

The Galileo System Time (GST)

As stated in § 1.1.1.1, an important element in combining different GNSS, apart from a geodetic reference frame, is the implémentation of a reference System time (GST for Galileo). Galileo will establish a reference time scale, GST, to support system's operations.

The GPS time and GST will be in general independent.

The metrological function (the accuracy in the dissémination of the Temps Universel Coordonnée, UTC) of the GST is the responsibility of the Galileo Time Service Provider (GTSP) which will cover matters related to design, implémentation testing and operations during the IOV phase.

The key element in the GST architecture will be the Précision Timing Facility (PTF) [START_REF] Hahn | Implémentation of the GPS to Galileo Time Offset (GGTO)[END_REF]. This element is in charge of the navigation timekeeping and will: through the extemal correction provided by GTSP;

• Provide GST to the orbit détermination and time synchronization process.

The PTF facility is located within the Galileo Control Centers (GCC).

The offset between TAI représentations derived from GPS and Galileo broadcast can be expected to be around 33 ns (95%) [START_REF] Moudrak | Timing Performance of Galileo Mission Segment (GMS)[END_REF] The GTSP is responsible for keeping GST aligned (steered) to TAI within tight spécification and predict the time offset from UTC (leap seconds).This is achieved by conducting time transfer measurements between the Galileo PTF master clocks and the timescales within the core UTC laboratories. These UTC core laboratories are the National Metrological Institutes of France, Germany, Italy, and UK. GTSP will provide its corrections to the Galileo Mission Segment (GMS) which will be responsible for ail ground functions related to Galileo mission implémentation. Among them is the génération of the GST. GTSP, after the end of the IOV phase and beginning of FOC phase, will constitute and provide support to the full Time Service Provider (TSP). GST will be available as a physical signal and will be fed to the Orbit Détermination and Synchronization Facility (OSPF) which will compute the orbits of Galileo satellites and predict their clocks versus GST.

The satellite clocks which will be installed on-board of the Galileo satellites are of two kinds:

• Rubidium atomic clocks ;

• Space Passive Hydrogen Maser clocks.

The estimated offset of GST from TAI will be broadcast in the Galileo navigation message.

1.1.3.5.1 The Galileo-GPS Time Offset (GGTO)

The residual offset between GST and GPS Time, GGTO, can be expected to be about 57 ns (95%) considering today's performance of GPS Time and the required performance of Galileo.

A schematic représentation of the GGTO is in Fig. 1234567. The GGTO will represent an important issue for GPS-Galileo interoperability, since it will cause bias between measurements in combined GPS/Galileo receivers.

Galileo Integrity

Whereas many Galileo user services benefït uniquely from the system's positioning accuracy, a rather large number of navigation applications will require the navigation information provided by the System with the highest confidence level possible. This is the case for SoL applications such as earth or air transportations. The integrity functions will be managed and executed from the Integrity Processing Facility (IPF) which is a real time Processing of the GMS that provides the broadcast satellite navigation data based on the GSS. In this case, with known positions of the GSS the actual position of the SV and with this the maximum error on the range (Signal-in-Space-Error, SISE) can be estimated [START_REF] Hernandez | GALILEO Integrity : The Ground Segment Computation Algorithm Perspective[END_REF], Oelher et al. 2004).

i Fig. 1-8 : SISMA estimations (m) of ail potential satellite positions for nominal SoL-FOC. The GSS stations are in white circles [START_REF] Hernandez | GALILEO Integrity : The Ground Segment Computation Algorithm Perspective[END_REF] If the SISE is larger than a certain threshold the satellite will be flagged "Don't Use". Next, and after certain False Aïarm (FA) vérifications, the following information is disseminated For more details on the whole integrity concepts the reader is suggested to look into [START_REF] Hernandez | GALILEO Integrity : The Ground Segment Computation Algorithm Perspective[END_REF]), Oelher et al. (2004) and [START_REF] Paimblanc | Impact of SISMA Computation Algorithm on User Integrity Performance[END_REF]. 1.1.3.7 Galileo In Orbit Validation Elément (GIOVE) In préparation for the development of the Galileo System, the European Space Agency From May 17 2006 till today GIOVE-A has been transmitting the signais illustrated The static analysis at the GESS sites (in Fig. 1-11) shows that mutlipath remains at relatively low levels for a cut-off angle of 10°. connected to the GIEN station, in Torino, (Table 1-4) was used as the reference clock for the whole expérimentation. The AHM was continuously monitored versus the INRiM's (Istituto Nazionale di Ricerca Metrologica) ensemble of atomic clocks and compared to extemal time référencé scales such as the UTC realised by the BIPM in France. During the analysis period the GIOVE-A was configured to transmit the L1 and E5 signais (Fig. 12345) using the nominal payload chain, driven by the RAFS Flight Model 4 (FM4) and Flight ModeI 5 (FM5) -the two on-board clocks. The C1C-C7Q and L1C-L7Q (Table 1-3) ionosphere-free code and phase combinations were selected for clock characterisation, and

were used together with the P1-P2 and L1-L2 ionosphere-free code and phase combinations from the GPS constellation. The ODTS solved for orbits, clocks, tropospheric delay, Inter-System Bias (ISB), which is the differential delay between the GPS and Galileo signal paths within the station. The ISB is the équivalent of GGTO in § 1.1.3.5.1, The estimated phase-offsets, with respect to the référencé AHM, are not the pure clock as tested on the ground but rather an "apparent" the receiver network. The Allan déviations expressing the frequency stability of the atomic clocks which are derived from the ODTS technique are illustrated in Fig. 1-12.

FREQUENCY STABILITY

Apart from the excellent performances of the two RAFS clocks, many frequency jumps occurred during the testing period especially after a payload switch-off According to [START_REF] Rochat | Orbit and Clock Characterisation RAFS Assessment and Lessons Learned[END_REF] The GLONASS System is being modemised based on the following main characteristics:

• Qualitative improvement of radio navigation signais. Introduction of the third frequency;

• Improvement in the stability and reliability of timing signais;

• Implémentation of inter satellite links.

In the next génération GLONASS-K satellites a third civil signal at the L3 band (1194.45 to 1208.97 MHz) as well as integrity information will be added.

In matters of signal interoperability with GPS and Galileo things become more complicated since GLONASS uses FDMA and not CDMA as the previous two GNSS (see § 1.1.1), Some statements made by Russians officiais are suggesting that maybe the CDMA protocol will be applied in the new GLONASS-K satellites at the third civil signal. GLONASS time is generated on the basis of a Central Synchroniser (CS) time.

13 Satellite atomic clocks hâve a daily stability which is not worse than 5x10' sec for the GLONASS-M satellites. The CS is a set of hydrogen clocks with a daily stability of 10'14 sec.

The time scales of the GLONASS satellites are periodically compared with the CS The first substantial efforts to create ties in between the reference frames of GPS and GLONASS hâve been realized through the International GLONASS Experiment (IGEX-98) [START_REF] Willis | GLONASS observation campaign (IGEX-98)[END_REF]. This effort continuée! by the International GLONASS Service -Pilot Project (IGLOS -PP), which is a pilot project of IGS, in order to track and analyze data from the Russian GLONASS satellite constellation. The project operated for a period of four years from 2000-2003[START_REF] Ch | GLONASS Pilot Project[END_REF]. The goals where to establish and maintain a global GLONASS tracking network collocated with dual-frequency combined GPS/GLONASS receivers, produce service (orbits, satellite clock estimâtes, station coordinates, earth orientation parameters), monitor and assess GLONASS System performances, fully integrate GLONASS into IGS products [START_REF] Slater | International GLONASS Service Call for Participation[END_REF]. Since June 8 2003 (GPS Week 1222), the CODE Analysis Center at the University of Bem has been computing rapid and final orbit products for the GLONASS satellites. CODE generates these GLONASS orbits at the same time as the GPS rapid and final orbits [START_REF] Slater | Timely rapid and final GLONASS orbits available from CODE analysis center[END_REF].

The combination for the GLONASS final products is performed since GPS Week 1300 at the IGS Analysis Coordinator [START_REF] Gendt | Status of the IGLOS/GLONASS combined products[END_REF]. The combined GPS/GLONASS IGLOS network is illustrated in Fig. 1-15. The main orbital characteristics for Compass satellites are: a semi major axis of 27800 km, an inclination of 55°and a circular orbit.

A preliminary measurement campaign made by [START_REF] Grelier | Initial Observations and Analysis of Compass MEO satellite signais[END_REF] EGNOS provides additional pseudorange measurements from the geostationary satellites. It consists of three geostationary satellites;

• The Beidou System which is the équivalent SBAS of china ( § 1.1.5);

• The Qnasi-Zenith Satellite System (QZSS) is Japan's SBAS which is a constellation of three satellites inclined by 45°, in elliptic orbits, with different orbital planes in order to pass over the same ground track. The first satellite launch is planned for the year 2009 (Kogure et al. 2006);

•

The Indian GPS and GEO Augmented Navigation (G AG AN) System is an independent seven satellite constellation that will seek to maintain compatibility with the other GNSS and augmentation Systems of the région (QZSS, Beidou). Of the seven satellites three will be geostationary and the other four geosynchronous.

The first payload in expected for 2007.

Summary

In this chapter we went through the most important characteristics of présent and future GNSS positioning Systems.

At the advent of the 21st century the total number of GNSS satellites is augmenting For example, in mutli-GNSS combinations of the future triple-ffequency geometryfree/ionosphere-free linear combinations of ranging measurements from the same satellite shall become available. These linear combinations will contain superposition of multipath and tracking signais in three or even more frequencies so information on phase multipath shall become available through observations in an absolute mode (single-satellite singlestation). Multiple frequencies combinations can be translated to multi-carrier phase ambiguities which can be used as constraints to ambiguity resolutions schemes. Fast ambiguity fixing will be possible over longer distances using signais and a rather elevated number of satellites. For instance, this will be very bénéficiai to GNSS kinematic applications in geosciences, as the détermination of coordinates, under rough conditions, of floating tracers in the open océan, for the validation and comparison of sea-level parameters.

Nonetheless, more frequencies and Systems do not always mean "easier life". On the contrary, the amount of work, for those concemed, combined with the complexity of the situation will grow tremendously. For example: conventional differencing techniques may not be possible due to different signais tracked by different receivers and channels or each signal component will hâve its individual bias induced by the satellite hardware and receiver hardware [START_REF] Wübenna | New GNSS Signais and Ambiguity Resolution[END_REF]. Finally, interoperability and compatibility will be the two driving mechanisms by which we will achieve a Unified Global Satellite Navigation System of Systems. The independence of each of the aforementioned Systems provides greater reliability and integrity for the users and leads to a certain compétition among the Systems.

Having ail these in mind the most important parameters of the existing GNSS Systems are summarised in Table 1-6.

GNSS hâve been serving the geodetic community since the early beginnings of the GPS System, during the 80's. Apart from a technological achievement, the GNSS is also a scientific achievement for Geodesy.

GNSS can provide geodesists with accurate and précisé positions by a measurement of the time-travel of an electromagnetic wave between a satellite in space and a GNSS receiver stationed on the surface of the Earth's crust. In order to achieve this goal the geodetic components of GNSS hâve to be taken into considération such as:

• The global Terrestrial Reference System (TRF) to which the geodetic points will be referenced together with the derived products from GNSS such as orbits and clocks, EOPs, station positions and velocities ;

• The geodetic GNSS network of stations ;

• The observational model errors degrading the précision of GNSS observations ;

• The prédiction of the physical processes that provoke displacements and deformations of the geodetic network of stations.

Ail these éléments are being combined together, in order to accurately and precisely estimate, in a least squares sense, the coordinates of geodetic stations.

For instance, when two sets of coordinates of the same network corresponding to two different epochs are compared for the dérivation of deformational parameters (e.g. océan tide loading constituents) the results dépend on the terrestrial reference frames used at both epochs.

In the next parts of this chapter we will see step-by-step the main parts that enter inside the duty tasks of a GNSS analyst and the scientific tasks of the présent report.

A synopsis of the functional models applied and the systematic errors acting on the GNSS observables is given. Troposphère and ionosphère delays are some of the most important factors of distortion in the accuracy and précision of estimated coordinates by GNSS; the unknown integer number of cycles of the carrier phases is an important source of biases; receiver clock errors such as clock jumps and dérivations from the GPS time and cycle slips during a measurement period can introduce important artifacts to the final positions estimâtes; variations of the center of phase of the GNSS antennas aboard the satellites and the receivers on the ground can significantly influence the scale of the System; rotations of the antennas can introduce biases; multi-path effects add noise to the final sériés of stations etc.

Ail these geodetic components of GNSS are taken into account simultaneously for the scientific investigations of this Thesis which are:

• The détermination of accurate and précisé deformation parameters of régional and local GNSS geodetic networks provoked by Océan Tide Loading (OTL)

displacements and the validation of predicted constituents ;

• The combined use of marine and terrestrial GNSS networks in order to observe water height variations of the Antarctic Circumpolar Current through the combined use of floating GNSS tracers (Buoys), tide gauge and altimetry.

Global Terrestrial Reference Frames

The physical establishment of a global Terrestrial Reference System (TRS) is accomplished through a global geodetic network based on the analysis of various geodetic techniques (Dermanis 200la). Its aim is to provide unified means for describing position by means of coordinates of discrète points on the Earth's surface. Alternatively, the TRS will be the mathematical object satisfying an idéal définition in which point positions will be expressed and a Terrestrial Reference Frame (TRF) will become its materialization [START_REF] Altamimi | ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications[END_REF].

On the other hand there is a need in geophysics for an Earth reference frame, i.e. a frame that refers to the behavior of the deforming earth as a whole involving ail its mass points and not just a set of discrète points confined on its surface. Such frames are indispensable in théories of earth rotation [START_REF] Munk | The Rotation of the Earth[END_REF] where the conversion schemes of a TRF to a geophysically meaningful Earth reference frame, such as the Tisserand axes frame, require having a straightforward comparison of the observed rotation of the terrestrial frame with respect to an inertial celestial frame. The geodetically produced TRF is generally different from the frame of Tisserand axes of the Earth's rotation theory where the relative angular momentum of its axes vanishes (Dermanis 2001a).

The optimal choice of the reference frame requires the introduction of an optimality criterion such that the apparent motion of the network points, as seen with respect to the reference System, is minimized. This condition introduces the origin and axes in a purely mathematical way by minimizing the apparent motion of the ITRF network points with respect to the reference System [START_REF] Dermanis | The ITRF beyond the linear model choices and challenges, VI Etotine-Marussi Symposium of Theretical and Computational Geodesy : Challenge and Rôle of Modem Geodesy[END_REF]):

• The origin is constant and defined by the barycenter of the N network points x (/)

(treated as unit mass points), t is the time (Eq. 2-1). In the case of TRS the origin is defmed by the center of mass of the whole Earth including océans and the atmosphère [START_REF] Altamimi | ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications[END_REF].

1 N -V x (0 -m = constant, \/t Ntf •
The axes give the orientation of the System where its évolution in time should be ensured by the Tisserand axes principal: ail relative angular momentum h (Eq. 2-2)

with regard to the horizontal tectonic motions over the whole Earth should vanish

(No-Net-Rotation). Eq. 2-2 N £[x,.(0x]-i(0 = 0, J 1 (sil' \/t
The conversion of the geodetic TRF to a Tisserand frame strongly dépends on the adopted hypothèses about Earth deformation.

Some of the relative mass motions on the surface of the Earth that contribute to the displacement of points of the geodetic networks are: plate tectonics, seismic events, atmospheric and oceanic tidal and non tidal loading, hydrological loading etc.

The International Terrestrial Reference Frame, ITRF

The history of the ITRF goes back to 1984. The First réalisation of ITRS was the ITRF88 and since then nine versions were established and published: ITRF89, ITRF91, ITRF92, ITRF93, ITRF94, ITRF96, ITRF97, ITRF2000 and the most recent one ITRF2005 [START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time-series of station positions and Earth Orientation Parameters[END_REF]. For more details regarding the history and description of ITRF the reader may refer to the list of ITRF papers given in the references of this Thesis [START_REF] Boucher | Results and analysis of the ITRJF94[END_REF][START_REF] Boucher | Results and analysis of ITRF96[END_REF][START_REF] Boucher | Results and analysis of ITRF96[END_REF][START_REF] Boucher | The 1997 International Terrestrial Reference Frame (ITRF97)[END_REF][START_REF] Altamimi | ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications[END_REF].

According to IERS the basic idea of ITRF is to combine station positions computed by various analyses centers which process observations of space geodesy techniques, such as VLBI, SLR and LLR, GPS and DORIS (Fig. 2-1). Each of these techniques and each analysis center matérialisés a different TRF.

, 1 Technique a 2 Techniques *3 Techniques ^Techniques The access of a simple user to the ITRF is accomplished through the use of the coordinates and velocities of the stations of each space geodesy technique.

The transition between two different reference frames consists of the transformation of the Cartesian coordinates of TRF1,X, to TRF2,X2 characterized by a 7 parameter Euclidian similarity transformation:

Where: T is the three dimensional vector of the origin translation T i, T2, T3; R is the orthogonal matrix of rotation that contains the set of the three Euler angles Ri, R2, R3; D = scale -1. The number of transformation parameters becomes 14 when we consider as well their évolution in time.

The TRF network combination model

As previously stated, the final ITRF frame will be the product of global combinations of the time-series of stations from ail the space geodesy techniques. The combination model consists of transforming each individual TRF of each technique to a given TRF. This is the same procedure in the case where a classical type of GNSS network is set up and the network's coordinates will be transformed to the desired TRF. These coordinates at some reference epoch are used as unknown parameters and their variation with time gives rise to displacements which are fonctions of time.

The combination model is based on Eq. 2-3 and a more expanded form for an individual solution 5, and each point i is:

X2=X{+T + D-X{+R-X Eq. 2-3
Eq. 2-4

Where: is the position of each individual solution (e.g. a weekly GPS solution) at epoch t's ; X's the velocity expressed in a given TRF k\Dk is the scale factor; TA the translation vector ; Rk the rotation matrix.

The combination (for the TRF) consists in: estimating positions X', at a given epoch In addition to the above équation, EOPs can be added in the combination process such as the pôle coordinates xp, yp , the universal time UTS as well as their daily time dérivatives xf,ÿp and LODs provided by the IERS [START_REF] Gambis | Monitoring Earth Orientation using space-geodetic techniques : stateof-the-art and prospectives[END_REF][START_REF] Altamimi | Long-term stability of the terrestrial reference frame[END_REF]:

UT = UT R f xf = xp + R, ç c Z, ÿps=ÿpc+^A , LOD = LOD +--R f Eq. 2-5
where / = 1.002737909350795 is the conversion factor from UT into sidereal time.

Considering LOD --A0

,A0is homogeneous to time différence, so that A0 =lday in dt time unit. The link between TRF and EOP is ensured through the 3 Euler rotation angles of Ri, R2, R3 plus their time dérivatives.

The Datum problem or Zéro order Design

According to Dennanis (1985) , coordinates of the points of a geodetic network define the position of the network with respect to the reference frame, or the position of a reference frame with respect to the network.

The normal équation System of weekly solutions, which is referring to Eq. 2-3, has a rank deficiency of 7 corresponding to the number of transformation parameters needed to define the reference frame while the normal équation of the global combination process into a long-term solution of Eq. 2-4 has a deficiency rank of 14.

In the case of coordinate's transformations, the number of degrees of freedom leaves the observations invariant [START_REF] Dermanis | Optimisation Problems in Geodetic Network with Signais, 3rd Course of the International School of Advanced Geodesy "Optimization and Design of Geodetic Networks[END_REF]. The datum defect or Zéro order design problem (Dennanis 1985) due to the rank deficiency can be overcome by means of a number of constraints on the parameters (coordinates or transformation parameters). Such constraints that define the reference frame without distorting the shape and size of the network are called minimal constraints. When added to the normal équations they reduce the number of independent parameters and allow for one unique solution.

The simplest way, of defining the reference frame or aligning a solution to the TRF in question, is by fixing the coordinates (at least 6, three for rotation and three for translation of the network) of a set of stations to their TRF values or by applying the minimal constraints to the parameters of the transformation in Eq. 2-3 and 2-4. For more details on minimal constraints the reader is suggested to look in [START_REF] Dermanis | Optimisation Problems in Geodetic Network with Signais, 3rd Course of the International School of Advanced Geodesy "Optimization and Design of Geodetic Networks[END_REF], [START_REF] Sillard | A review of algebraic constraints in terrestrial reference frame datum définition[END_REF], [START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time-series of station positions and Earth Orientation Parameters[END_REF].

Nevertheless, it is known that geodetic observations are not, in general, insensitive to ail degrees of freedom of a similarity transformation. For example, a technique such as VLBI is sensitive to orientation and not to the origin of the coordinate System. GPS is sensitive, to a certain degree, to geocentre but not to orientation. The above properties are of course dépendent on the distribution of the network, and a continental network has, in any case, a low sensitivity to geocentre especially when relative positioning is performed. So in the case of a GPS continental network which is viewed as a plan from the satellite height the geometrical problem is équivalent to defming a 2-D reference frame associated to a plan while we hâve to define a 3-D reference frame. Therefore, 7-4 = 3 degrees of freedom hâve to be defined.

Up to now the current time évolution of the ITRF is defined as linear to account mainly for tectonic plate motion while no deformation model or geocentre variations are taken into considération [START_REF] Altamimi | Long-term stability of the terrestrial reference frame[END_REF][START_REF] Dermanis | The ITRF beyond the linear model choices and challenges, VI Etotine-Marussi Symposium of Theretical and Computational Geodesy : Challenge and Rôle of Modem Geodesy[END_REF]).

Week numher Fig. 2-2 : 12 years of weekly geocenter time-series wrt ITRF2000 from SLR [START_REF] Coulot | Analysis of 12 years (1993-2004) of Satellite Laser Ranging data[END_REF] The geocentre variations are estimated either by dynamic or géométrie methods. The dynamic method is based on the estimation of the degree one terms of the gravitational field while the géométrie method is based on the estimation of the three translation parameters (in Eq. 2-3) with respect to an assumed geocentric ITRF (Fig. 2-2). The geocentre motion undergoes annual, semi-annual, diumal and semi-diumal variations due to mass distributions (atmosphère and océans) of the solid Earth (including the interior) as seen in Fig. 2-2 [START_REF] Watkins | Observations of Tidally cohérent diumal and semidiumal variations in the geocenter[END_REF], Dong et al. 1997, Bouillé at al. 2000[START_REF] Moore | Geocentre variation from Laser tracking of LAGEOS1/2 and loading data[END_REF][START_REF] Dong | Origin of the International Terrestrial Reference Frame[END_REF], Blewitt 2003[START_REF] Coulot | Analysis of 12 years (1993-2004) of Satellite Laser Ranging data[END_REF], Lavallée D. et al. 2006).

The Combination Research Center (CRC) project

Up-to-date two types of TRS réalisations exist inside the IERS. The one is official and the other is a pilot project.

The first is formed by using the final reference frame products (station time-series, positions and velocities) of each Technique Centre (TC) and by stacking them into a global combination process. This is the today's procedure in creating the ITRF. For that purpose the IERS relies on each TC themselves organized in International Services (IGS, International VLBI Service; IVS, ILRS, and International Doris Service; IDS) whose first rôle is to promote the appropriate use of the geodetic technique. These services gather EOPs and reference frames inputs from the different analysis Centres and generate combined products or normal équation files in a commonly adopted format (Software Independent Exchange, SINEX). Usually these products are achieved independently per technique by each TC without having the necessary consistency (for instance due to different a-priori models and software). Then these products are gathered by IERS in order to be combined in the global combination process that will form the final ITRF.

The second approach enables the pilot project named Combination Research Centers (CRC), which is under development by the IERS [START_REF] Biancale | Towards a new strategy for mutli-technique combined sériés of EOP and TRF[END_REF]. The leader of this project in France is the GRGS.The IERS CRC hâve the task to study a homogeneous way for insuring consistency in the création of an ITRF. This is succeeded by:

• combining ail techniques first at the level of each Analysis Centers;

• using if possible a unique software, or at least the same a priori models for analyzing different techniques;

• generating simultaneously EOPs and TRF;

• evaluating the gain of the method.

The rôle of the CRC is to become, in a certain meaning, an analysis centers for ail techniques and products [START_REF] Biancale | Towards a new strategy for mutli-technique combined sériés of EOP and TRF[END_REF]). In The CRC approach has the advantage that any inconsistencies created in the today's ITRF process by the use of different ad-hoc models and software by each analysis center, for each space geodesy technique, will be extremely minimised. The big advantage of the GRGS CRC approach is that it uses a unique geodetic software GINS (Géodésie par Intégrations Numériques Simultanées) for ail the space geodesy techniques illustrated in Fig. 2-4 developed and maintained by the CNES GRGS team. This software is being used for: orbit computations around any planetary body (Earth, Sun, other planets or small bodies); for gravity field modeling of the Earth (EIGENGL04s) observatories in order to study the deformations the Alps (in Fig. 234567), the Japanese GEONET, the Swedish SWEPOS, the Swiss AGNES, the German ASCOS and SAPOS, the Austrian APOS, the Hellenic HEPOS etc. The primary objective of the IGS is to provide the reference System for a wide variety of scientific and practical applications involving GNSS. To fulfil its rôle the IGS produces a number of "fundamental" products used in the current Thesis which are:

• Data from a global network of over 380 permanent, geodetic GNSS stations operated by more than 100 worldwide agencies [START_REF] Dow | Meeting the Challenge : PIow can the International GNSS Service (IGS) Contribute to the Global Geodetic Observing System (GGOS)[END_REF];

• Reference frame products like station time-series, positions and velocities ;

• GPS and GLONASS satellite orbits and clocks and receiver clocks ;

• EOPs;

• Station spécifie Tropospheric Zenith Delay (TZD) parameters ;

• Global ionosphère maps.

The most principal ACs that participate in the production of the IGS reference products are:

• The Center for Orbit Détermination in Europe, AIUB, Switzerland (CODE) According to the IGS's strategie plan (Blewitt et al. 2006) and high quality processing, GINS GNSS software is being used. The today's overall quality of GRGS GPS orbits in terms of agreement when compared to the final IGS sp3 products, is being evaluated and could be better than 5 cm (3D-RMS).

The GNSS Observations: models and errors

The most important aspects of the observation équations for GPS are reviewed. For more information the reader is referred to, e.g. [START_REF] Xu | GPS Theory, Algorithms and Applications[END_REF], Springer (2000), Brockmann (1997), [START_REF] Rothacher | Orbits of Satellite Systems in Space Geodesy[END_REF]. In the mathematical models of this section the following notation is used: T*{t-r,t)is the tropospheric refraction and the effect is the same for both code and phase (does not dépend on the frequency) ; dr{t) and ds(t-r) are instrumental internai time delays in the receiver and the satellite; mr(t -r,/) is the multipath effect; v,\r{t) are random errors in the code and phase ; Nsxlr{t -T,t) is the unknown integer number of cycles or else called the integer phase ambiguity.

Linear combinations of phases and codes

In order to eliminate some of the effects in Eq. 2-6 and 2-7 we may form différences or combinations of the original observations équations.

Single (SD) and Double différences (DD)

The Single Différences (SD) is the linear combination that éliminâtes: the satellites clock error if the combination is between two stations rA, rB and one satellite s; the receiver's clock error if the combination is between two satellite and one stations; the carrier phase ambiguity if the combination is at two different epochs between a satellite and one station.

Eq. 2-8

The Double Différences (DD) is a linear combination of simultaneous measurements or the linear combination of two single différence measurements at the same epoch (Fig.

In this linear DD observation both the satellite and receiver clocks effects are eliminated or extremely minimised.

The synthetic observations such as the SD and DD are correlated and their variancecovariance matrix and weight matrix will not be diagonals. According, to the error propagation law if b are the linearized model of observations with Cb = cri their variancecovariance matrix, the synthetic observations //will hâve Cb-=DCbDras a variancecovariance matrix.

2-9).

Ls,Sk = Ük -LSi

Eq. 2-9 Eq. 2-11

2 1 1 2 2.3.2.2
The ionosphere-free combination (L3)

From Eq. 2-6 and 2-7 ionosphere-free (iono-free) combinations can be formed The wavelength of this combination is Aj = 6.3 mm. The same relations are valid for the ionosphere-free ambiguity N3. The ionospheric path delay is practically eliminated. It is the main combination used in the un-differenced and DD level.

The wide-lane combination (Lwl)

The wide-lane combination has the advantage to create a synthesized observable with a very crL big wavelength of ÀWL =86.19 cm which favourizes small errors --in the estimation of ^WL The narrow-lane combination is:

^jnl=F t-CA A "''A-A) =--(77L\ + 60L2) Eq. 2-14 /tj + A2 y j /
The wavelength ( ÀNL = -----= ^-= 10.71 cm) of this combination is useful when we The iono-free ambiguity from Eq. 2-12 can be written as:

J1 J 2 J1 J2 = 7rf7y(/A,,-/2^) Eq. 2-16 J1 J2 cfi Nw, + F-fl "'U+/2) w,
Then by using the Melbourne-Wiibbena [START_REF] Melbourne | The Case For Ranging in GPS Based Geodetic Systems[END_REF] combination:

- T (A A \.Pl) T -(^2A ~-Api A /t| + /L, m.
Eq. 2-17

We can estimate a-priori values for the wide-lane ambiguity. From Eq. 2-13 we get:

^MW ~Aw(^l ^2) Next, the best combination of wide-lane and Ni ambiguities that gives the estimation of the ionosphere-free N3 ambiguity the closet to an integer value is investigated. Once the space of the différence of the fixed iono-free ambiguity minus the real one has been checked

for an upper bound (divided by the narrow lane wavelength) and the relative standard déviation of two successive combinations is more than 50% then the iono-free ambiguity will be fixed. An example of Nwl ambiguities distribution around their integer values in terms of a cycle can be seen in Fig. 2-10. This is the main philosophy of the Quasi Ionosphère Free (QIF) ambiguity fixing strategy which it has been implemented in Bemese [START_REF] Hugentobler | Bemese GPS software Version 4.2[END_REF]) and in GINS software. For more details on this type of ambiguity fixing, by the use of the linear combinations, look in [START_REF] Hugentobler | Bemese GPS software Version 4.2[END_REF], Blewitt (1989) and Dong and Bock (1989).

New GNSS signais, new combinations

As previously mentioned in Chapter 1, with the arrivai of Galileo, the three ffequencies in GPS and GLONASS and the four in Compass a whole new horizon for new linear combinations between GNSS frequencies has opened.

For instance, the use of triples frequencies will allow for Three Carrier Ambiguity Résolutions (TCAR) to be achieved with only observations in the line-of-sight (undifferenced) instead of double différences. In parallel there will be benefits for multipath détection. Till now no single-station multipath from dual phase observables exists. The only known way to extract multipath information is through residuals of short baseline processing [START_REF] Estey | TEQC: The Mutli-Purpose Toolkit for GPS/GLONASS Data[END_REF]. This method requires two stations and has the major drawback that residuals are not referred to individual satellites and multipath errors might get mixed if the stations are too close together. The triple-frequency phase combinations provide a valuable indication of phase multipath from single-station data, which is not available in today's two-frequency GNSS. The limitation of this indicator is that multipath for individual frequencies cannot be extracted as is the case for variations in the code observables [START_REF] Simsky | Three's the charm, triple-frequency combinations in future GNSS[END_REF]).

According to [START_REF] Wübenna | New GNSS Signais and Ambiguity Resolution[END_REF] ail the aforementioned linear combinations will be based in the following model:

I =2 comb CL !hLi+!hLQ n Y A J A A A Eq. 2-19
Where: n,m,k are integer coefficients. The apparent frequency fcomh and wavelength Acomb will also be a function of these coefficients.

fcomb=n\-A+n2-f2+nHf,+ -

1 ^comb n. n~, n,

\ h

Eq. 2-20

So if we consider ail the signais from the four GNSS described in Table 1-6 we can form several combinations for wide lanes and narrow lanes, or with big wavelengths or even more combinations with low ionospheric influence such as: The effect of an orbit error dp on an estimated baseline component is given by the The accélérations that perturb the orbit of a GPS satellite and add errors in its final positions are:

• Earth's oblateness (C20) ;

• Non-sphericity of the Earth gravity potential ;

• The Moon-Sun and Planets gravitational accélération ;

• The solar radiation pressure;

• The Earth's solid and océan tides ;

• Relativistic effects ;

• The Earth's albedo ;

• The satellite's thermal re-emission ;

The évaluation of the précision in GNSS POD can de accomplished through comparisons to an extemal reference. For instance, the estimated GPS orbits can be evaluated by a simple comparison to the more précisé IGS sp3 orbits (see §2.2.1). An example of such comparison is the GRGS évolution of the GPS POD in 2 years from ~20 cm to ~10 cm 3D-RMS with respect to the IGS final orbits, applying ail the necessary perturbation corrections previously mentioned (can be seen in Fig. 234567891011). The perturbation forces are mainly separated in two big categories: the gravitational and non-gravitational ones. Today the influences of these forces on the GNSS satellites are very well modelled. Nonetheless, the most important non-gravitational force that of the Solar Radiation Pressure (SRP), is still under investigation. A study of inter-model comparison as well as the impact on the POD of the GNSS satellites will be presented in § 3.2.2.1.

Observational model errors of GNSS

Since May, 2, 2000 the Sélective Availability (SA), a mean of dégradation of the GPS signais' précision, has been shut off under the U.S. DoD's policy. When SA was active three types of data were degraded: the broadcast orbital information, the broadcast value of the satellite clock offset and the satellite oscillator frequency. The most important one was the dithering of the frequency of the satellite oscillator which was directly affecting the phase observables used in geodesy [START_REF] Feigl | A scheme for reducing the effect of sélective availability on précisé geodetic measurements from the global positioning System[END_REF].

Double and single différences or linear combinations on the same frequency hâve the advantage to eliminate a certain number of "nuisance parameters" that would reduce the précision of the GNSS observations but not ail. On the other side in Précisé Point

Positioning applications (Cao and Chen 2004, Cheng et al. 2002, Héroux and Kouba 2001, Kouba and Héroux 2000[START_REF] Zumberge | Précisé Point Positioning for the efficient and robust analysis of GPS data from large networks[END_REF], the presence of précisé satellite clocks offset values and the estimation of station clocks are unavoidable. Consequently, the exact knowledge of hardware or environmental related error models becomes mandatory.

These errors appear in the pre-processing stage and can be detected through raw-data snooping procedures or during the estimation phase of the final coordinate GPS time-series and can be compensated with the introduction of proper ad-hoc error functions in the observational model.

For instance, cycle slips and clock jumps are one of the most significant sources of systematic errors in the GPS observations and proper corrections must be applied at the preprocessing level. Examples of such corrections applied in real data sets are presented in the following sections. Additionally, satellite orbit errors, propagation effects, clock errors, relativistic effects, antenna phase center variations, antenna rotations (phase wind-up) and multipath, ail provoke systematic and random effects on the phase and code pseudo-ranges during the main processing scheme of a GNSS coordinate time-series solution. A description on some of these effects and notably troposphère, ionosphère and antenna phase center variations is given in the following.

Clock jumps are provoked from poor performance receiver oscillators which deviate from the GPS time scale (or UTC). For instance a clock jump of 1ms will provoke a discontinuity of ~300km on the code observables and an integer number of cycles in the phase observables: 1575420 for L1 and 1227600 for L2. The clock will reset in order to be kept within 1 ms of the nominal sampling time. Both the recorded time and the pseudorange and phase measurements will show a discontinuity corresponding to 1 ms. Theses discontinuities should be removed by applying corrections. One way is as follows: from Eq.

2-6 the pseudo-range from the known codes is:

The jumps are recorded in Sr. The corrections to the observables will be c-ôr for the code and / -Sr for the phase. Where c = 2.99792458e + 08 m/sec is the velocity of light, and f the frequency in L\ or L2.

Clock Jumps

Eq. 2-22

Let us examine 5 separate cases where the impact of these clock jumps on the observables of the phases and codes is quantified:

• lsl Case: The GPS station BRST (Brest, France).

The receiver of this station is a Trimble 4000SSI and the time record inside the RINEX file for day-of-year 197 2004 shows that the receiver's clock effectuâtes 1 ms resets every 1 h (Fig. 23456789101112). It seems that the record time of the RINEX file has been corrected except for the Cl observables. In order to further apply the standard correction (multiplied by the jump) on each observable we will hâve to artificially add the jumps in the phases or in the ambiguities. Though, the first choice is préférable. If in any case these corrections hâve been applied already, then in the resulting ambiguities we will notice large standard déviations.

Cycle slips

Cycle slips are integer discontinuités in the carrier phase data caused by receivers loosing lock on GPS signais. A prerequisite to high précision GPS-based geodesy is the reliable détection and where possible, correction of cycle slips [START_REF] Blewitt | An automatic editing algorithm for GPS data[END_REF]).

For détection and réparation of cycle slips several algorithms exist [START_REF] Kleusberg | GPS data preprocessing with DIPOP 3.0[END_REF][START_REF] Lichtenegger | GPS-data preprocessing for cycleslip détection[END_REF][START_REF] Bastos | Fixing cycle slips in dual-frequency kinematic GPSapplications using Kalman filtering[END_REF][START_REF] Han | Carrier phase-based long-range GPS kinematic positioning[END_REF][START_REF] Wamant | Application of the wavelet tranform for GPS cycle slip correction and comparison with Kalman filter[END_REF].

One of the most frequently used is that of the higher order time différences of the raw data time-series. The scheme consists of forming the différences of the multiples of a certain polynomial order n as An+lLk = AnLk -AnLk_x . The main disadvantages of this method are that data-set-specific tolérance values hâve to be set (time différences that are greater than the tolérances indicate the presence of a cycle slip). As GNSS data at the observation level contain noise, the efficient détection of a cycle slip will be a function of it.

For instance, synthesised data of linear combinations can be used for the formation of theses fmite différences. As such any eventual perturbations due to nuisance parameters (e.g. ionosphère) will be eliminated and cycle slips can be detected above the noise level of the data time-series. But this is not always the case for ail combinations and ail types of data as we will see in the following examples. This method is currently implemented in the GINS GNSS software.

As an example, in Fig. 2-17 I présent the 4th order time différences of each data-set of the previously mentioned GPS stations (BRST, ZIMM, PALM, BOPII, BS07) by forming at every case the synthetic observations from:

• the Melboume-Wübenna (Eq. 2-17) combination;

• the ionosphere-free combination (Eq. 2-12);

• the ionospheric geometry-free combination ( Eq. 2-15);

The time différences of the Lmw combination présent a rather high noise level (left column of Fig. 2 -17). Firstly, at the stations that are in motion (MW combination is independent from geometry) like BOHI (Fig. 2-17a) and BS07 (Fig. 2-17b), the noise is ~10 m. This reflects the fact that both receivers make use of the less précisé Cl code. The same is the case for the stable stations like BRST (Fig. 2-17d) and ZIMM (Fig. 2-17e). The noise is smaller at PALM because it has the only receiver among these stations that is using the more précisé PI code. Immediately we understand that for the stations that make use of the Cl code the noise RMS errors are even larger than one wide-lane cycle thus making the détection of a cycle slip not possible below the amount of noise in the raw timeseries of the Melboume-Wübenna combination. On the contrary, in the case for PALM, the noise level reaches ~20 cm well below 0.5 wide-lane cycles (Springer 2000), and cycles slips or outliers become détectable as can be seen in Fig. 2-17c.

In the Ionosphere-free combination (middle column of Fig. 2 In conclusion, one of the most important issues in the pre-processing level of raw GNSS data is the détection and réparation of cycle slips. The quality of the clocks with visible or apparent frequent jumps, from each receiver, and the kind of linear synthesized combinations used together with the dynamic State of the GNSS station (moving or stable)

are also critical factors that need to be taken into account so as to efficiently detect ail possible cycle slips and eliminate outliers.

Troposphère

The correction of the delay of radio waves by the neural atmosphère (the non-ionized) is most often defined in terms of the contribution of the hydrostatic and wet components of the troposphère [START_REF] Niell | Global mapping functions for the atmosphère delay at radio wavelengths[END_REF].

The zénith delay is determined by the intégration of refractivity vertical. The atmosphère is very close to hydrostatic equilibrium meaning that surface pressure is given by the vertical intégration of density. Since the first term in refractivity dépends only on density, its vertical intégration will dépend only on surface pressure. This intégral is called the "Zenith Hydrostatic Delay (ZHD)" or as often mentionned "dry delay" [START_REF] Herring | Connections between atmospheric modelling and vertical motions estimation and models[END_REF]. The water vapor delay (second term in refractivity) is not so easily integrated because of distribution of water vapor with height. Surface measurements of water vapor pressure (deduced from relative humidity) are not very effective because it can be dry at surface and moist above and visa versa [START_REF] Herring | Connections between atmospheric modelling and vertical motions estimation and models[END_REF]. The effective method is to sense the whole column of water vapor. This can be done either by terrestrial ground measurements with Water Vapor Radiometers (WVR) or by laser profiling, LIDAR. Both methods are very expensive. Another approach in a more global and cheaper way is to use global numerical weather prédiction models of the European Center for Medium-Range Weather Forecasts (ECMWF) and the National Center for Environmental Prédiction (NCEP). They provide values every 6 hours. These models hâve the disadvantages that they contain large uncertainties in the Arctic régions and that local troposphère variability is not easily

detected.

An example of these models of dry and wet corrections over Europe, at midnight on the 5th of May 2004, from the ECMWF model is illustrated in Fig. 2-18.

In order to relate tropospheric delay (azimuth-independent part of the neural atmosphère) at lower zénith angles (Zenith Tropospheric Delays, ZTD, or path delays, ZPD), spécial mapping functions are used [START_REF] Marini | Correction of satellite tracking data for an arbitrary tropospheric profile[END_REF][START_REF] Davis | Geodesy by radio interferometry : Effects of atmospheric modelling errors on estimâtes of baseline length[END_REF][START_REF] Niell | Global mapping functions for the atmosphère delay at radio wavelengths[END_REF] (right) station height différences between VMF and NMF GPS solutions (Boehm et al. 2006); NMF : Niell mapping function [START_REF] Niell | Global mapping functions for the atmosphère delay at radio wavelengths[END_REF], GMF : Global Mapping Function (Boehm et al. 2006b), IMF : Isobaric Mapping Function [START_REF] Niell | Improved atmopsheric mapping functions for VLBI and GPS[END_REF], VMF : Vienna Mapping Function [START_REF] Schuh | VMF and IMF mapping functions based on data from ECMWF[END_REF]).

The azimuth-dependent part of the neural atmosphère [START_REF] Davis | Ground-based measurements of the gradients in the wet radio refractivity of the air[END_REF][START_REF] Bar-Sever | Estimating horizontal gradients of troposphcric path delay with single GPS receiver[END_REF]) is described by the north and east gradients. Both are used to détermine the gradient at the azimuth of the observation, which is then mapped with the gradient mapping function to the élévation of the observation [START_REF] Boehm | Troposphère gradients from the ECMWF in VLBI analysis[END_REF].

The choice of the mapping fonctions affect mostly:

Ionosphère

The ionosphère refraction is the signal delay respectively phase advance due to the free électrons in the Earth's atmosphère. As a dispersive medium for microwave signais, the amount of the refraction index will be dépendent on the signal's frequency and on the total électron content (TEC) in the atmosphère. The TEC can vary significantly during the diumal rotation and annual révolution of the Earth around the sun and during the solar cycle activity (every ~11 years).

In précisé positioning applications we usually form the synthetic ionosphere-free L3 combination of L1 and L2 phase observables. This combination is sufficient enough to eliminate the First order zénith ionospheric group delay (phase advance), which according to [START_REF] Bassiri | Higher-order ionospheric effects on the global positioning System observables and means of modelling them[END_REF] , [START_REF] Fritsche | Impact of higher-order ionospheric terms on GPS estimâtes[END_REF], ranges between ~1 m toi6 m for L1 and ~2 m to 27 m for L2. The second and third order ionospheric delays are not eliminated within the L3 combination. [START_REF] Bassiri | Higher-order ionospheric effects on the global positioning System observables and means of modelling them[END_REF] hâve estimated the effect of the ionospheric group delay of the second and third order to be 1.6 cm and 3.3 cm and to .86 mm and 2.4 mm for L1 and L2 respectively. [START_REF] Fritsche | Impact of higher-order ionospheric terms on GPS estimâtes[END_REF] hâve demonstrated that the GPS stations residuals after a 7 parameter transformation with respect to ITRF2000 indicate a southward shift of 1 mm to 4 mm in horizontal and a latitude-dependent change in station height of ~5 mm at the maximum, only when the lst order ionospheric term is considered. [START_REF] Heflin | Comparison of a GPSdefined global reference frame with ITRF[END_REF] obtained a shift in the origin of x ~+ 5.0 mm, y ~-1.9 mm, z ~+ 3.7 mm for a GPS-derived global reference frame relative to ITRF2000.

If a millimétré level accuracy is to be accomplished in a global GPS network positioning approach, at least the second order effect has to be taken into account. This is not the case for a régional or local network using the DD approach were the remaining ionospheric effects will be differentiated inside the DD algorithm.

The tracking/satellite Antenna Phase Center offsets

The antenna phase center offset is the 3D position vector of each carrier phase center inside the physical body of the GPS antenna with respect to an extemal Antenna Reference Point (ARP).

The phase response of GPS tracking antennas does not correspond to an idéal point source. The signal wave-fronts of constant phase do not form perfectly hemispherical shells.

Instead, the phase center can vary depending on viewing direction. If these antenna effects are not being accounted for, several cm (IGSMAIL 5189) can occur in estimâtes of the antenna position and thus in the station's coordinates.

The antenna Phase Center Variations (PCVs) and their influences on positions of stations and the scale relative to an TRF of a GNSS network hâve been till recently a major issue of discussions inside the geodetic community [START_REF] Wu | Effects of antenna orientation on GPS carrier phase[END_REF][START_REF] Menge | Results of absolute field calibration of GPS antenna PCV[END_REF][START_REF] Mader | GPS antenna calibration at the National Geodetic Survey[END_REF], Springer 2000[START_REF] Rothacher | Receiver and satellite antenna phase center offsets and variations[END_REF][START_REF] Zhu | Satellite antenna phase center offsets and scale errors in GPS solutions[END_REF][START_REF] Schmid | Estimation of elevation-dependent satellite antenna phase center variations of GPS satellites[END_REF][START_REF] Ge | Impact of GPS satellite antenna offsets on scale changes in global network solutions[END_REF], Schmid et al. 2005a, Rothacher and Schmid 2006, Bar-Sever et al. 2006, Schmid et al. 2006[START_REF] Wübenna | Absolute GNSS Antenna Calibration with a Robot : Repeatability of Phase Variations, Calibration of GLONASS and Détermination of Carrier-to-Noise Pattern[END_REF], Gendt et al. 2007[START_REF] Herring | Impact of Absolute Phase Center Models on GPS Reference Frames[END_REF][START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time-series of station positions and Earth Orientation Parameters[END_REF]).

According to IGSMAIL 5189 in the IGS ACs Workshop held at Silver Spring in 1996 it was decided that relative antenna phase center offset corrections would be applied by June, 30, 1996 for the first time. These corrections were determined realtive to a reference Dome/Margolin choke ring antenna type T (AOAD/M_T) from a short-baseline field measurements procedure [START_REF] Mader | GPS antenna calibration at the National Geodetic Survey[END_REF]. With respect to this "relatively determined" phase center offsets the station-specific antenna PCVs were measured as a function of the élévation angle of the GPS satellites. A similar procedure was used to calibrate the GPS satellite's transmitting antennas for each block by Mader (2000) but was never used operationally (U. Hugentobler personal communication) .

Nevertheless, several problems occurred from the use of these "relative" values which were mostly related to discrepancies and corrélations, such as in between: tracking antenna offsets and PCVs; satellite antenna offsets ; estimated station heights and estimated troposphère parameters; scale différences of the IGS TRF and ITRF. Another issue was the fact that these relative phase center corrections were only valid for small range baselines.

Springer (2000) has demonstrated ail these difficulties. The solution was to use an extemal calibration procedure for the tracking antennas known as "absolute" phase center corrections. In this way [START_REF] Schmid | Estimation of elevation-dependent satellite antenna phase center variations of GPS satellites[END_REF] hâve found that transmitting antenna phase center corrections (offsets and PCVs) were possible to be determined by using absolute tracking antenna models [START_REF] Menge | Results of absolute field calibration of GPS antenna PCV[END_REF]. [START_REF] Ge | Impact of GPS satellite antenna offsets on scale changes in global network solutions[END_REF] hâve demonstrated that estimated satellite-specific offsets by using the relative tracking antenna models, for satellites belonging to the same block, are not homogeneous. Both the estimated offsets and the network scales of the re-adjusted solutions proved that the IGS offsets lead to a scale bias of about 1 ppb over 7 years.

The switch to the "absolute" antenna corrections models (for offsets and PCVs The réduction of the scale inconsistency with respect to the ITRF had an immédiate impact on the stations' height position time-series and consequently on the correlated TZD parameters. Schmid et al. (2005a) hâve shown that the troposphère bias between GPS and VLBI drops down to -0.8 mm for satellite-specific absolute antenna models wrt to a 5.3 mm for relative models.

Modeled stations displacements

In this paragraph some of the basic displacement model corrections applied on the GNSS stations will be presented. These corrections are included in the IERS 2003 updated conventions of June 20 2007 (IGSMAIL 5614) and they mostly concern:

• Océan Tide Loading displacements (one of the most important);

• Non-tidal océan loading displacements;

• Center of mass corrections due to océan tide mass ;

• Effect of the solid Earth tides (the most important) ;

• Displacements due to rotational deformation caused by the polar motion ;

• Displacements due to océan pôle tide loading (caused by the centrifugal effect of polar motion on the océans) ;

• Displacements due to atmospheric loading ;

• Displacements due to hydrological loading ;

The fortnight, diumal and semi-diumal time domain is the main characteristic of most of the aforementioned station displacements. The océan tide loading that this Thesis is investigating on is thoroughly investigated in Chapter 4. The low-frequency displacements (annual, semi-annual, decadal) are mainly those related to tectonic activities like plate motion, post-seismic deformations, land subsidence etc. In the following, only the displacements due to hydrological loading, atmospheric loading, and effects of the solid Earth, center of mass corrections and non-tidal loading will be discussed.

Non-tidal loading displacements

The non-tidal loading deformations are caused by non-tidal variations of the sea level mainly due to atmospheric pressure forcing and wind effects. 3 days and at high latitudes [START_REF] Carrère | Modelling the barotropic response of the global océan to atmospheric wind and pressure forcing -comparisons with observations[END_REF].

A new hydrodynamic finite element model MOG2D-G (2D Gravity Waves model) has been created by [START_REF] Carrère | Modelling the barotropic response of the global océan to atmospheric wind and pressure forcing -comparisons with observations[END_REF]. This model takes into account the high frequency (HF) atmospheric forced variability of the global océan. MOG2D is barotropic, non linear and time stepping [START_REF] Lynch | A wave équation model for finite element tidal computations[END_REF].

In Fig. 2-21 the displacements due to non-tidal océan loading for a set of GPS stations, dispersed on the geographical Coastal area of Brittany, France, between 47°-50°N orth-Latitude were calculated. The maximal loading has several mm to 2 cm variability with periods from ~10 days to ~30 days. In the présent example the loading effect is identical to ail stations. So its impact on the final position time-series will dépend on the strategy of the positioning scheme. If the GPS network is a régional one and the processing is done by forming DD baselines (relative positioning) then these displacements will be eliminated by the différentiation process of the DD algorithm. Though, if the network is expanded to a bigger area, like a global network or the positioning mode is absolute such as On the other hand, the predicted loading effects are insensitive to this counter balance motion of the Earth's geocentre. While using GPS for validating océan tide models, the stations of the network will already contain this geocentre motion. As such the two frames defined by the océan tide models and the GPS are inconsistent. A correction must be applied to the predicted displacements.

For instance, when a régional network is being used, every translational motion of the geocentre will map into the stations' time-series if the GPS satellite orbits are held fixed in the processing scheme. When these time-series are used for detecting high-frequency displacements due to océan loading, they already contain the geocentre motion. In order to be comparable with the océan tide model prédictions, the latter hâve to account for the geocentre motion, as Schemeck at http://www.oso.chalmers.se/%7Eloadinu/cmc.html demonstrates. This will be the case were a global GNSS network is used and translational parameters (un-correlated) are not estimated, or in the case of a régional network the positioning scheme is based upon un-differenced observables. For a régional network with DD baselines this geocenter motion will be eliminated, if not at least extremely minimised inside the différentiation process of the baseline formation thus bringing the two frames into consistency.

Displacements due to atmospheric loading

Temporal and géographie pressure variations in the atmosphère provoke vertical surface mass loading displacements of the Earth's crust. According to vanDam and [START_REF] Herring | Détection of atmospheric pressure loading using very long baseline interferometry measurements[END_REF] these loading displacements due to changes in the atmospheric pressure can account for up to 24 % of the total variance in the GPS height time-series estimâtes. The detected loading amplitudes are larger at higher latitudes where pressure variations are more important.

The principal method for calculating the displacements of geodetic points due to atmospheric loading mainly falls into two categories.

The first is based on the use of the gravitational potential of a simple layer, which is induced by the atmospheric masses and it can be derived from the atmospheric surface pressure and its variations [START_REF] Biancale | Mean Annual and Seasonal Atmospheric Tide Models Based on 3-hourly and 6-hourly ECMWF Surface Pressure Data[END_REF]. This method makes extended use of the development of the potential in spherical harmonies and the hypothesis of an elastic

Earth where the displacement is proportional to the excitation. The loading on the surface is calculated from the pressure grids of global numerical models such as ECMWF. These models take into account both the constant part of the atmosphère and its high-frequency variations mainly due to the diumal and semi-diumals solar (Si and S2) tides [START_REF] Biancale | Mean Annual and Seasonal Atmospheric Tide Models Based on 3-hourly and 6-hourly ECMWF Surface Pressure Data[END_REF].

The second one consists from computing the atmospheric loading displacements by convolving FarrelTs elastic Green's functions (Farrell 1972) with global pressure data.

Green's functions describe the response of the Earth to a point load on its surface. While they are determined by the angular distance between the load element and the station point, they are assigned to each grid element and are then multiplied by the atmospheric load in that element (vanDam and Flerring 1994). The results are summed over ail grid units to provide the radial and horizontal displacements at the station point.

In Fig. 2-22 a comparison of the displacements due to océan loading, atmospheric loading, pôle tides and solid Earth tides over two GPS stations is given. GRAZ (Austria) station is situated in the Northern hemisphere and KOUR (French Guyana) station very close to the equator. Nevertheless, GRACE gravity field does not contain the degree one geocentre deformational component as GPS does. A correction must be applied to the displacements issued from GRACE, according to Blewitt (2003). that the GRACE's loading time-series hâve not been corrected for the geocentre motion and some mm error should be considered.

Summary

The purpose of this chapter is to introduce an updated description of the most recent issues in GNSS observations and which hâve occupied my research during the last period.

The geodetic components of what make the GNSS a valuable tool for geodesists were overseen. From the modem implémentation of a TRF to the high and low frequency displacements of the discrète geodetic points on the surface of the Earth's cmst, everything is connected.

An updated budget of the systematic effects on the GNSS observables and the ways with respect to an extemal reference point (ARP) will dépend on the antenna's calibration method used. Additionally the phase center not being a constant point will vary depending on the viewing direction of the observations. Furthermore, it has been demonstrated that non-tidal oceanic loading and hydrological loading can provoke significant displacements of geodetic stations upon the Earth's crust, with low and high-frequency spectrum, and which if not modelled can provoke misinterpreted signais in the final GNSS time-series.

The complété and updated budget from this chapter on the effects acting on the geodetic parameters of the GNSS constituents (stations, TRF, observations) is summarised in the following Table 2-5 . At the beginning of this Thesis, GINS was designed for standard GNSS operation:

• Processing of global GNSS networks ;

• daily and weekly mean-solutions in a weighted least square sense;

• Position time-series in a X,Y,Z geocentric coordinate System ;

• Float ambiguity solutions ;

Step 1: The station file

An extemal utility is used to get the stations file in a format compatible to GINS. Some of the information about the stations should be concentrated in a SINEX format file which will serve as input for this utility. The information must contain:

• The name and DOMES number of the station's marker (ITRF format) ;

• The type of the station (SLR, DORIS, GPS, VLBI, ...) ;

• The marker's position in XYZ coordinates ;

• The eccentricity vector between the marker and the antenna phase center ;

• The type of the antenna (IGS conventions) for GPS stations ;

• The reference datum of the coordinates and the linear velocities.

The final outcome will be a station file adapted to GINS' format.

3.1.2

Step 2: The pre-processing phase

The pre-processing phase consists of multiple operations. The broadcast GNSS ephemeris and clocks are downloaded. The PDGDECAL module takes care of the millisecond clock jumps (see § 2.3.4.1) in the RINEX record time. Next the cycle slip détection is performed with the aid of the time différences as described in § 2.3.4.2, Approximative values of the wide-lane ambiguities are estimated in order to serve as input for the iono-free observable.

Additionally, it is possible to specify individual thresholds for the code and phase observations, above which a cycle slip will be defined.

Modified and edited RINEX files will serve as input to PDGR90. Inside these new RINEX files the estimated NI and Nw ambiguities are listed along with the other observables for phase and code flagged by the number of corresponding cycle slips.

The PDGR90 forms the un-differenced observation file. The program takes care of incomplète or absent observables and links the observations to the stations file, the broadcast clocks and ephemeris, and the GPS constellation information. The un-differenced output file contains the ionosphere-free combination (see § 2.3.2.2) for each station and for each satellite. Several passes could be eliminated depending from the number of cycle slips detected and the élévation of the satellites, so care must be taken for spécial cases. This fde can be used directly in GINS for the absolute-positioning mode.

DoubleÇO is responsible for the formation of the DD from the un-differenced observation file given out by PDGR90. This module uses the stations file to calculate the baseline lengths between the different stations présent in the un-differenced observation file.

Independent baselines are formed with priority to those that hâve the biggest number of common satellite observations between stations. The output DD file is used in GINS for the relative positioning mode.

Step 3: The strategy implémentation and adjustment

The exejoadatm and exejoadoce scripts take as input the stations file and give as output the 3D atmospheric and océan tide loading displacement coefficients in amplitudes and Greenwich phase-lags for each station.

Next the GDF must be tuned with the proper key functions that will détermine the strategy followed and executed by GINS.

The module PREPARS accounts for any ad-hoc models and observations such as station displacements, EOPs, gravity field, etc., by concatenating the corresponding files.

Calculations are not performed in this module; it préparés the complété data set for subséquent processing in GINS.

GINS processes the DD or un-differenced observations and calculâtes the partial dérivatives of the required geodetic parameters (station positions, EOPs, orbital parameters, troposphère parameters, ambiguities, etc.). In a weighted least squares sense, several itérations are performed, during which the geodetic parameters are adjusted and certain observations are eliminated based on the élimination residual criteria specified inside the GDF. It is possible to either fix or not fix the estimated ambiguities. The itérations will proceed till convergence of the final residuals. As an output we get the final estimâtes or normal équations that can serve as input for DYNAMO.

An example of the models used in GINS is listed in The estimated geodetic parameters (station coordinates time-series and post-fit residuals, troposphère zénith delays, ambiguities, orbital parameters, EOPs) with the associated un-certainties are the final outputs.

Validations

After the implémentation of the aforementioned modifications a certain sériés of validations test were performed before proceeding to the final studies.

The validation tests are mostly separated into two large categories, those in terms of position time-series and POD.

For the First case, I used the 102-day observations of the G2 GPS dedicated campaign serving to study the OTL in Brittany (see § 4.2.2.2) and I compared the estimated coordinate time-series and local OTL constituents to those from the solutions of other software and notably : GAMIT 10.21 [START_REF] King | Documentation for GAMIT GPS analysis software[END_REF], GIPSY/OASIS II [START_REF] Zumberge | Précisé Point Positioning for the efficient and robust analysis of GPS data from large networks[END_REF] and Bemese 5.0 [START_REF] Dach | Bemese GPS software version[END_REF]).

In the second case, inter-comparisons between the final GINS' GPS orbits, estimated with different SRP models, to the IGS sp3 précisé orbits were performed. Additionally, SLR observations and comparisons of the range residuals of the distance between the satellite and the observation site obtained from both GINS and IGS sp3 orbits were also used.

Furthermore, the network effect to the reference System of the GPS SLR orbits was quantified as well as the détermination of the perturbation periods and orbital éléments of the First Galileo satellite GIOVE-A.

Intra-software position time-series comparisons

In the First part of the validations I collaborated with research teams from the Laboratoire de Géodésie et Géomatique (L2G) of the Ecole Supérieur des Géomètres et Topographes (ESGT), the Laboratoire de Recherche en Géodésie (LAREG) of Institute Géographique National (IGN), the Institute de Physique du Globe de Strasbourg (IPGS).

The aforementioned GPS data processing solutions of existing software were used.

The aim was to validate the modifications in GINS GNSS software in matters of highfrequency positioning of a local or régional GNSS network.

Data sets and strategies

Four independent software position time-series solutions of 102 days from 9 GPS campaign stations were compared. The strategies followed at each of the four solutions are summarised in The validation analysis is divided into four different steps:

1.

High-frequency position time-series between the four solutions for one station on a short neriod (Fis. 3-2). The site CHER was selected as représentative of the results from ail stations. A periodic signal is présent in ail vertical and horizontal components. The four solutions seem to be globally consistent in terms of periodicity and peak-to-peak displacements.

2.

Différences in terms of Root Mean Square (RMS) scatters, in 3D (Fig. 3-3). Bemese and GINS solutions are in good agreement and show smaller scatter than the 2 other solutions. GIPSY solution exhibits the strongest signal for this component. For the east comportent, the two groups are less separated and Bemese and GINS solutions still hâve the best agreement. The four solutions hâve the highest discrepancies at MANS.

For the vertical component, we can notice that GAMIT solution disagrees with the other solutions for four stations (BRST, DIBE, PAIM, and TREV) showing a much stronger scatter. In total GAMIT solution seems to always exhibit the largest scatter for whatever component considered.

3.

Linear régression corrélation coefficients of each 3D time-series solution from the 9 stations are calculated. The results are illustrated in For the vertical component, the mean corrélation coefficient is 77 % if ail solutions are merged. GINS' solution seems to be very well correlated to the others in vertical as well as in horizontal. The corrélation coefficient in the vertical exhibits the 80 % level compared to GAMIT's and Bernese's solutions and 69 % level compared to GIPSY's solution.

In the north component, the corrélation with GAMIT's and Bemese's solutions amounts to 72 % and 80 % respectively, contrary to about 62 % with GIPSY's solution. In the amplitudes ail strategies hâve disagreements which are constrained to the level of discrepancies between models and initial corrections applied to each solution. Consequently, the comparisons are valid up to the level of discrepancies between the ad-hoc models.

In conclusion GINS' GPS position time-series results were compared to those of three well established, globally known, scientific software packages and the level of agreement between the aforementioned tests validâtes the current modifications.

The support from: J. Nicolas, L. Morel, S. Durand (L2G of ESGT), M. Vergnolle and M.-N. Bouïn (LAREG/IGN) and F. Masson (IPGS) who provided GPS data and solutions from Bemese, GIPSY-OASIS, and GAMIT/GLOBK, is greatly acknowledged.

POD validations

The POD validations are separated in two parts. The first is concentrated in the implémentation of the SRP models for the GPS satellites and the impact on the accuracy comparing to the final IGS sp3 orbits. The second one is focusing on the SLR POD évaluation of the GIOVE-A first Galileo satellite and the SLR network effect on the reference System of the GPS 35-36 satellites.

The statistical interprétations were performed by using internai and extemal RMS misfit overlaps of 2-day arcs according to Eq. 3-1. An orbit overlap is defined by the comparison of the satellite's position between the common (here 1-day) time-span of two successive orbits:

H. arc 1 arc2\" x -X rrnSmW = I v / V «
Eq. 3-1 rmsiD = y IrmsLw + ™4""g + rm4r"s, Where x"rc] and xarc2 are the 3D geocentric coordinates of the GNSS satellite from the lst and 2nd arc respectively and n is the total number of common points in the overlapping arc.

Improving Solar Radiation Pressure (SRP)

As previously mentioned in paragraph § 2.3.3 SRP is the most important non-gravitational perturbation on the position State of the GNSS satellites and not only. Its possible impact on the Z-shift of the geocentre of the GPS frame compared to ITRF has been evocated by [START_REF] Herring | Impact of Absolute Phase Center Models on GPS Reference Frames[END_REF]. [START_REF] Urschl | Assessing the quality of GNSS orbit models using SLR[END_REF] showed that when modelling SRP a signal in the geocentre time-series in the Z-translation at -351 days appears. This period corresponds to the draconic year (= the "GPS year": the interval required for the constellation to repeat its inertial orientation with respect to the sun) of 352.43 days. [START_REF] Ray | Anomalous Harmonies in the Spectra of GPS Position Estimâtes[END_REF] and Ostini et al.

(2007) demonstrated the existence of this signal in the residuals of GPS stations coordinates time-series. They pointed out that this period cannot be interpreted in the geophysical sense.

About one percent of the accélération due to SRP is acting in a direction other than that of the incident solar light [START_REF] Hugentobler | GPS satellites: Radiation Pressure, Attitude and Résonance[END_REF]. Direct SRP can be pictured as the net momentum imparted to the SV by photons striking and recoiling from its opaque surfaces. Indirect SRP (predictable and anomalous) is caused for example by:

• the effects of the Earth's albedo radiation pressure;

• the satellite's heat flow re-radiated from the body's surface. This force is directed along the positive radial direction when the heating source is the Earth and to ail directions for the heating coming from the sun. Part of this force could explain the Y-bias correction [START_REF] Duha | Thermal re-emission effects on GPS satellites[END_REF]);

• the resuit of out-gassing from the apogee engine, the solar panels, the multilayered insulation that wraps the satellite body [START_REF] Fliegel | Global Positioning System radiation force model for Geodetic Applications[END_REF][START_REF] Fliegel | Solar Force Modelling of Block I1R Global Positioning System Satellites[END_REF][START_REF] Slabinski | Observed Outgassing Accélération of GPS Blobk IIR Spacecraft[END_REF]) ;

• the along-track accélération produced by a force in the body fixed +Y or -Y direction that is along the nominal axis of the solar-panel center beams.

Misalignments of these beams or of the solar-sensors could provoke a force for which a Y-bias must be accounted for. During and after an éclipsé, misalignments are more severe. The misalignment angle is sometimes called yaw-bias (Bar-Sever 1996, [START_REF] Bar-Sever | Fixing the GPS Bad Attitude: Modeling GPS satellite Yaw During Eclipse Seasons[END_REF][START_REF] Hugentobler | GPS satellites: Radiation Pressure, Attitude and Résonance[END_REF].

In general an exact représentation of the spacecraft's attitude is needed when we model SRP (Fig. 345). As such the following referentials are used:

• R (radial), T (tangential), N(normal) to the orbital plane ;

• Z (points towards the Earth center), Y (points along the nominal axis of the solar panels), X (complétés the System);

• D (points towards the incident solar light), Y (points along the nominal axis of the solar panels), X (complétés the System). o 6 is the angle between the incoming solar ray and the normal to the surface .

•

The Rockwell analytical models T20 and T30 with empirical augmentation developed by [START_REF] Fliegel | Global Positioning System radiation force model for Geodetic Applications[END_REF] and [START_REF] Fliegel | Solar Force Modelling of Block I1R Global Positioning System Satellites[END_REF]. T30 was the most recent update for the Block-IIR inside GINS ;

• The University College of London (UCL) analytical model (used only for Block-IIR) which simulâtes the incident photon flux using a pixel array [START_REF] Ziebart | Combined radiation pressure and thermal modelling of complex satellites: Algorithms and on-orbit tests[END_REF]. It was recently implemented in GINS as well;

•

The empirical updated version of the "GPS Solar Pressure Model 1997" (GSPM.97)

for Block-IIA and IIR SRP model by Bar-Sever and Kuang (2003). From Fig. 3-7 we principally conclude that the POD performances, with a simple dynamic parameterisation, hâve better agreement when using the updated GSPM.97 model.

The three SRP models for the Block-IIR s/c, T30, B-W and UCL give a différence of 2 cm with respect to the GSPM.97 model. The other two models for Block-IIA s/c, T20 and B-W

give the largest différences of the order of ~7 cm with respect to the GSPM.97 parameterisation.

Internai vs external overlaps

In this paragraph I study the performances of each of the four SRP models by adjusting different orbit dynamic parameters in each case. The goal is to reach a significant improvement of the parameterization for the B-W model by adding more empirical forces to the final adjustments. Results from these tests are illustrated in Fig. 3-8 trough 3-11.

The abscissa contains the 3D-RMS misfits made with successive GPS orbits compared intemally (only GINS GPS orbits) and the ordinate the 3D-RMS misfits of the external comparison between GINS GPS orbits and IGS sp3 orbits. The time period is 16 days the same as in Fig. 3 Internai vs extemal 3D-RMS misfits for GINS GPS orbits with the Rock T20 and T30 SRP models in four different parameterisations. Units are in meters. ?YV?': * V:'î :

' iiiiiiiiiiiiiiiiiiiiiiiimiiimi •••• • ' t : •••••: t ' >-ï 1 f" \ ' • * 1 :-î v ? ; v >
+ .14.

. 1..: 4.4..:.:.jl.:.4..: 1 . 1 . :

.i.i. : i.i.; l.i .L.i.i ; i . . .... J .1 ' ... J

Il II II 1 1 ! Il I M 1 1 1 1 1 •f7 *••*•»•'•-4••»•*•«?•
' V 'T ! T T : r | • V t : r ' *• T t !**
•'••r-vr i * r r :-r r :• 44 4.4-14-44-4-14-444--I 4-444-

•UifH-fiflif i-H-i-F}F ! : T:': ! • f :'1":

• *•!•?•«?• !-f •»!• <••?•?- • 4 •? • •••*•»••• TyrTTj'yn :'v 1 1 i l J..; - J.. :
1 -1

: : 1 : : : . 1 : : : : 1 : : : : 1 : : : : » : : : : 1 : : : :

'77:TïTV7Tï7T7'7V:T7:T7':'7':T7TV7T7'rV7' .i.;..;. ,:.x.i.i..;. j..;. j..j.j.

: ; : : 1 : : : : 1 : ? : ; 1 . : : : I : ; : : I : ; : : I : ; : : < ! t ! {< ! t} ! ? ! V ? ! ? ? y? ! ? tj ? ! ! i ?

ül'îî'ri'V •?"!'T'ï,i,?'!v ; î i i ;

• i-? :

-I V ? ! v | î-> î <-} !•':"! <- <••: !• i l•:••>•!•? 1 : •> ! :' l ! ? ! !- iï* :S ÎWM'
L-ipv?:

+*4 -Y ::

1 1

: t : M : : 1 : : : : i j : 5 : i : : : : i : : : : Furthermore, it seems that we cannot distinguish easily which attitude System, in the case of the B-W SRP model, is the most appropriate for the harmonie accélérations. For this reason the scale factor which will absorb ail un-modelled variations of direct SRP forcing was calculated. It is évident that the lower the correction to this scale factor the better the model will be. The tests are concentrated only on the B-W SRP model.

SLR residuals test

According to [START_REF] Urschl | Validation of GNSS orbits using SLR observations[END_REF] the SLR bias residual is the différence between the SLR observed range and the computed range (GNSS orbit and ITRF SLR site coordinates). Those observed range biases for GPS 35/36 were found to be -3.1 cm and -2.8 cm respectively with respect to the IGS final orbits from [START_REF] Urschl | Validation of GNSS orbits using SLR observations[END_REF]. The resulting range residuals are primarily an indicator of the radial accuracy of the microwave orbits. Thus SLR measurement provides a completely independent mean for validating microwave orbits. This method is applied here in order to evaluate the performances of GINS GPS orbits with respect to the IGS final orbits. In the same period of March 13 through 28 2005 the predefined strategy for the GPS microwave orbit estimation was applied:

• B-W S RP model ;

• One scale factor, accélérations in X and D directions plus 2 per révolution terms for every day-arc included ;

• Phase-wind-up corrections to the effect of circularly polarised radiation on the phase measurements;

The histograms in Fig. 3-14 and Fig. 3-15 represent SLR range biases and RMS range residuals per station (standard déviation) and show respectively that the existing quality of the GINS microwave orbits is that of the IGS ACs. By introducing the B-W model for direct SRP together with accélérations in the D and X directions, the mean range bias of GINS' microwave orbits, for both GPS 35/36 s/c, has reduced to -2.9 cm with respect to a -3.7 cm when the IGS orbits are used. The mean SLR stations' RMS residuals (standard déviation) with respect to the GINS' micro wave orbits are less dispersed than those to the IGS orbits, at least for this testing period, and vary respectively around 4 cm (GINS orbits) and 4.5 cm (IGS orbits).

In conclusion, the tested comparisons of the 3D-RMS misfit overlaps and SLR range biases to the IGS final orbits show that the current SRP B-W model together with the new dynamic configuration in a solar-oriented attitude referential, results in GINS GPS orbits of quality comparable to the one from IGS ACs.

Calculations and comparisons from D. Dobler's engineering diploma dissertation, which I co-supervised, were greatly appreciated.

SLR network-effect on the GPS 35 and 36 reference frame

In this study we are using 10 days of SLR data, for the GPS 35 and 36 satellites, from June 6 through 16 2006. In this period most of the SLR stations where pointing to the GIOVE-A satellite and the SLR tracking data for the two GPS satellites hâve always been sparse. In this investigation the challenge consists in discovering the achievable orbit accuracy of GINS with sparse tracking data for the two GPS satellites and quantifying the SLR network effect on the GPS reference frame with respect to the ITRF. The analysis of the SLR orbits for both GPS satellites is based on the overlaps to the précisé IGS sp3 orbits and on the residuals in radial, normal and along-track directions. Transformation parameters between the fitted SLR arcs and the IGS sp3 orbits are adjusted.

The présent methodology has been applied many times in the last 10 years and many studies, like [START_REF] Pavlis | Comparison of GPS S/C orbits dermined from GPS and SLR tracking data[END_REF], [START_REF] Appleby | Comparison of SLR measurements and orbits with GLONASS and GPS microwave orbits[END_REF], [START_REF] Hujsak | Sequential Orbit Détermination for GPS 35 and GPS 36 using SLR data from NRL@SOR[END_REF] hâve investigated the undergoing problems of SLR sparse tracking orbit détermination.

Table 3-4 and 3-5 compare the fitted orbits to the IGS sp3 orbits in terms of position différences in the radial, normal and tangential directions. The RMS is at the level of 3 cm in radial, 47 cm in cross-track and 23 cm in along-track direction for GPS 35.

GPS-35 RMS Misfits (cm)

Earth Along (Tangential) For the case of GPS 36 the level of agreement is respectively 2 cm, 9 cm and 25 cm in the radial, along-track, cross-track directions.

When one station in the Southern hemisphere tracks GPS 36, for the same period, the RMS misfit, compared to the one for GPS 35, drops down by a factor of 2. This reflects the effect of the SLR network distribution in the Southern hemisphere.

In order to further quantify any systematic effects on the GPS orbit reference frame, a 7-parameter Helmert transformation between the SLR-only orbits and the IGS sp3 orbits is applied. .01 x 10J +/-.1 x 10'3 Rz (arcmin)

-.24 x JO 2 +/-.1 x 10'3

S (ppb)

.712820 x 10'lo+/-.2x 10'9 S (mm)

1.9 +/-5.

Rx (arcmin) -.30 x 10'3 +/-.5 x 10'4 Ry (arcmin) .04x10'3 +/-.5 x 10"4 Rz (arcmin)

-.14 x 10 2 +/-.5 x 10'4 Both Z-translation coefficients are significant with 60 mm (± 10 mm) and 45 mm (± 5 mm) for GPS 35 and 36 respectively. This offset may reflect the non-homogeneity of the SLR tracking stations in the global network. In addition, there is a factor of 8 différence in the scale for GPS 35 and 36 with respect to the reference frame defined by the IGS sp3 orbit.

This effect is related to the poor number of Southern tracking SLR tracking stations.

Finally, the overall misfit of SLR-only orbits calculated by GINS is 2 cm to 3 cm in radial direction for GPS 35 and 36 satellites. The consistency of the reference frame varies in between 4 cm to 6 cm in the z-shift and 0.1 cm to 1.6 cm in the scale for GPS 35 and 36 respectively. The first of theses campaigns has taken place during May 22 and July 24 2006, with the participation of 13 globally distributed SLR stations (Fig. 3-16) and it continues up-today.

I présent the results for the GIOVE-A SLR-only POD with GINS for the period that The network of global SLR stations is illustrated in Fig. 3-16 and the estimation strategy is described in Table 3-8. The RMS of the overlap misfit analysis is given in Fig. 3-18 (a). The misfit residuals are of the order of 3.6 m and 420 m in 3D, 30 cm and 86 m in radial, 1.4 m and 344 m in along-track and 3.3 m and 240 m in cross-track (tangential), for the same two overlapping dates respectively. Immediately, we conclude that for these two periods of time, major unexpected perturbation events or manoeuvres of the satellite, for which our dynamic model cannot account for, must hâve taken place. These outliers cannot hâve been provoked from an insufficient number of normal points since for both arcs the total number of observations is 95 and 104 normal points respectively as seen from Fig. 3-18 (b).

••••••«•• ••• * H i \j i . V • •• • •• Date
To conclude, the capacity to estimate SLR-only orbits for GIOVE-A s/c has been implemented and evaluated in the GINS GNSS software. The generated orbits are intemally accurate to the level of 5-10 cm radially as can be seen in Fig. 3-18 (a) and (c).

Unknown maneuvers and perturbations are a critical issue for the GIOVE-A POD.

These maneuvers took place somewhere during June 27 to July 1 2006 and October 16 to 21 2006 as seen from the pre-fit and post-fit mean residuals of ail the SLR stations and the internai RMS overlap analysis in Fig. 3-17 and Fig. 3-18. Not announced maneuvers or unmodeled perturbations can be dealt with the adjustment of stochastic puises during the perturbation period.

I hâve used an analytical B-W SRP model with approximate specularity and reflectivity coefficients. A further improvement in the POD will be the adjustment of these coefficients together with the LRR arrays offsets in at least one "GPS year" time period by making use as well of the most accurate radiometric observations in L\ and E5 bands.

Summary

At the beginning of this chapter the basic modifications of the updated GINS GNSS software were presented. The processing scheme of GNSS data with GINS software has been described in a step-by-step process. Validation tests of the new modifications were separated into two large categories.

The GINS' high-frequency estimated GPS position time-series were cross compared to the ones issued from well-known scientific software packages. These software were :

GAMIT 10.21 [START_REF] King | Documentation for GAMIT GPS analysis software[END_REF], GIPSY/OASIS II [START_REF] Zumberge | Précisé Point Positioning for the efficient and robust analysis of GPS data from large networks[END_REF]) and

Bemese 5.0 [START_REF] Dach | Bemese GPS software version[END_REF]). The comparisons were made using the observational set of 9

GPS dedicated campaign stations used in order to study OTL in Brittany (see Chapter 4).

The comparisons hâve demonstrated the validation of the modifications issued for the first time in the GINS software. The linear corrélations of more than 80 % with respect to the other solutions and the agreement in the periodicities of the high-frequency time-series indicate the high level reliability of GINS' results.

During the second set of validations tests the ability and performance of GINS to give accurate and précisé POD results for the GPS satellites against a sériés of recently implemented SRP models was investigated. More emphasis was given to the newly modified B-W SRP model for GPS satellites. The GINS' GPS orbit tests were based on internai and extemal comparisons to the IGS sp3 orbits. Successive arcs with 1-day common segment overlaps were evaluated. The statistical interprétations were based on the internai and extemal RMS misfit of Eq. 3-2. The internai 3D-RMS misfits were found to be 5 cm with the inclusion of periodical terms in the solar oriented and orbital plane directions. The extemal 3D-RMS misfit compared to the IGS orbits varied between 5 cm and 10 cm. By comparing the variations of the post-fit residuals of the estimated scale factor for each case the cohérence of the dynamical parameterization was demonstrated. Histograms of SLR range residuals and biases were calculated. The SLR observed ranges were computed using GINS and IGS microwave orbits for both GPS 35 and 36 satellites. The respective biases produced were: -2.9 cm and -3.7 cm when GINS and IGS orbits were used. The mean SLR station RMS range residuals with respect to the GINS' microwave orbits were found to be about 4 cm. These were less dispersed to those calculated with the IGS orbits of 4.5 cm.

Finally the B-W SRP parameterization in a solar-oriented attitude referential was selected as the idéal configuration.

Furthermore, the précision of the SLR-only POD for the GPS 35 and 36 satellites and the SLR network effect on the orbit reference frame were quantified. The précision was found to be around 2 cm to 3 cm radially and the consistency of the SLR reference frame with respect to the IGS reference frame arises up to 4 cm -6cm in the z-shift and 0.1 cm - networks in Brittany, France

In § 2.4 of this thesis, it is mentioned that océan tide loading is one of the most important reasons for periodic displacements at geodetic stations after solid Earth tides. In Fig. 2-22 of the same chapter this type of effect has been quantified compared to displacements due to atmospheric loading, solid Earth tides and pôle tides. The response of the océans, unlike for the solid Earth, is strongly dépendent on local and régional conditions that affect fluid flow.

This chapter, which represents the main part of my PhD Thesis, is referring to the study of Océan Tide Loading (OTL) displacements and validation of models through the use of the GNSS technology.

According to the IGS Position paper "Identification and Mitigation of GNSS errors" research activities should be stimulated in studying the effects of suspected error sources in the position time-series of geodetic stations. Ail aspects of GNSS geodesy are potentially involved from field observations through data analysis and interprétation [START_REF] Hugentobler | Identification and Mitigation of GNSS Errors, IGS workshop[END_REF]).

As such, I studied the option of using GNSS as a validation tool for océan tide models in a complex Coastal area, that of Brittany, through the comparisons of observed (from GPS) versus predicted (from tide models) OTL 3D-displacements. The order of the observed 3D-displacements is most of the time superior to the magnitude of errors induced in the GNSS observations. Nevertheless, for the correct interprétation of the geophysical signal, together with the validation process, the following aspects that can affect the accuracy of the final positions of GPS stations and their estimâtes are simultaneously analysed:

• The datum stability ;

• The influence of OTL on the TZD parameters ;

• The aliasing effects of un-modelled OTL signais on the position time-series ;

Modelling OTL

The crustal loading at a particular location due to a given tidal harmonie is computed by integrating the tide height with a set of Green's fonctions which define the Earth's rheology and relaxation deformation models, carrying the intégration over ail océan masses. The total loading may be obtained by summing the effect of ail harmonies.

The complex OTL displacement (amplitude and phase) at every point on the solid Earth surface's, colatitude and longitude (9, A ) are computed as: Au = ff G{wih(p',A')sm 9'dd'dA.' Eq. 4-1 J JOcecm where h is the tidal height at the point of colatitude 9' and longitude À' ; G(i//) is the Green's fonction computed from the load Love numbers. For the vertical displacement, the Green's fonction dépends only on the h'n numbers: where Pn(cos y/) are the Legendre polynomials of order n, G the gravitational constant, g gravity, y/ the angular distance between the application point of the load (d',A') and the observation point ( <9, /1 ) : cos!// = cos <9 cos#' + sin#sin#'cos(T -A'), Eq. 4-3

Equivalently the horizontal components are derived from the horizontal displacement load Love numbers/', and as there is no horizontal displacement for n = 0 :

The final loading effect will be expressed in amplitudes and Greenwich phase lags summed over the global surface tidal grid for vertical, eastward and northward directions. Validation of OTL models through observations in complex Coastal areas becomes mandatory for geodetic applications of high précision such as the détermination of the Earth's rheology (Baker andBos 2003, Baker at al. 1996), the estimation of Vertical Land Motion Rates (VLMR) at tide gauge sites by examining the long time-series of geodetic stations for any spurious signais or even the implémentation of new océan tide models through the use of the Loading and SelfAttraction (LSA) term.

In Coastal régions OTL can cause vertical motions of several centimeters and horizontal motions over a centimeter, large enough to be measured with space geodetic techniques such as GPS [START_REF] Vey | GPS measurements of océan loading and its impact on zénith tropospheric delay estimâtes: a case study in Brittany, France[END_REF][START_REF] Dragert | Océan loading corrections for continuous GPS: a case study at the Canadian Coastal site Holberg[END_REF][START_REF] Khan | Determintation of semi-diumal océan tide loading constituents using GPS in Alaska[END_REF].

Furthermore, long-period GPS height time-series in areas with strong OTL displacements can suffer from un-modelled sub-daily periodic ground displacements [START_REF] Penna | Aliased tidal signatures in continuons GPS height time-series[END_REF]. Such effects of periodic displacements can be largely propagated by "data averaging", adopting a GPS processing session length equal or close to the period of the displacement considered [START_REF] Penna | GPS height time-series: Shortperiod origins of spurious long-period signais[END_REF][START_REF] Stewart | Investigating the propagation mechanism of unmodelled systematic errors on the coordinate time-series estimated using least squares[END_REF]. The resuit is that these tidal signais will appear in the final coordinate time-series as aliased signais (see § 4.2.6) with longer periods than the original semi-diumal and diumal signais. The effects in long time GPS sériés can reach amplitudes of several mm [START_REF] Penna | GPS height time-series: Shortperiod origins of spurious long-period signais[END_REF]. For example, periods of -13.6 days hâve been found in GPS time-series when combining VLBI and GPS for the development of combined UT1/LOD and nutation time-series (J. Ray personal communication) which were attributed to tidal effects. As such accurate prédictions of such displacements are needed.

The purpose of this study is to evaluate a sélection of océan tide models around the shelf of Brittany and Cotentin, in the northwestem part of France, through GPS positioning.

In the past, [START_REF] Llubes | Observation gravimétrique des surcharges océaniques : premières expériences en Bretagne[END_REF] used an FG5 absolute gravimeter and compared the observed variations of five days in gravity with water height variations from a tide gauge in Brest and loading prédictions from the CSR3.0 model [START_REF] Eanes | Diumal and semidiumal tides from TOPEX/POSEIDON altimetry[END_REF]. [START_REF] Vey | GPS measurements of océan loading and its impact on zénith tropospheric delay estimâtes: a case study in Brittany, France[END_REF] compared the observed GPS OTL signal of 8 sites with the FES98 (Le [START_REF] Provost | A hydrodynamic océan tide model improved by assimilation of a satellite altimeter-derived data set[END_REF]) and the GOTOO.2 (Ray 1999) océan tide models over three days and evaluated the impact of OTL signais on the estimated tropospheric zénith delay parameters. Both studies produced preliminary results because their analysis intervals did not allow accurate and robust validations of the OTL prédictions.

We cross compare up-to-date OTL GPS observations over a longer time span to a sériés of predicted OTL estimâtes from a more recent and larger sélection of océan tide models than the previous studies, and perform accurate OTL validations. Furthermore, we quantify the différences of two OTL algorithms and analyse the GPS high-rate OTL estimâtes for spurious signais (multipath). Additionally, the geographical distribution of our GPS campaign stations, allows us to study the geographical propagation of the OTL signal further land-inwards from the English Channel and thus validate the OTL models in a larger area than the previous studies.

In section 4.2.1, we briefly review the selected global and local tide models and the two OTL algorithms. We describe the tides and the GPS data used in the study région in section 4.2.2. In that section, we also discuss our innovative strategy approach for the measurement of GPS OTL displacements and analyze possible systematic errors that may be présent in the GPS time-series. Section 4.2.3 présents the comparison of the GPS OTL observations with the model prédictions, through the misfits of a root mean square and chisquare statistical indicators, and the évaluation of océan tide models. Further on sections 4.2.4 , 4.2.5 and 4.2.6 examine the impact of the datum stability on the observed OTL parameters, the influence of OTL on the estimated TZD parameters and finally the aliasing periods of the OTL signatures propagated from 24-hour batch solutions on low-frequency GPS coordinate time-series.

4.2.1 Océan tide models and océan tide loading 4.2.1.1 Océan tide model sélection Subséquent to the launch of the TOPEX/Poseidon (T/P) satellite, the geodetic community has undertaken a huge effort to improve or develop new tidal models, with the objective of attaining a cm accuracy level in tidal prédiction, necessary to meet the altimetry product requirements [START_REF] Lyard | Modelling the global océan tides: modem insights from FES[END_REF][START_REF] Provost | Océan tides for and from TOPEX/POSEIDON[END_REF]. The overall success in improving tidal prédiction accuracy is based on the data assimilation of altimetry analysis on one hand and hydrodynamic/assimilation modelling on the other.

There are still however discrepancies between océan tide models, especially in continental shelf régions with high loading effects like in the northwest European shelf (including Brittany), Japan (Khan and Hoyer 2004), Australia [START_REF] Penna | Océan loading considérations for GPS processing around Australia[END_REF], In Coastal areas, the tidal spectrum can become very complex because the semidiumal and diumal frequencies are mixed with a large number of non-linear, "shallow-water tides", having frequencies within the long-period, diumal, semi-diumal, ter-diumal, and higher bands. These frequencies are conséquence of the non-linear interactions between the tidal waves (résonances) and friction phenomena as they propagate in shallow water (Andersen et al. 2006).

In this study, we hâve used seven océan tide models as illustrated in Table 4-1.

These models consist of gridded amplitudes and phases of the eight or even more major tidal constituents such as: M2, S2, N2, K2, Ki, Oi, Pi, and Qi. Six of these models are global and one is régional, namely the North East Atlantic (NEA) tidal atlas (Pairaud I. personal communication).

GOTOO.2 uses 286 cycles of T/P data to adjust to the a priori FES94.1 hydrodynamic model. It also assimilâtes 81 cycles of ERS-1 and ERS-2 data at latitudes outside the T/P coverage. NA099.b has 5 years of the MGDRB (Merged Geophysical Data Records génération B) of the cycles 9-198 of T/P and uses an improved hydrodynamic model derived from [START_REF] Schwiderski | Océan tides, II, a hydrodynamic interpolation model[END_REF] by estimating loading effects more precisely [START_REF] Matsumoto | Océan tide models developed by assimilating TOPEX/Poseidon altimeter data into hydrodynamic al model: A global model and a régional model around Japan[END_REF]. The CSR4.0 model is based upon 239 cycles (6.4 years) of T/P altimetry which is used to solve for corrections to CSR3.0 orthoweights in 2x3 degree spatial bins (2 deg. lat.).

These orthoweight corrections were output on the 0.5°x 0.5°grid of CSR3.0 and then added to the CSR3.0 values to obtain the new model.

TPXO.6.2 uses 324 cycles of T/P data with some small local areas corrected with higher resolution local inverse solutions, while additional data sets were assimilated for the Ross and Arctic Seas. It also incorporâtes improved bathymetry for the circum-Antarctic seas (King et al. 2005). It best-fits, in a least-squares sense the Laplace tidal équations and the observations. TPXO.7.0 is a more recent version of TPXO.6.2. For the FES2004 atlas, the assimilated data set is composed of 671 tide gauges, plus 337 T/P and 1,254 ERS altimétrie crossover points. No ERS 1/2 data are assimilated in the FES2004 solution for the S2 constituent. ERS 1/2 data were included (by mistake) in the FES2004 atlas computation for the K2. H+T/P (0.5°x 0.5°) Global CSR4.0 [START_REF] Eanes | Diumal and semidiumal tides from TOPEX/POSEIDON altimetry[END_REF][START_REF] Eanes | The CSR3.0 global océan tide model: Diurnal and semi-diumal océan tides from TOPEX/Poseidon altimetry[END_REF] T/P (0.5°x 0.5°) Global FES2004 (cor. K2)c [START_REF] Letellier | Etude des ondes de marée sur les plateaux continentaux, hèse doctorale[END_REF][START_REF] Lyard | Modelling the global océan tides: modem insights from FES[END_REF] H+T/P+ERS+T/G (0.125°x 0.125°) b Latitude x Longitude c cor. K2, K2 from FES2002 as advised by [START_REF] Lyard | Modelling the global océan tides: modem insights from FES[END_REF] Due to the sun-synchronous orbit of ERS 1/2, the ortho-tides (or generalized admittance harmonie analysis) for S2 did not yield sufficient accuracy, especially in the shelf and Coastal régions, which apparently had a side effect in the solution for K.2-The recommendation is to use the FES2002 K2 instead of the FES2004 K2 tidal élévation solution [START_REF] Lyard | Modelling the global océan tides: modem insights from FES[END_REF]. n north-latitude, with a 1/60°resolution. It is completed with the FES2004 grid (1/8°r esolution) outside the local area in view to cover the whole oceanic surface. This action is necessary since surface displacement variations will not only be sensitive to local tide variations, even if the station is close to the coast, but also to global tides.

Computation of OTL displacements

Predicted OTL 3D-dispiacement amplitudes and phase-lags were computed for each of the GPS stations, using the web-based 'Océan Tide Loading Provider' facility olfg/olmpp (http://www.oso.chalmers.se/-loading/, accessed December 6 2005) for TPXO.7.0, TPXO.6.2, GOTOO.2, NA099.b, CSR4.0, FES2004, whereas a modified version called géochargeV3.0 of the load89 OTL program from [START_REF] Francis | Global charts of océan tide loading effects[END_REF] was used for FES2004 and NEA2004 (M. Llubes personal communication). The complex OTL displacements (amplitude and phase) at every point on the solidEarth's surface, in colatitude and longitude {9,À) are computed from Eq. 4-1.

Both, the olfg/olmpp and géochargeV3.0 OTL algorithms rely on a point-wise intégration of the load tide, which according to [START_REF] Schrama | Three algorithms for the computation of tidal loading and their numerical accuracy[END_REF], properly evaluate the tidal heights along a Coastal geometry.

4.2.2

The GPS data analysis and estimation of the OTL displacements.

The tidal characteristics of the région

The French part of the northwestem European shelf is a région where tides are Furthermore, non-linear semi-diumal, ter-diumal and higher bands cannot be neglected, since they can resuit into OTL displacements of a few mm mostly in the vertical direction. However, given that many of these shallow water constituents hâve a spectrum very close to the integer multiples of the orbital period of the GPS satellites (Ki, K2 K3, K4, K5 etc.), their signais cannot be easily distinguished with GPS data, as we will see further on.

The diumal constituents do not contribute much to the tidal signal over the English Channel which is a typical feature of tides within the Atlantic Basin (Le Provost and Fornerino 1985).

GPS data set of the NW-France tide loading campaign

In order to study the intense loading phenomena an experimental multitechnique campaign was organized by the French group G2 (Géodésie -Géophysique).

The campaign consisted of operating a total of twelve semi-permanent GPS stations during a period of almost four months from March 3 through June 19 2004.

Due to data latency problems, we examined GPS OTL displacement estimâtes from eight of the twelve campaign stations. The data were collected from the eight GPS stations for the time span of around 104 days, as listed in Table 4-2. Fig. 4-2 and Fig.

4-3 illustrate the geographical distribution of these eight GPS campaign stations

together with the FES2004 predicted vertical displacements for M2

In order to realize the reference frame in a rigorous and most optimal way, and decorrelate the tropospheric estimâtes [START_REF] Vey | GPS measurements of océan loading and its impact on zénith tropospheric delay estimâtes: a case study in Brittany, France[END_REF], these stations are included in a régional network of 14 European stations from the IGbOO reference network (Ferland 2003), which is presented in Fig. 4-2.

6 W 4'W 2 V/ 0' 2 E
Fig. 4-2 : The IGS and GPS Brittany campaign network

Estimation strategy employed

As previously mentioned by King et al. (2005) and Khan and Tscherning (2001), the methods for determining the OTL harmonie constituents of surface displacements using GPS mainly fall into one of two categories. The First consists of determining 1-4 hour batch-sized sub-daily positions using GPS relative positioning techniques, in which the site motion due to OTL is regarded as negligible during each batch solution.

Each of the position estimâtes can then be processed as independent tide gauge measurements from which the harmonie coefficients of OTL displacements can be computed. However, accurate ambiguity fixing and tropospheric zénith delay estimation must be achieved (Melachroinos et al. 2006a, 2006b[START_REF] King | Spurious periodic horizontal signais in subdaily GPS position estimâtes[END_REF][START_REF] Vey | GPS measurements of océan loading and its impact on zénith tropospheric delay estimâtes: a case study in Brittany, France[END_REF][START_REF] Dach | The Océan loading effect in the GPS Analysis: A case study in the Antarctic Peninsula Région[END_REF][START_REF] Dach | Influence of the océan loading effect on GPS derived précipitable water vapor[END_REF][START_REF] Dragert | Océan loading corrections for continuous GPS: a case study at the Canadian Coastal site Holberg[END_REF], Blewitt 1989[START_REF] Melbourne | The Case For Ranging in GPS Based Geodetic Systems[END_REF].

GPS station

North The second method involves estimating the harmonie displacement constituents and the positions of the GPS stations simultaneously. Although this method offers batch solutions using longer observational periods and therefore more accurate geodetic positioning results, it is more complicated to implement. It requires significant modifications of GPS processing software, as well as longer periods of data in order to effectively de-correlate the OTL displacement parameters [START_REF] Ian | A comparison of GPS, VLBI and model estimâtes of océan tide loading displacements[END_REF], King et al. 2005[START_REF] Allinson | Stability of direct GPS estimâtes of océan tide loading[END_REF]).

During my study, an intermediate method which mostly relies on the manipulation of normal équation Systems before solving for the final estimâtes was implemented. In this way, 1 succeeded in having long enough observational periods for accurately fixing the ambiguity parameters followed by the independent extraction of OTL displacement coefficients. This GPS estimation strategy is similar to that employed in Melachroinos et al. (2006aMelachroinos et al. ( , 2007)). The GPS data were processed and éditée! on a site-by-site and day-by-day basis using the latest version (7.1) of the GINS/DYNAMO multi-technique scientific software package of the Centre National d'Etudes Spatiales (CNES) and the Groupe de Recherches de Géodésie Spatiale (GRGS) [START_REF] Lemoine | Temporal gravity field models inferred from GRACE data[END_REF]).

The general processing scheme consists of two steps: in the first step the Earth tides, pôle tides and the IERS Earth orientation parameters (EOPs). For the stations displacements due to OTL the predicted values from FES2004 are used. The IGS sp3 orbits [START_REF] Kouba | A guide to using international GPS service (IGS) products[END_REF] are kept fixed. Corrections for relative antenna phase center variations [START_REF] Mader | GPS antenna calibration at the National Geodetic Survey[END_REF] according to IGS standards and atmospheric loading from 6-hour gridded (ECMWF) atmospheric pressure data (Biancale and Bode 2006) are applied. The phase observations are weighted with an a-priori sigma of 3.5 mm according to an empirical law. The empirical law is based on an exponential évolution of the DD post-fit residuals as a function of the élévation of the GPS satellites. Outliers are rejected using a three-sigma criterion. Ambiguities are fixed to their integer values with a rate greater than 95 % after the sixth itération. Tight constraints of 1 mm are applied to the 14 IGS stations for the datum définition. Finally, the estimated geocentric positions for the GPS campaign stations from the 24 h solution are used as a-priori input in the second step.

A new itérative least squares scheme accounts for ail the available data in the second step (-104 days). 24-hour batch-solutions are computed including adjusted campaign stations, in the same régional network of the 14 IGS stations for reference frame stabilization, and daily normal équations with hourly-partials for campaign stations positions in a local geodetic System, henceforth called quasi-observables, were calculated subsequently. The entire aforementioned configuration of the main estimation process from the first step is applied. The area of the régional network is large enough that errors introduced into station coordinates are comparable to those of a global stabilization [START_REF] Tregoning | Effects of atmospheric pressure loading and sevenparameter transformations on estimâtes of geocenter motion and station heights from space geodetic observations[END_REF]. In order to obtain a strong sensitivity of the troposphère estimâtes from GPS, a eut off angle of 10 degrees was selected [START_REF] Tregoning | Accuracy of absolute précipitable water vapor estimâtes from GPS observations[END_REF]. Hourly tropospheric zénith delay parameters using apriori values from the ECMWF model and a [START_REF] Guo | The Harvest experiment: Monitoring Jason-1 and TOPEX/POSEIDON from a California off-shore platform[END_REF] Marini-type hydrostatic and wet mapping fonction are estimated. A sampling interval of 30s is applied and ambiguity fixing is successfol after the sixth itération up to 87 % and more for ail daily arcs. The coordinates of the campaign stations are held fixed to their apriori values from the first step till convergence of the solutions.

The DD L3 linear observation model up to convergence of the LS-procedure, considering EOPs and the coordinates of GPS satellites and campaign stations fixed, hâve the following form (here, a simple example of a single DD baseline is presented):

Where: àLk AB and t^L{AB are the DD ionosphere-free phase pseudo-range linearized observables in between the A, B stations and i,k and i,j GPS satellites respectively; /l^is the wavelength; ATABl and A7^t are the linearized DD tropospheric zénith delay parameters at the selected estimation interval /, in the présent case one every hour, for the total duration of the 1 -day solution; AN*AB p and ANl'AB p are the ionosphere-free DD ambiguities referring to the uninterrupted passage p of the satellites i,k and i,j over the A and B station. When a cycle-slip or a brake is detected in the passage a new ambiguity is created thus a new observation équation; n is the total number of observation équations; 5 is the total number of unknowns and r in the number of eliminated parameters (clocks, ionosphère etc.); VAB is the DD error-vector that contains everything else that is not modeled, like multipath or noise of the GPS observables.

After convergence, a last itération is done in order to create the quasiobservables of the station positions at the selected period of one hour. Usually 7 or 8 itérations were necessary to converge to sub-cm residuals. At this stage, the DD ionosphere-free linearized observation équation takes the form given in Eq. 4-6:

Eq. 4-5

(î-r)xl

Eq. 4-6

Where: n'B'k are the i, j, k satellite-station B unit-vectors from the station's antenna phase center towards the satellite's antenna phase center in the terrestrial frame;

AT'kBI and ATab , are the already linearized (observed -from the previous itérations)

DD tropospheric zénith delay parameters after convergence; and Au*5 = Au^-Au* are the linearized (observed -a-priori) local geodetic position vectors (in East, North, Up)

with partials created for every selected interval h (in this case one hour); AN'k4B p and ANijAB /;are real number ionosphere-free DD ambiguities, which represent 10 -12 % of the remaining non-fixed ambiguities.

Secondly, a final inversion is done using the DYNAMO software. At this stage, ail daily normal équation Systems are solved independently and the reference frame stabilization is realized through the fixed positions of the GPS satellites and the tight constraints of 1 mm to ail IGbOO positions, in a local geodetic System (North, East, Up), of the 14 IGS stations. Ail IGS site motions hâve been previously corrected using an apriori OTL model and atmospheric loading.

Moreover continuity constraints of 3 cm per hour to ail campaign stations are applied according to Eq. 4-7:

time interval h and h-At; Atis the time-length of one hour.

This means adding a side-band (non zéro) normal équation in order to connect two consecutive hourly coordinates. This technique allows filtering any remaining outliers from the itérative scheme. Care is taken when this observational équations are added so that the continuity constraint is large enough to allow the station's coordinates û* (h) -û* (h -At) = 0 ± 3cw( continuity Eq. 4-7

Where: u'A(h) and ûy' (h -At) are the 3D-coordinate vectors for station A at the to vary due to the true OTL displacement within an hour, based on the highest OTL modeled amplitude in the région.

After the final inversions of the daily normal équation Systems, tidal harmonie coefficients are estimated using standard algorithms [START_REF] Foreman | Manual for tidal heights analysis and prédiction[END_REF]) and the estimated GPS position time-series are processed as independent tide gauge observations in North,

East and Up components.

With regard to the Rayleigh criterion, the duration of the recorded or modeled time, necessary to separate two frequencies fx and/2, must be >t r (Foreman \f\ ~~fi\ 1977). Therefore, the présent study cannot separate ail the OTL displacement components as the séparation of S2 and K2 requires nearly 300 days [START_REF] Godin | The analysis of tides[END_REF] These four major constituents are sufficient indicators of tide model accuracy [START_REF] Andersen | Intercomparison of recent océan tide models[END_REF]. For the constituents that are closest in frequency like Kj and Pj or K2 and S2, I applied the inference technique from [START_REF] Foreman | Manual for tidal heights analysis and prédiction[END_REF] by excluding Pi and K2. This relies on the principal that if the length of a spécifie tidal record is such that certain constituents cannot be included directly in the analysis, such as Kj and S2, they can be estimated by inferring their amplitudes and phases from neighbouring constituents. Mean values for Pi and K2 from ail the global océan tide models are used in this technique. This approach is préférable because the errors of the tide models used will hâve a minor impact on the constituent analyses.

Furthermore, this will not be the case if the summation, Ki + Pi or K2 + S2 is considered, instead of the séparation by inference of these waves, which will be significantly more polluted from the GPS noise (especially the one with the smallest amplitude, Pi). Since the Ki period (see Table 4-3) is very close to the GPS constellation repeat period (-23.933 hours), biases are expected to appear in the final constituents estimâtes, especially at the integer multiples and combinations of this period (King et al. 2005[START_REF] Allinson | Stability of direct GPS estimâtes of océan tide loading[END_REF]).

The diurnal and semi-diumal constituents are a small subset of tidal constituents.

Hence, nodal corrections to each constituent are applied in order to account for the modulating lunar node effect (McCarthy and Petit 2004[START_REF] Cartwright | Corrected Tables of Tidal Harmonies[END_REF][START_REF] Cartwright | New Computations of the Tide-Generating Potential[END_REF].

Comparison of GPS estimâtes with modelled OTL dispiacement constituents

GPS estimâtes of OTL displacements

The 3D OTL displacement coefficients of GPS estimâtes are given in Table 4-4.

These estimâtes show the significant magnitude of the OTL phenomenon along the coastlines of Brittany and at the eastem entry of the English Channel. We can see that heading from the DIBE (Le Diben) station towards the East along the coastline, the amplitudes of this station for M2, S2 and N2 reach the maximum values of 32.8 mm, 10.35 mm and 7.5 mm in the vertical direction, respectively.

The M2 OTL wave has its lowest amplitude of 7.0 mm in the vertical, at BAYE (Bayeau), further inside the channel. The K| wave has its strongest amplitude of 9.45 mm in the vertical, at YGEA (Saint Ygeaux) which is situated further inland south from PAIM (Paimpol). A quick glance at the geographical variation of the estimated values for M2 and S2 reveals that they are consistent with the distribution of the predicted OTL displacements in the vertical direction as seen from Fig. 4 semi-diumal displacements can reach the maximum of 12 cm, 3 cm and 2 cm peak-topeak respectively in vertical, easting and northing direction in DIBE, while they decrease when entering the English Channel. The maximal horizontal, in easting and northing, and vertical displacements for MALO and CHER are around 2 cm, 3 cm and 9 cm and 4 cm, 2 cm and 6 cm peak-to-peak respectively. Ail stations hâve almost the same number of days of observations. The Ki constituent has the largest formai errors for ail stations especially in horizontal. This is due to the orbital errors of the GPS satellites and multipath around the monument's environment that propagate at this frequency [START_REF] Ragheb | GPS sidereal filtering: coordinate-and carrier-phase-level strategies[END_REF][START_REF] Larson | Improving the précision of high-rate GPS[END_REF][START_REF] Choi | Modified sidereal filtering: Implications for high-rate GPS positioning[END_REF].

Another indication of this relationship between repeatable GPS satellite geometry at a sidereal period and multipath [START_REF] Larson | Improving the précision of high-rate GPS[END_REF] is the fact that significant displacement signais appear near the integer multiples of the orbital periods (at Ki/3, Ki/4, Ki/5, K]/6 etc.). By introducing the frequencies of these "fictitious" OTL displacement signais into the harmonie estimâtes solution significant amplitudes of a few mm as listed in The modeled and estimated constituents of OTL displacements were not corrected for the sub-mm motion of the centre mass of the océan, which causes a counterbalancing tide in the mass centre of the solid earth. [START_REF] Schemeck | Océan loading tides in space techniques and implications for mass center variations[END_REF] proved that differential frame motion between the GPS stations and the satellite orbits is not affected by the center of mass tide. Nonetheless, an error of 1.5 mm in amplitude and 2°to 4°in phase-lag for the modeled constituents may exist (O. Francis personal communication). That would hâve been the case if our network of stations was global and not régional, or if our positioning strategy was based on an absolute mode and not a differential one. From the moment that a DD approach was applied on a régional network, the motion of the geocentre induced from the fixed positions of the GPS satellites into the GPS stations time-series will be extremely minimized, if not eliminated, as a common parameter inside the différentiation process of the DD algorithm. Through this approach, a consistent reference frame was achieved for the modeled and the estimated GPS OTL constituents.

Since no error budget is given for the amplitudes and phases of the tide models, we assumed that the modelled derived estimâtes are error free.

Spatial variations of OTL displacement

The phasor-diagrams of GPS and model estimâtes of OTL displacements are formed for the M2, S2 semi-diurnal constituents at DIBE station, and going eastwards, at MALO and CHER (Fig. 4-5 to 4-7). From the same plots we observe the spatial longitudinal variation of the OTL displacements at the entry of the English Channel. The tendency is an increased OTL effect for the stations situated at its entry like DIBE and MALO.

The GPS estimâtes of the horizontal displacements in M2 are in sub-mm agreement with the models within their 95% error confidence for DIBE and CHER. The observations in vertical displacements are in agreement at the mm-level with the models. The GPS measurements can very well distinguish the M2 constituents in the vertical component as is already the case for DIBE and CHER. Nevertheless, the observed amplitude at DIBE seems to be smaller by 3-5 mm to the closest in agreement prédiction.

The détection of the vertical OTL displacements for S2 still remains a tricky task For ail three stations the vertical observations précédé in the phase-lag ail OTL prédictions and the discrepancy rises to the mm-level. The northward and eastward estimâtes for S2 seem to agréé in the sub-mm level at ail stations within their 95% error confidence.

At MALO, which concentrâtes the strongest non-linear semi-diumal tides of the région the GPS estimâtes of vertical and horizontal displacements for the M2 wave hâve the greatest disagreement in the phase-lag to ail models. The S2 wave follows the same pattern as in the other two stations. There is a sub-mm agreement in the northward and eastward observations and a steady phase-lag advance in the vertical.

In order to correctly assess the levels of agreement between the models and GPS estimâtes, MALO is excluded in the following analysis. I assume that strong un-modeled non-linear OTL interactions in the semi-diumal band are probably responsible for the models disagreements in the phase-lag with the GPS estimâtes at this station. Le [START_REF] Provost | Tidal spectroscopy of the English Channel with a Numerical Model[END_REF] hâve shown that when the M2 wave propagates through the Mont St-Michel Bay, the local friction and résonance phenomena create localized strong nonlinear interactions with some energy transfer towards semi-diumal (2MS2, 2SM2, 2MN2, SNM2, MSN2, MNS2, L2, P2, V2, A,2 etc.) or higher bands (such as M4).

Nevertheless, this assumption is not defmite and more investigation will be done in a future study.

The discrepancy between models seems to vary significantly as well. A sub-mm agreement in the horizontal constituents of S2 at CHER and DIBE stations is observed.

At MALO, the horizontal discrepancies rise up to 1 mm. At the same station, in the vertical, the différences vary from 2 to 5 mm. For the other two stations, the disagreement reaches up to 2.5 mm. For M2 the différences become larger since this wave has higher amplitudes than S2. AU models seem to agréé worst for MALO in both vertical and horizontal components. The maximum level of disagreement in the vertical rises to 1.5 cm, whereas it is 4 mm in the eastward direction.

4.2.3.2.2 Misfit statistics of GPS/models OTL displacements

In order to assess the level of agreement of the GPS and predicted estimâtes of OTL displacements, the methods proposed by [START_REF] Ian | A comparison of GPS, VLBI and model estimâtes of océan tide loading displacements[END_REF], King et al (2005), and [START_REF] Allinson | Stability of direct GPS estimâtes of océan tide loading[END_REF] are followed. We First form the RMS misfits of GPS versus modeled OTL displacements. For n=l, N GPS sites at each component direction j for each tidal loading model k and for the four constituées (M2, S2, N2 and Ki) the root mean square misfit will be:

1 jy +z sîK^gps))jn \ (co^OA. )+/sir(d\ )).fi )] Eq. 4-8

Where A and d>, stand for the tidal amplitudes and Greenwich phase lag respectively.

The calculated models misfits for the seven selected sites (MALO is excluded) are shown in Fig. 4-8. GPS/Model misfits correspond to TPXO.7.0, TPXO.6.2, GOTOO.2, NA099.b, CSR4.0, and FES2004 from olfg/olmpp, and to FES2004, NEA2004 from géochargeV3.0, in bars left (black) to right (white). Note that for ail models the Ki constituent represents the highest disagreement in the vertical and eastward components. This vérifiés the aforementioned sources of biases at the orbital period of the GPS satellites and is compatible with previous conclusions by Thomas (2006) and [START_REF] Schenewerk | Vertical océan loading deformations derived from a global GPS network[END_REF].

The FES2004 model seems to perform the best in terms of agreement with the GPS estimâtes. The level of agreement is 0.3 mm for the east, 0.2 mm for the north and 1.8 mm for the vertical component of the M2 constituent. The two algorithms are performing equivalently with a small exception in the horizontal components of M2. For this constituent, the géochargeV3.0 OTL prédictions for FES2004 seem to be more in agreement with the GPS estimâtes. The différences with respect to olfg/olmpp FES2004 prédictions are 0.5 mm in east, 0.6 mm in north and negligible in vertical. In addition to observing the relatively large Ki GPS/models misfits, I comment that for the models that agréé best with the derived GPS estimâtes (FES2004, GOTOO.2, CSR4.0) the misfits for lunar constituents such as M2 and N2 compared to the misfits for solar constituents such as S2 and Kj, seem to be smaller. This effect is due to GPS related systematic errors biasing the constituents (S2 and Ki) at solar frequencies [START_REF] Ian | A comparison of GPS, VLBI and model estimâtes of océan tide loading displacements[END_REF]).

Together with the RMS misfits analysed previously, a weighted chi-square statistic for each of the derived sets of GPS estimâtes using ail 7 models, is defined. The uncertainties of the GPS estimâtes are propagated into the chi-square statistic whereas for the models we adopted an error free assumption (valid for our reference System).

The chi-square statistic is:

4 3 N /2 = c=1 y=l n=\ (A?Ps(C0^^GPs) + A (C0^^A ) + Z SiK^/t ))c,7> ) °GPS(cJ,n)
Eq. 4-9

Eq. 4-9 was calculated for a set of seven stations (MALO excluded). We hâve estimated statistics for a set of 3D parameters in ail components and for each component separately. Table 4-6 describes the results of this comparison. Once again the superior performances of the FES2004 are shown. Second in GPS/models agreement are the NEA2004, GOTOO.2, and CSR4.0 while the TPXO.7.0, TPXO.6.2 and NA099.b hâve the poorest fit to the GPS estimâtes. Despite the fact that Ki observable contains/introduces biases it was not excluded from the analysis.

Checking on the datum stability

In this experiment the influence of the stabilisation sites (the network effect) on the final GPS time-series of a European GPS-network which comports from 16 RGP stations and some IGS-EUREF stations is evaluated in a first place and then to the final OTL estimâtes of the GPS campaign stations. For this experiment I used the GAMIT/GLOBK software package to analyse data for a period of 80 days in 2004. The level of consistency between a solution of a selected GPS network aligned to a tightly fixed reference frame of the IGS stations and a solution using the "free-network" approach [START_REF] Heflin | Global Geodesy Using GPS without fiducial sites[END_REF] with looser constraints, is quantified. The impact on the OTL estimâtes is estimated as well.

For the "free-network" approach I used a global IGS stabilisation network together with a régional, from the EUREF network, and for the "tight constraints" I used the EUREF-IGS network. Both types of networks can be seen in Fig. 456789. Nevertheless, the drawback of the "loose constraints" approach is that a strong corrélation exists between the free network solution and the a-priori positions of the GPS stations. The constraints applied must be loose enough so as not to bias the intermediate network results. Especially the GPS campaign stations can strongly influence the solution due to their erroneous a-priori non-adjusted coordinates. This corrélation is observed for every IGS-stabilisation site and increases for the remote sites located at the edge of the network. In this case we applied different sets of a-priori constraints. We observed that in the présent case with 5/10 cm constraints on the IGS stations (horizontal and vertical respectively) and 10/20 cm on the campaign stations (horizontal and vertical respectively) and by taking into account different sets of IGS stabilisation sites (remote stations removed) this behaviour was not reproduced anymore. The datum définition was established by the application of a 7-parameter

Helmert transformation between the individual coordinates of our network and the global reference frame defined by the IGS stabilisation sites.

The two approaches were evaluated by comparing the resulting WRMS of the différences of the two solutions with respect to the mean standard déviation of the timeseries. The WRMS différences were of the order of 3.4 mm, 4.0 mm and 9.4 mm in North, East and Vertical and the mean formai errors for the "tight" and "loose" approach were respectively in North, East and Vertical: 6.1 mm 3.3 mm, 9.7 mm and 3.0 mm, 2.8 mm, 10.4 mm. The overall consistency between the two approaches is at the mm level. Their différences are not significant because they are below the formai errors of the final position estimâtes.

From the consistent results of the "tight" and "loose" solutions I conclude that for the time-span of the current campaign both approaches give équivalent results in terms of précision and accuracy.

In the current study I applied the "tight" constraints approach on set of selected IGS stabilisation sites.

Influence of vertical displacements on TZD parameters

The high corrélation between the troposphère parameters and the vertical site displacements is very well known. Meteorological applications of GPS-derived Précipitable Water Vapor (PWV) require that these parameters are estimated with an accuracy of 1 mm or better. An error of 8 mm in the TZD parameters will resuit in an error of about 1.2 mm of PWV according to the rule of thumb from [START_REF] Bevis | GPS meteorology : remote sensing of the atmospheric water vapor using the global positioning System[END_REF].

An un-modelled sub-daily OTL effect may seriously affect the estimated troposphère parameters. Previous studies from [START_REF] Dach | Influence of the océan loading effect on GPS derived précipitable water vapor[END_REF], [START_REF] Dragert | Océan loading corrections for continuous GPS: a case study at the Canadian Coastal site Holberg[END_REF][START_REF] Vey | GPS measurements of océan loading and its impact on zénith tropospheric delay estimâtes: a case study in Brittany, France[END_REF] and [START_REF] Urschl | Validating océan tide loading models using GPS[END_REF] hâve demonstrated the impact of OTL on the ZTD estimated parameters. In order to better investigate the influence of the tidal loading on the zénith path delay parameters I computed the différences of hourly estimated TZD parameters from a solution where OTL prédictions were applied to the GPS stations from the FES2004 model and from the ones obtained without OTL corrections. This operation removes everything that is of non-tidal and origin common to the two TZD time-series, such as multipath. The latter propagate into the TZD time-series due to the corrélations with the vertical component. In Fig. 4-11 the TZD time-series in the case were OTL displacements are applied for ail tidal waves to ail GPS sites, is illustrated. Peaks in the power spectrum of spurious signais are located at multiples of the repeat orbital period of the GPS satellite (K2, K3, K4 etc.). It is obvious that such corrélations introduce erroneous estimâtes in the TZD parameters that can reach several mm as seen in Fig. 4-11. The largest of those is 5 mm detected in the K4 frequency, équivalent, according to the rule of thumb, to 0.8 mm of PWV. The results here show that TZD parameter estimâtes can be significantly biased if océan loading effects are not accounted for properly. Additionally there is a strong propagation of multipath effects due to the high corrélation with the vertical site's coordinates which will bias the final TZD estimâtes at the order of some mm if we do not consider proper mitigation techniques. The aliasing to longer wavelengths will strictly dépend on the sampling rate of the discrète output solutions which may beat each other to cause additional spurious effects in the GPS height time-series [START_REF] Penna | GPS height time-series: Shortperiod origins of spurious long-period signais[END_REF]).

As such, I repeated the previous experiment of the Brittany OTL campaign by

Processing 24-hours non-overlapping solutions. To create the mismodeling scénarios, seven GPS height time-series were generated per site, using ail available data (Table 4-2). The procedure and options are the same as in the 24-hours straightforward solution of described in § 4.2.3.1. First, corrections were applied for ail eight principal constituents M2, S2, N2, K2, Kj, 0|, Pi, and Qi as well as for Mf, Mm and Ssa. This procedure was then repeated except ail principal OTL constituées were modelled but M2 and N2. The 24-hours solutions in which ail eleven principal tidal constituées were modelled to obtain GPS height time-series per site were used in order to check the total remaining long wavelength signal arising from océan tide model errors. The OTL prédictions for each site were effeceated with géochargeV3.0 and FES2004. Next the height time-series resulting from the solution with ail predicted OTL displacement constituées but M2 and N2 were used in order to evaluate the level of admittances (ratio of amplitude of spurious long-wavelength output signal in the height time-series to amplitude of predicted periodic displacement).

Fig. 4-14 : The least squares spectral lobs of the GPS height time-series for four représentative stations. In black are the harmonies from a solution were the M2 and N2 prédictions were not applied. In red is a solution were ail the OTL prédictions were applied but M2. Units are days (x-axis) and métrés (y-axis).

In order to extract the propagated long-wavelength amplitudes from the GPS height time-series a least squares spectral analysis was established (G. Balmino personal communication). The aliasing periods used in these scénarios were two: the 13.66 days beat-period for M2, and the 9.13 days beat-period for N2. The later were chosen according to the conclusions from [START_REF] Penna | Aliased tidal signatures in continuons GPS height time-series[END_REF], [START_REF] Stewart | Investigating the propagation mechanism of unmodelled systematic errors on the coordinate time-series estimated using least squares[END_REF] The periodicities at which significant peaks are expected for M2 and N2 where simultaneously estimated using the GPS height time-series corrected from ail eleven OTL constituents. The harmonie analysis estimation was effectuated by least squares.

As seen in Table 4-8 there are significant réductions to the amplitudes and admittances of the 13.66 and 9.13 days spurious signais with respect to

Summary

The capacity of GPS to détermine OTL displacement coefficients in one of the world's Coastal areas with the highest and most complex OTL phenomena was demonstrated.

Our strategy of GPS OTL extractions is based on 24-hour period observations for robust ambiguity resolution. An inversion scheme of final normal équations Systems based on tight constraints to IGS stations for the datum définition and continuity constraints on hourly coordinates of the GPS stations in a local geodetic System, was implemented. After solving in daily batches, the estimated GPS time-series were processed as independent tide gauge measurements in the harmonie analysis. The amplitudes and Greenwich phase-lags for four of the major OTL displacement coefficients in Brittany and Contentin were estimated. Thus, we hâve implemented a new GPS processing strategy to calculate OTL constituents.

Limited by the duration of the GPS campaign we were only able to extract GPS OTL coefficients for four of the most energetic tidal constituents, namely M2, S2, N2

and Ki. We hâve shown that the GPS technique is capable of distinguishing between the modeled OTL displacements at 95 % confidence level in ail three directions for ail campaign stations.

Nevertheless, in the vertical direction GPS had the weakest performance in distinguishing the OTL displacement constituents of K). We believe that this is mostly related to multipath effects (for the waves close to the repeat period of the GPS satellites) and errors in the GPS orbits.

Multipath effects propagated to frequencies equal to the integer multiples of the GPS orbital repeat period were found. Hence "fictitious" signais at these periods can bias GPS tidal loading coefficients of shallow water constituents. This effect shows the drawbacks of the GPS technique in distinguishing OTL displacements of the shallow water interactions (like SK3 or S4). Multipath mitigation techniques could be tested in our case. These effects are mainly due to the 2:1 commensurability of the orbital period of the GPS satellites and the sidereal day where the partial tides K\ and K2 are highly correlated with the orbital period [START_REF] Urschl | Validating océan tide loading models using GPS[END_REF]. Therefore this situation could also be improved by using data from GLONASS (repeat period 22.434-h) or the future Galileo (repeat period 28.158-h) and Compass (repeat period 25.682-h) satellites in a combined GNSS data processing scheme because their révolution period is outside the 2:1 commensurability.

Nevertheless, highly energetic shallow water and non-linear interactions in the semi-diumal and higher band in the région of St-Malo are assumed to be the reason for significant différences in the Greenwich phase-lag and amplitudes of modeled and predicted OTL constituents. These effects are contained in the M2 GPS OTL displacement estimâtes as seen from the phasor-plots of By calculating an RMS misfit and a chi-square statistic of the complex différences, for the four major constituents M2, S2, N2 and Ki between the OTL displacement estimâtes from GPS and model grids, we conclude that FES2004 is the most accurate model for the région. Second in accuracy are the NEA2004, GOTOO.2 and CSR4.0 models. The NEA2004 grids are in good agreement with the GPS estimâtes but from the présent results they do not seem to offer more information despite the higher resolution of its grid. The TPXO.7.0, TPXO.6.2 and NA099.b hâve the poorest performances in terms of agreement with the GPS estimâtes. Therefore, we recommend to exclude them from further use in the région. Their 3D différences, which are given in Table 4-6 for FES2004, reach 5.2 %. Possible causes are the interpolation scheme applied and the use of a different set of Green's functions. Onsala's web-based olfg/olmpp algorithm uses the Gutenberg-Bullen Earth model [START_REF] Farell | Deformation of the Earth by Surface Loads[END_REF]) while in géochargeV3.0 we used the input set of [START_REF] Pagiatakis | The response of a realistic earth to océan tide loading[END_REF] Green's functions based on the PREM Earth model [START_REF] Dziewonski | Preliminary reference Earth model[END_REF].

The olfg/olmpp refînes the tide model in a 3°x 3°box centered on the station. Since in this région the FES2004 model has relatively high resolution grid cells (0.125°x 0.125°), we forced the géochargeV3.0 to use the nearest grid value. The 5.2 % relative différence in the chi-square factor of the GPS/model OTL prédictions from the two OTL programs is consistent with the conclusions from [START_REF] Bos | An estimate of the errors in gravity océan tide loading computations[END_REF] conceming OTL software discrepancies due to the integrated Green's functions (~0.2 %) and the nearest grid value instead of bilinear interpolation (-7 %).

The impact of the network effect on the final OTL estimâtes was tested. From the consistent results of the "free network" -"loose constraints" and "tight constraints" experiments I conclude that for the current campaign both approaches give équivalent results in terms of précision and accuracy.

The resulted TZD parameters were found to contain spurious signais due to multipath présent at the multiples of the repeat period of the GPS satellites. Furthermore the impact of un-modelled OTL signais on the PWV estimations was quantified.

Spurious signais were found in the long-period time-series of the GPS campaign stations of 24-hours solutions corrected for ail OTL waves but M2 and N2. The latter were examined using a least squares harmonie spectral analysis. The most prédominant periods are those of-13.66 days and -9.13 days. These signais propagate in the 24hours GPS time-series with admittances that vary from 18 % through 39 % for the M2 -13.66 day signal and 46 % through 90 % for the N2 -9.13 day spurious signal. Then OTL displacement prédictions from FES2004 and TPXO.7.0 were accounted for ail tidal waves including M2 and N2. The comparison of the remaining amplitudes of spurious signais at the same periods demonstrated that a validation method using the 24-hours GPS time-series is possible. Again the most accurate emerging from this comparison is FES2004.

I fmally conclude that GPS is capable of measuring OTL displacements with high accuracy and précision in 3D, and it constitutes an accurate and efficient technique for evaluating océan tide models in complex régions like Brittany. et al. 2003), the most recent one on the Gavdos island of Crete in Greece (Pavlis and Merticas, 2007) and in the mean sea-level studies in the Aegean and Black sea [START_REF] Müller | Validation of marine geoid models in the North Aegean Sea using satellite altimetry, marine GPS data and astrogeodetic measurements[END_REF][START_REF] Tziavos | Mean sea level and sea surface topography studies in the Black Sea and the Aegean[END_REF]).

In the présent case such a technique is extended to a larger area, the Drake Passage. It is used to détermine the absolute sea surface Dynamic Topography (DT), the Sea Surface-Height (SSH) and derived geostrophic current and transport in this région which is a key place to observe the strong Antarctic Circumpolar Current (ACCt) and its variability. The latter will form the second part of my research project.

For the ACCt observation the required quantity is the absolute DT which is the sea-level relative to the geoid: DT = MDT + SLA Eq. 5-1

Where: MDT is the mean dynamic topography and SLA is the sea-level anomaly which is the residual component of the SSH and the Mean SSH (MSSH).

Précisé estimation of the MDT and SSH is needed. A good way to evaluate a high resolution, highly accurate MDT is to estimate the différence between the MSSH (computed from altimetry and kinematic GPS) ail along the DRAKE passage and the geoid or the gravity anomalies in the area: DT = MSSH -geoid Eq. 5-2

The latest gravimétrie missions such as CHAMP and GRACE hâve allowed great improvements of our knowledge of the geoid. Nonetheless, the resolution of the latest geoid models like EIGENGL04S (-400 km) not being sufficient enough for our purposes, additional absolute gravimétrie observations were effectuated ail along the passage.

The three main objectives foreseen for this project are:

Background of the DRAKE GPS campaign

The ACCt is one of the most important current in the world in terms of volume, transport (around 135 Sv =135-106mVs) and extension (up to 3000 km). It is freely moving around the Antarctic continent, conveying heat, sait and particles from one océan to the other, affected by the ice melting and exchanging a lot of energy with the atmosphère during its circumpolar trip. Thus, its rôle is essential in the climate System.

The Drake Passage is the place where the ACCt becomes the narrowest (around 700 km) making thus its observation and/or monitoring more easy as seen in the black box The first DRAKE campaign (Fig. 5-2) from January 14 through February 8, 2006 (C. Provost project manager LOCEAN, http://www.locean-ipsl.upmc.fr), was a unique opportunity to know more about this strong and influent current which is not so well known even if several studies and campaigns hâve been conducted previously. The objectives of the Drake campaign were essentially to measure through the Drake passage the magnitude and variability, from intra-seasonal to inter-annual, of the ACCt transport, based on two years long moorings, dense hydrographie stations, and coincident répétitive altimétrie sea-level profiles for more than 15 years. To complété this multi-sensors observatory, an additional innovative GPS technique was tentatively proposed to collect sea-level measurements with respect to geodetic reference stations along the southward and northward trajectory of the "Polarstem" vessel [START_REF] Ménard | Sea level and sea-state measurements by GPS, FS POLARSTERN[END_REF].

The kinematic GPS survey provided a lot of independent sea level

Data collection and editing

The 1 Hz GPS data sets from a total of 50 buoy-ship sessions hâve a mean duration of 2 hours each. The configuration of each one of them is using one antenna on a GPS waverider buoy and three other antennas on the research vessel "Polarstem". The receivers on the vessel were collecting data in a continuous mode ail along the passage. An accurate calibration of the vessel's FL is First required in order to use the onboard GPS stations for measuring the SSH in a consistent reference frame, ITRF2000 in this case, before cross-comparing these independent GPS sea-level data with the coincident altimeter data along the 104th Jason-1 ground-track. The définition of the FL of the research vessel "Polarstem" is defïned through the GPS on-board antenna and the antenna of the wave-rider buoy as below: FL = hse-hbe+b Eq. 5-3

Where: hse is the ellipsoidal height of the Ashtech Receiver antenna on-board "Polarstem"; hhe is the ellipsoidal height of the GPS buoy; b is the height of the GPS buoy Antenna Reference Point (ARP) with respect to the mean sea surface.

The calibration campaigns were performed at the two terminais (Asmar and Gas terminais) near the Punta Arenas harbour (Fig. 5-4). The two places where vessel and co-located GPS-buoy water level measurements hâve been simultaneously realized are described in Table 5-1. These observation periods are henceforth referred to as the lst and 2nd calibration periods. Independent positions were determined for the buoy and ship receivers during these two calibration periods. These solutions were subsequently used to dérivé the floating lines.

GPS Station Description

Antenna Height Détermination

The ARP above the mean SSH was calibrated in a basin at the location of the Observatory of Midi-Pyrenees for two configurations of the buoy. Though, as the fresh water of the basin does not hâve the same density with sea-water (33.2 psu), we accept a mm-level error in the height estimate. For the first configuration we found a position of

3.

The three sets of normal équations formed for the three independent baselines are then combined using DYNAMO, to get the stacked normal équations. These normal équations are then simultaneously inverted to get the final position timeseries. Tight constraints are applied to the ITRF 2000 coordinates of the IGS stations PARC and RIOG for each independent baseline.

Results of the 1st calibration period

The estimated SSH time-series of a total duration of 75 min for the buoy (PAB1) and the "Polarstem" antenna connected to the Ashtech receiver (POLA) are shown in Fig. Till today there are no tide models publicly available for the Magellan's straits where Puntas Arenas is situated.

5-8 and

By performing the différences of the two SSH time-series the FL of the vessel during the lst Calibration period is calculated. From Fig. 5-10 we understand that the ship's mean FL is -33.8 m ± 14.6 mm below the GPS antenna phase center. From the same Fig. 5-10 we see that the FL is rather constant with the exception of small trends between 20 min after the beginning of the session and 20 min before the end of the session. There is also high-frequency variations coupled with the graduai increase of the FL. This increase in the floating line could be attributed to the offloading of equipment at the Asmar terminal during the lst Calibration period which suggests a decrease in the weight of the ship. Finally the FL is determined with an RMS error of less than 1.5 cm.

Results of the 2nd calibration period

The common duration of the buoy and the ship observations in the second calibration is 30 minutes ( From Fig. 5-13 we understand that the movement of the buoy is much more dynamic in the second session than in the first. This is clearly seen by comparing Table 5-2 with Table 5-3 were the RM S error is remarkably higher for PAB2. During the First period the buoy moved in an almost E-W direction of 3 m and 1 m in the N-S direction within 75 min. In the second session the buoy moved within a bigger area of 9 m in E-W and 3 m in N-S within 30 min. This is an indication of the fact that PAB1 shows significantly less dynamic movement than PAB2. This could also explain the numerous loss-of-lock events associated with PAB2. As the buoy's dynamic State gets rougher, smaller time steps will produce results with better précision but nonetheless our processing scheme in GINS needs further improvements for the highstate dynamic cases especially in the open océan. The 2nd FL is determined in Fig. 5-14 by differentiating the two SSH time-series for the buoy and the ship. The FL shows high-frequency variations, but compared to the First calibration does not show a long-term graduai change. We observe that the FL is now at 33.2 m ± 42.2 mm about 60 cm less than the FL of the lsl Calibration period. This implies that the weight of the vessel has increased, which is entirely possible as the ship was fuelled of the Gas terminal at the time of the second session.

The Vessel's attitude détermination

The ultimate aim of the GPS positioning is to realize globally referenced coordinates of the vessel's GPS antennas in the ITRF2000. Additionally, the gravimétrie observations are a product of accélérations sensed from the accelerometers of a Strapdown Inertial Measnrement Unit (SIMU) on-board the "Polarstem". The heart of the SIMU is the Dynamic Reference Unit (DRU) of the Marine Inertial Navigation System (MINS, http://www.l-3klein.com). The Inertial Sensor Assembly (ISA) of the DRU is built up of 3 FIONEYWELL production-model GG 1342 Ring Laser Gyros (RLGs) and 3

Sundstrand QA2000 accelerometers with associated electronics and high voltage power supply.

The GPS antennas will serve as constraints for the détermination and re calibration of the IMU's accélérations ail along the Drake Passage. Prior to this installation the offsets (lever-arms) between the IMU and the GPS ARP need to be known with sub-mm précision in order to avoid systematic perturbations of the Lever- Where: C" = R3 (-(//) R, (-0)R2 (-<?) is the rotation matrix of the 6-frame to the //frame; is the lever-arm vector in the b-frame centered either at the GPS antenna phase center or at the reference center of the IMU; xllGPS is the 3-D vector of the antenna's position in the //-frame (previously transformed from the Earth fixed e-frame) containing the attitude perturbation; xji^will be the 3-D vector of the antenna's position in the //-frame.

The attitude variations could be determined by the measured angles of roll-çp, pitch-0 and yaw-t// of the IMU's RLGs gyroscopes.

As far as it concems the propagation of the b-frame in the observed accélérations, there are terms that will be measured by the gyros that do not represent true body motion. The tangent //-frame will rotate as the vehicle moves over the elliptical Earth, and although this term is small, it is felt by the gyros. The earth's rotational rate will also be felt by the gyros, and is included in the body frame propagation as well.

The final errors in the GPS SSH time-series can reach 5-15 cm due to the perturbations induced from attitude variations.

A case where the effect of the attitude perturbations on the GPS antenna final coordinates will be amplified due to the LAE is given in Fig. 5 Additionally, since POLB is further from the vessel's centre of equilibrium (considering that this is the centre of the 6-frame) the length of the lever arm will add an amplified effect on the variations of the coordinates projected on the //-frame, namely the LAE (Melachroinos 2004). In this case the corrections according to Eq. 5-4 should be applied.

Validations of the current GPS kinematic method

Part of the validation of the implemented GPS kinematic approach was accomplished extemally by the use of an independent data-set, under more or less the same calm environmental conditions, from two GPS-buoy campaigns at Spring Bay in Tasmania The next steps in this research project are already planned:

1. The kinematic GPS processing will be extended to the whole DRAKE data set (in the open sea and at the Jubany and O'Higgins Antarctica bases for further validation). This part will be divided into two tasks. The first task will be to upgrade the GINS GNSS software for addressing the ambiguity resolution issue in high dynamics State environments. Then I will define the best strategy for a long-baseline précisé estimation of the coordinates of the GPS antennas fixed on the buoy and on the research vessel Polarstem. Tropospheric zénith delay parameters will be constrained through the combinations of independent baselines of permanent IGS stations and the use of ECMWF model. The second task is related to the évaluation of the impact of the ship's attitude variations, mostly in roll, pitch and yaw, through the use of the attitude law given by the inertial measurement unit on-board the ship. Here again necessary software modifications and algorithm developments of the Eq. 5-4 in the observational model will be implemented and validated. The software package TRACK developed at MIT [START_REF] Herring | TRACK GPS Kinematic Positioning Program[END_REF] will be used to re-process ail ship and buoy sessions for the empirical internai validation. TRACK is a kinematic software initially developed by [START_REF] Chen | GPS Kinematic Positioning for the Airbome Laser Altimetry at Long Valley, California[END_REF] for the use in airbome laser altimetry.

2. Once ail software modifications are implemented and validated I will be ready to proceed with the détermination of the ship's position at every second of its southward and northward cruise. Thus, GPS sea-level profiles (SSH) will be determined ail along the Polastem's trajectory and the Jason-1 104 ground track.

SWEl parameters will be extracted.

3. Next, collocated SSH, MSL and SWH altimétrie profiles from Jason-1, ENVISAT (and GFO) will be cross-compared with the coincident GPS derived SSH, MSL and SWH profiles and analyzed in order to interpret the différences in terms of errors (as for instance the impact of the sea State bias SSB in the altimétrie SSH profiles or in the GPS results). Additional comparisons with in-situ SWH observations during the campaign and with sea-state models will be performed. By these comparisons I will be able to finalize a complété error budget including a study of the impact of a multi-GNSS (GPS+GLONASS+GALILEO) constellation on the kinematic solution. Then recommendations to improve the error budget for further projects (The Drake campaign of 2009) will be given.

From the current expériences an error budget of the GPS SSH estimations can be formed in 4. The estimated geoid profile (or gravity anomaly profile) from GPS MSSH estimâtes will be cross-compared:

• with the altimétrie and gravimétrie measurements collected during the campaign;

• with the GRACE geoid models EIGEN-GL05S (200 km resolution) and the more refmed model EIGEN-GL05C (55km resolution) gravity model [START_REF] Lemoine | Temporal gravity field models inferred from GRACE data[END_REF];

• if possible, with the first GOCE observations after its launch in spring 2008.

• Interprétations of the different results will be the desired outcome.

5. The computation of the ACCt's sea-level signature will be the final goal together with derived parameters and their variability based on altimetry, GPS and on the estimated geoid profiles used as references. For validation purposes, additional comparisons with climatology, in-situ known estimâtes and model outputs (e.g. Mercator) will be realized.

The anticipated results will bring a fully validated GINS version for processing GPS data in a kinematic mode which we intend to promote in the international community for Cal/Val and océanographie activities.

The knowledge and expérience gained will be used for extending this kind of GPS survey to other régions through dedicated campaigns or opportunity campaigns.

Recommendations resulting from the présent study will be applied for the next DRAKE campaign scheduled for the beginning of 2009 in order to improve the technique, reduce the error budget and consolidate the 2006 DRAKE scientific results.

Altimetry Cal/Val issues will benefit from our expérience in validating altimetry data off-shore and over large distances from the coasts minimizing radiometer errors (absence of large pollution in the altimeter's footprint at ~40km from the coasts).

Problems like ambiguity resolutions and multi-GNSS constellation combinations over long baselines for the détermination of high précision coordinates in GPS kinematic mode and at high dynamics State, which remain nowadays a challenging part of geodesy, will be studied.

Finally benefits from our geodetic approach for oceanography in régions like the Drake Passage that are suffering from a lack-of-data and model uncertainties, will be significant.

I would further like to express my gratitude to Dr. Y. Ménard and PEng. M.

Faillot for giving me this opportunity to work and develop this project into a Post-Doc contract.

6 Conclusions -Perspectives

Realized work

The work realized during the last three years was coordinated with the efforts of the CNES/GRGS group to improve and to promote the GINS software package in the geodetic community by producing valid scientific results.

Through the guidance and plans of my supervisors these efforts were divided into two main parts: 1) the first part was oriented towards the development and validation of the software; 2) and the second part was aiming at the scientific interprétation of observations from dedicated campaigns of terrestrial and maritime GNSS networks. The GINS' estimated GPS high-frequency position coordinate time-series comparisons were made using the observational set of 9 GPS dedicated campaign stations used in order to study OTL in Brittany. The linear corrélations of more than 80 % with respect to the other solutions and the agreement in the periodicities of the highfrequency time-series indicated the high level reliability of GINS' results. During the POD validations more emphasis was put on the newly modified B-W SRP model for the GPS satellites. The GINS' GPS orbit tests were based on internai and extemal comparisons to the IGS sp3 orbits. The internai 3D-RMS misfïts were found to be 5 cm with the inclusion of periodical ternis in the solar oriented or orbital plane directions.

The extemal 3D-RMS misfit compared to the IGS orbits varied between 5 cm and 10 cm. Histograms of SLR range residuals and biases were also compared. The SLR observed range for both GPS 35/36 satellites were computed from a sériés of GINS and IGS GPS 35 and 36 microwave orbits. The respective biases obtained were: -2.9 cm from GINS and -3.7 cm from IGS. The mean SLR station RMS range residuals with respect to the GINS' microwave orbits were found to be about 4 cm. These were less dispersed to those calculated with the IGS orbits of 4.5 cm. Finally the B-W SRP parameterization in a solar-oriented attitude referential was selected as the idéal configuration.

Furthermore, the précision of the SLR-only POD of the GPS 35/36 satellites was found to be 2 cm to 3 cm radially and the SLR network effect affected the orbits' reference frame up to 4 cm -6cm in the z-shift and 0.1 cm -1.6 cm in scale, for the two orbits (from June 6 to 16 2006 of the experiment) respectively. The SLR-only POD for GIOVE-A was realized for a period from June 5 through November 25 2006 and the radial précision was evaluated to 5-10 cm.

6.1.2 Geodetic interprétation of observations from dedicated campaigns of terrestrial and maritime GNSS networks (part 2)

For the first time in the GRGS research activities, these types of studies were performed using a modified GINS GNSS software package.

The capacity of GPS to détermine OTL displacement coefficients at 95 % confidence level in ail three directions and evaluate océan tide models in one of the world's Coastal areas with the highest and most complex OTL phenomena was demonstrated and an original method was implemented. The loading signais for M2, S2, N2 and Ki, were extracted from the GPS observations of a dedicated campaign that took place for about 104 days from March through June 2004. These observed GPS OTL constituents were compared to the predicted OTL estimâtes from seven océan tide models TPXO.7.0, TPXO.6.2, GOTOO.2, NA099.b, CSR4.0, FES2004 and the régional NEA2004. Phasor plots of the GPS and predicted M2 OTL coefficients hâve demonstrated strong discrepancies in the vertical in the area of St-Malo, around 20°for the phase-lag and ~1.5 cm for the amplitude. These were attributed to strong non-linear effects of the sub-diumal band mapped onto the GPS time-series, which according to le Provost and Fornerino (1985) are the highest in the région at this location. As such, it was proposed, that a good way to constrain these non-linear effects in the assimilation of the loading and self attraction terms for the océan tide models, is to include the GPS observed OTL constituées. Furthermore, the ter-diumal and higher frequencies of the GPS OTL spectrum, seems to suffer from unmodeled multipath effects that propagate in periods of the integer multiples of the repeat orbital period of the GPS satellites around the Ki frequency. As such, the order of the multipath effect on the GPS OTL estimâtes was quantified that maps into these frequencies with amplitudes of ~5 mm and can seriously bias estimated shallow water GPS OTL constituées. In this case multipath mitigation techniques should be tested. In parallel the différences between the predicted FES2004 OTL coefficients from two OTL programs, olfg/olmpp and géochargeV3.0, with respect to the GPS observed OTL constituées were quantified. These différences were found to be of the order of -5 % and agréé with previous sedies in discrepancies between OTL software [START_REF] Bos | An estimate of the errors in gravity océan tide loading computations[END_REF]. The causes are mostly located in the different set of Green's fonctions and interpolation scheme used. From the RMS and chi-square statistical indicators it was derived that the most accurate model for the région is the FES2004. From the consistent results of a "free network" -"loose constraints" and "tight constraints" solution the impact of the network effect on the final OTL estimâtes was tested.

It was concluded that for the current campaign both approaches gave équivalent results in terms of précision and accuracy. Furthermore, an estimated set of TZD parameters was found to contain spurious signais of -9 mm in amplitude at the multiples of the repeat period of the GPS satellites mainly due to multipath effects originating from the corrélations with the vertical component of the GPS stations. Furthermore, the impact of un-modelled OTL signais on the PWV estimations was quantified. When accounting for ail OTL prédictions except for M2 and N2 in a set of 24-hour solutions during the whole campaign period, spurious signais were found at fortnight periods in the GPS campaign-stations time-series. The latest were examined using a least squares harmonie spectral analysis. The most prédominant periods found are those of -13.66 days and -9.13 days which are in agreement to previous studies from [START_REF] Penna | Aliased tidal signatures in continuons GPS height time-series[END_REF], [START_REF] Stewart | Investigating the propagation mechanism of unmodelled systematic errors on the coordinate time-series estimated using least squares[END_REF] and Penna et al.

(2007) about aliasing effects on 24-hours GPS solutions of un-modelled OTL displacements. These signais propagate in the 24-hours GPS time-series with admittances that vary from 18 % through 39 % for the M2, -13.66 day signal and 46 % through 90 % for the N2, -9.13 day spurious signal larger than those found in [START_REF] Penna | GPS height time-series: Shortperiod origins of spurious long-period signais[END_REF]. When OTL displacement prédictions from FES2004 and TPXO.7.0 accounted for ail tidal waves including M2 and N2, the remaining amplitudes of spurious signais at the same periods verified again that the most accurate model for the région is The second project proposes to use a global set of TG collocated with GPS and DORIS techniques in a consistent TRF. The set of TG sites will be carefolly chosen. Emphasis will be given to TG situated in areas with strong geological and geophysical interest such as Polar Régions, Alaska and Greenland.

The TG observations corrected from any vertical motion will be used for the calibration/validation of T/P, Jason-1 and Envisat drifts and GSLR estimations in the next step. The implemented procedure will be applied on Jason-2 which will be launched in 2008. Finally a calibrated and validated value of the GSLR will be the bénéficiai outcome.

Both projects should hopefully be fmanced by Post-Doc grants.

IOC-

  beloved wife Marie and precious daughter Estelle, to my mother Evanthia, to my brother Alexander and to my belovedfather Anthony who is not présent in this world with us anymore" "A ma femme bien aimée, Marie, et notre fille adorée, Estelle, à ma mère Evanthia, mon frère Alexander, ainsi qu 'à mon père bien aimé, Antoine, qui n 'est plus parmi nous " "Zzrjv afioÀâzpsuzq yvvaiKa zqç Çcorjç pou Mapl, azrjv noXvzigrj KÔpouXa paç EazsXXa,

Fig. 1

 1 Fig. 1-1 : DOR1S: the French space geodesy System. FIow does it work? Courtesy CLS (available at http://www.cls.fr/html/doris/principe_fr.html)

  Fig. 2-21 : Non-tidal loading displacements from MOG2D model at GPS stations in between 47°-50°N on the shelf of Brittany. (Time-series are from J. Marty of CNES/GRGS)

Fig. 3

 3 Fig. 3-8 : Internai vs extemal 3D-RMS misfïts for GINS GPS orbits with the B-W SRP model in four different parameterisations. Units are in meters 144

  modifications récentes et validées dans la troisième partie pour le positionnement par GNSS dans GINS, sont utilisées. La méthode implémentée a pour but d'utiliser une campagne GPS destinée à évaluer/valider les modèles de marées dans la région. L'impact des déplacements verticaux non modélisés des stations géodésiques sur les paramètres troposphériques est quantifié. D'ailleurs, la stabilité du datum (système de référence) utilisé pour l'alignement des solutions GNSS sur le système de référence terrestre et ses influences sur les séries temporelles finales des coordonnées des stations sont examinées. Les effets du repliement du spectre sur des séries temporelles des stations dues aux mouvements verticaux mal or non modélisés sont démontrés. Finalement, les performances de sept modèles globaux et régionaux de marées et les différences des deux logiciels utilisés pour les prédictions des mouvements dus à la surcharge océanique, dans la région, sont quantifiées. Dans la cinquième partie j'analyse les observations des données cinématique d'une campagne GPS dans l'océan Antarctique abord des bouées et un bateau de recherche pendant le passage du DRAKE au sud de Chili. La campagne DRAKE a été dédiée à comparer et valider les observations altimétriques et océanographiques pour l'étude du courant circumpolaire Antarctique. Les résultats sont préliminaires et se concentrent plutôt sur la définition de la ligne de flottaison du bateau par l'utilisation combiné GPS -bateaubouées. Les perspectives et la planification pour la continuation du projet en Post-Doc sont présentées.

For

  example, in the International Earth Rotation Service (IERS) standards it is mentioned that the coordinates of geodetic points attached to the solid surface are used for the realization of a Terrestrial Reference System (TRS) and the détermination of the Earth Orientation Parameters (EOPs). This System is a spatial reference System co-rotating with the Earth in its diurnal motion in space. A Terrestrial Reference Frame (TRF) is a set of physical points with precisely determined coordinates in a spécifie coordinate System (IERS 2003). The connection of the TRS to the Celestial Reference System (CRS) is accomplished through the EOPs. The EOPs are a by-product of the positioning of a set of reference points on the Earth's surface that participate in its daily rotation, polar motion and annual révolution around the sun.Précisé point positions are also important in interdisciplinary oceanographicdynamic topography of the sea, océan tide model validations, tectonics, volcanology etc.

  the position of a moving target or a stable geodetic point on the surface of the Earth has been troubling geodesists since the very beginning of the Greek civilization. One of the classical methods used was the measurements of angles and distances combined with astronomical observations. The first of these measurements was done by Eratosthenes in 230 BC. He introduced the first estimation of the Earth's radius by simultaneously comparing the time of the sun's zénith during the summer solstice at local noon in the town of Syene on the Tropic of Cancer, and the time where the angle of élévation of the Sun would be 1/50 of a full circle (7°12') south of the zénith at his hometown of Alexandria. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 stadia (1 stadio = 185.2 m). He rounded the resuit to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The estimated Earth's radius was calculated at 7427824.8 m 16 % too large.If Eratosthenes has used as a unit the Alexandia's stadion (158.3 m) the estimation of the Earth's radius cornes to 6348945 m 0.3 % smaller. Albeit their long âge and history, part of these methods are still being used nowadays.In the early 60's with the apparition of the first radio technique such as the Transit/NNSS (Navy Navigation Satellite System) we hâve entered the era of a new révolution in positioning applications. The principal of this System was based on measuring the Doppler effect of a moving target with respect to a stable station in order to measure the relative velocity. The Doppler technique was also developed in the 80's by the Centre National des Etudes Spatiales (CNES, FR) with the DORIS (.Doppler Orbitography by Radio-positioning Integrated on Satellite) System (Fig.1-1).

Fig. 1

 1 Fig. 1-1 : DORIS: the French space geodesy System. How does it work? Courtesy CLS (available at http://www.cls.fr/htrnl/doris/phncipe fr.html)

  Recherche et de Combinaison (CRC) ; 3. Deformations of local geodetic networks observed by GNSS and kinematic positioning of floating tracers (this Thesis); These directions are cohérent with the motivations of GRGS to propose the use of GINS at laboratories around the world as an alternative to already well established scientific software such as:

  second, was the validation of GINS' results through comparisons to other software and notablyGAMIT 10.21 (Ring and Bock 2005), GIPSY/OASIS II[START_REF] Zumberge | Précisé Point Positioning for the efficient and robust analysis of GPS data from large networks[END_REF]) and Bernese 5.0[START_REF] Dach | Bemese GPS software version[END_REF]) and which was treated together with the participation of several French research teams. The last part was assigned to the scientific évaluation and tide models' validation by comparisons to the estimated GPS océan tide loading constituents in the diumal, semi-diumal, third, fourth, fifth and sixth-diumal spectral bands. 4) And finally, I hâve processed the GPS kinematic data from a dedicated campaign (buoy and Ship) in the DRAKE passage south of Chile for the cross comparison and calibration of altimétrie and océanographie parameters in the area. Part of this work is still in progress and the continuation should be assured hopefully by a Post-Doc grant. d) This Thesis A technical and historical description of ail existing and future GNSS Systems is given in the first chapter of this manuscript. In the second part the geodetic components of GNSS are sub-divided into four categories: a) The terrestrial reference frame, b) the geodetic GNSS networks, c) the GNSS observational models and errors, d) the GNSS station displacements.In the third part a general présentation of the GNSS capacities inside GINS software together with the recent modifications are presented. Validation tests of these new functionalities, through intra-software différences on the estimated time-series of geodetic stations and through POD of the GPS satellites compared to extemal references, are presented in the same chapter.In the fourth part, the study of observed and predicted océan tide loading displacements and their validations through a new dedicated GPS campaign in Brittany and Contentin at the northwestem part of France, is presented.

  1.1.2 The Global Positioning System, GPSGPS is based on a network of initially 24 active satellites placed into orbit by the US Department ofDefense (DoD). The GPS baseline constellation of 24 satellites consists of six quasi-circular MEO planes at a nominal average orbit semi-major axis of 26559.7 km with an inclination of the orbital plane of 55 degrees with reference to the équatorial plane. 1.1.2.1 The development phase GPS is an active program over 30 years. The history of its development phase till full operational capability is summarized in the following synopsis (Hothem 2006): • In 1973 started the development which is an underway of separate programs; • In 1978 the first satellites were developed and launched; • The first operational satellites went into orbit in 1989; • The System reached Initial Operational Capability (IOC) in 1993; • And obtained FOC in 1995. The System actually exceeds the baseline constellation with 31 orbiting satellites after the last successful launch on November 17 2006. 1.1.2.2 The modernization Plan The current constellation of GPS satellites consists of: • 16 II/IIA operational satellites; • 12 IIR satellites, modemizing up to 8 Block IIR satellites ; • 3 IIR-M satellites launched on September 25 2005, September 14 2006 and November 17 2006. Before December 2005 the Standard Positioning Service (SPS) was provided by the C/A code on the L1 frequency and the Précisé Positioning Service (PPS) provided by the P(Y)code on L1 and L2 (Fig. 1-1).

Fig. 1

 1 Fig. 1-1 : The GPS Signal Spectrum, présent and future. (Source CNES)

  L1C civil signal will exist in addition to the C/A code in order to ensure backward compatibility with older receivers. During the 2006 and 2004 joint statement agreement between EU & US in matters of GNSS coopération, L1 band was optimized as the common baseline open service signal for GPS & Galileo. The FOC of the Block III phase is expected around 2020.

Fig. 1

 1 Fig. 1-3 : The GPS Operational Control Segment. (Source US DoS)

  The EU Transport Council resolution on March 23 2002 puts the Galileo project in action; • In the same year cornes the création of the Galileo Joint Undertaking (GJU) enterprise. The rôle of GJU was to coordinate and manage the In Orbit Validation phase (10V) up to the sélection of the System's operator during the launch of the FOC phase; • Starting of the IOV phase beginning of 2004; • During the final conclusions' policy of the EU Transport Council of the 10/12/2004

Fig. 1 -

 1 Fig. 1-6 describes the GTRF network of the GSS stations.

Fig. 1

 1 Fig. 1-6 : Initial GTRF network at the beginning of IOV, -100 locations, (Source GGSP)

  Fig. 1-7 : GPS time versus GST and the GGTO bias in the navigation solution. (Source DLR.)

  to the user: o Navigation Message: SISA values for the satellites updated every 30 sec; o Integrity Message: the sigma of the différence of the estimated SISE and an unbiased one (Signal-in-Space-Monitoring-Accuracy, SISMA, Fig. 1-8) together with the integrity flags (IF) updated every 30 sec; o Alerts and connectivity status : each alert is coded with 4-bits and 16 different States can be accessible to the user (Don't use, Not Monitored, 14 States OK with corresponding SISMA ranging from 30 cm to 520 cm).

(

  Fig. 1-9 : The GIOVE-A satellite. (Source ES A)

Fig. 1 -

 1 Fig. 1-10 : C/No ratio for GIOVE-A code observables compared to GPS's C/A code (Navaro-Reyes 2007).

  Fig. 1-11 : Code multipath estimation on static environement in GIOVE's infrastracture. S1RD is the required performance for Galileo as it is described in the SIS-ICD (Navaro-Reyes 2007)

Fig. 1 -

 1 Fig. 1-12 : Frequency stability of one of the RAFS clock of GIOVE-A (Rochat et al. 2007). Notice the very good comparison between ground tests, spécifications and the INRiM's Hmaser stability

Fig. 1 -

 1 Fig. 1-13 : The GLONASS development program update. (Source Russian Fédéral Space Agency)

Fig. 1 -

 1 Fig. 1-14 : A GLONASS-M spacecraft

  time scale and are steered to UTC. Corrections to each on-board time scale relative to GLONASS time and UTC are computed by the control segment and uploaded to the users through the broadcasted ephemeris. The GLONASS time scale is periodically corrected for the integer number of leap seconds simultaneously with UTC corrections (see § 1.1.3.5), This happens by changing énumération of second puises of on-board clocks of ail GLONASS satellites.Between GLONASS time scale and UTC there is a constant 3 hours différence.1.1.4.5 GLONASS Coordinate SystemThe GLONASS broadcast ephemeris describes a position of transmitting antenna phase center of a given SV in the PZ-90 Earth-Centered Earth-Fixed reference frame. The PZ-90 System is a global System developed by Russia, similar to WGS 84 of GPS. It was realized by positioning 26 ground stations established from observations of the Geo-IK geodetic satellite ('http://www.fas.org/spp/guide/russia/nav/geo.htm), including : photographing it against a star background; Doppler measurements; laser ranging; and satellite altimetry[START_REF] Boucher | ITRS, PZ-90 and WGS 84: current realizations and the related transformation parameters[END_REF]. It also included electronic and laser measurement of GLONASS and Etalon satellites.

Fig. 1 -

 1 Fig. 1-15 : The IGLOS GPS/GLONASS network on Sept. 04 2007 (Courtesy of IGS).

  using the CNES tracking and recording System, has revealed Compass' signais spectrum in E2/L1 (Galileo/GPS), E5 (Galileo), and E5b (Galileo) bands. Fig. 1-16 illustrâtes the spectrum of the future Compass System.

Fig. 1 -

 1 Fig.1-16 : The Compass/Beidou frequency plan, which overlay GPS/Galileo signais[START_REF] Grelier | Initial Observations and Analysis of Compass MEO satellite signais[END_REF]).

  significantly. Up-to-day only one GNSS System is fully operational (GPS), one more is under modernisation (GLONASS) and another two are in their first implémentation stages (Galileo and Compass). Together with these global positioning Systems other régional complementary segments hâve been developed or are under development like: EGNOS in Europe; WAAS in the US; Beidou in China; QZSS in Japan; GAGAN in India. Currently the number of functional GNSS satellite vehicles raises up to 41 plus ~9 régional. In the near future, with the completion of Galileo -GLONASS -Compass this number will include more than a hundred satellite vehicles. As such, the future for ultra-high précision positioning in geosciences (Geodesy, Oceanography, Geophysics, Volcanology etc.) and in sociétal applications (Navigation in urban areas, fleet management, security of life, agriculture, automation etc.) becomes very promising.

Fig. 2

 2 Fig.2-1 : Co-location sites embedded in the implémentation of ITRF[START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time-series of station positions and Earth Orientation Parameters[END_REF]

  t0 ; velocities X'c expressed in the combined frame c; transformation parameters Tk, Dk, Rk at an epoch tk and their rates T*, Dk, Rk from the combined TRF to each individual frame k.

  Fig. 2-3 : The two ways of creating an ITRF

2. 1

 1 Fig.2-4 : The GRGS CRC structure scheme[START_REF] Biancale | Towards a new strategy for mutli-technique combined sériés of EOP and TRF[END_REF]

Fig. 2

 2 Fig. 2-5 : The EPN/EUREF GPS permanent network

Fig. 2

 2 Fig. 2-7 : The Réseau GPS Permanent (RGP) of the French Institute Géographique National (IGN) (left) and the REGAL permanent GPS network for the tectonic surveillance of the Alpes (right).

Fig. 2

 2 Fig. 2-8 : The IGS tracking stations network at Sept. 4 2007 (Courtesy of IGS)

Fig. 2

 2 Fig. 2-9 : The Double Différences of Single Différences

  the integer ambiguity cycles A^Lfrom this combination. It is often used for ambiguity resolution on the DD level. Lwl = -y(-U, -) = -(771, -60 ) xwl = n<-n2 2.3.2.4 The narrow-lane combination (Lnl)

  Fig. 2-10 : Distribution of the wide-lane ambiguities Nwl (in cycles) (source Noveltis)

  dx are baseline length and baseline component error andt/p, p are orbit error and satellite distance respectively.

Fig. 2 -

 2 Fig. 2-11 : GPS orbit overlaps from GRGS vs IGS comparison

Fig. 2 -

 2 Fig. 2-12 : BRST: (left) Cl pseudo-range; clock jumps are visible every hour. (Right) L1 observable; the clock's resets provoke interruptions in the satellites passages every hour. Y-axis units are in meters for Cl and cycles for Ll. X-axis units are epochs for 30s acquisition time of doy 197

Fig. 2 -

 2 Fig. 2-13 : ZIMM: (left) Cl pseudo-range; clock jumps are visible every hour. (Right) Ll observable; the clock's resets do not seem to hâve an effect on the phase observable. Y-axis units are in meters for Cl and cycles for Ll. X-axis units are epochs for 30s acquisition time of doy 197

•

  3rd Case: The GPS Station PALM (Palmer, Antarctica) An Ashtech Z-XII3 receiver is used for this station. It records data every second. It is being used as a reference station for the altimétrie cross-validation experiment south of the Drake Passage (see Chapter 5). No discontinuities are observed inside the RINEX file neither during the screening of the phase and code observables as illustrated in Fig. 2-14. The clock of this receiver behaves normally.

Fig. 2 -

 2 Fig. 2-14 : PALM: (left) PI pseudo-range; no clock jumps exist. (Right) L1 observable; Y-axis units are in meters for PI and cycles for Ll. X-axis units are epochs for ls acquisition time of doy 017 2006.

Fig. 2 -

 2 Fig. 2-16 : BS07: (left) Cl pseudo-range; two distinctive clock jumps exist. (Right) Ll observable the same two jumps exists here; Y-axis units are in meters for Cl and cycles for Ll. X-axis units are epochs for ls acquisition time from epochs 06 1 17 16 56 53.0000000 to 06 1 17 18 4 15.0000000.

Fig. 2 -

 2 Fig. 2-17 : (a) BOHI, (b) BS07, (c) PALM, (d) BRST, (e) ZIMM, (Left column) Melboume-Wübenna : LWM, (Center column) Iono-free : L3, (Right column) Geometry free Lion. Y-units are in meters and X-axis units are in epochs of 30s or ls.

  -17) we observe three different situations. Firstly, at the two buoys, BOHI and BS07, the noise level remains high enough around 4m because these stations are in constant motion and the ionosphere-free combination can not eliminate the geometry. Secondly, at PALM the noise level is around ~6 cm which reflects the high quality of this station and its clock. Thirdly, the time différences for ZIMM and mostly for BRST represent several sudden peaks related to the clock's resets for both cases (see further up in the cycle slips examples). Though it worth noting that in the record time inside the RINEX file of ZIMM we do not see any of these jumps appear, as previously noted during the cycle slips examples. That means that there is a discontinuity in the phase observables not visible in the screening graph of Fig.2-13.In the geometry-free combination (right column) the noise level reduces significantly for ail cases. It must be noticed that this combination leaves the influences of the ionosphère.Remarkable réduction of the noise is observed for the moving buoys BOHI and BS07 (~50 cm). With this combination, apart from the geometry, we eliminate as well the receivers' clocks errors. The advantage is more obvious in the case of stations with clock jumps, such as BRST and ZIMM, where the peaks disappear as seen from Fig 2-17dand Fig 2-17e. In these two stations the noise level drops down to ~50 cm. Even for PALM there is a factor two réduction of the noise when compared to the ionosphere-free combination.

Fig. 2 -

 2 Fig. 2-18 : (left) A-priori wet and (right) dry corrections from the ECMWF model. Scale bars are in meters

  Fig. 2-19 : (left) Height équivalent (y-axis in mm) scatter for 5°minimum élévation from Niell (2005) and

•

  the time-series of station positions. According toNeill (2005),[START_REF] Vey | Influence of mapping fonction parameters on global GPS network analyses: Comparisons between NMF and IMF[END_REF]. and[START_REF] Tesmer | Effect of different tropospheric mapping fonctions on the TRF, CRF and position time-series estimated from VLBI[END_REF] the mean station height différences présent the largest offsets in high latitudes (Fig.2-19).[START_REF] Tesmer | Effect of different tropospheric mapping fonctions on the TRF, CRF and position time-series estimated from VLBI[END_REF] hâve shown that discrepancies between time-series of station heights computed with different mapping fonctions reveal annual periodic signais with amplitudes up to 5 mm.• the ZTD parameters. The cut-off élévation angle sensitivity from[START_REF] Vey | Influence of mapping fonction parameters on global GPS network analyses: Comparisons between NMF and IMF[END_REF] has showed ZTD différences larger than 3 mm for an élévation mask réduction from 15°to 3°.• the scale, origin and geometry of the Terrestrial Reference Frame. Scale différences between TRF realizations reflect the corresponding "mean height différences" between TRFs. Origin différences reflect the corresponding geocentre translation différences. According to[START_REF] Vey | Influence of mapping fonction parameters on global GPS network analyses: Comparisons between NMF and IMF[END_REF] and[START_REF] Tesmer | Effect of different tropospheric mapping fonctions on the TRF, CRF and position time-series estimated from VLBI[END_REF] the effect of mapping fonctions on the scale in one year can reach 0.2 ppb (parts-per-billion 10'9) corresponding to 1.3 mm in the height on the Earth's surface, and to 3 mm in the origin.

  ) and those inferred by them (for the satellites' antennas) took place onNovember, 6, 2006 (IGSMAIL 5438).The new IGS reference frame IGS05 réalisation was established onOctober, 9, 2006 together with the long expected ITRF2005[START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time-series of station positions and Earth Orientation Parameters[END_REF]) on October, 5, 2006. Soon after the application of the new antenna models,Gendt et al (2007) hâve demonstrated the impact on the IGS' scale consistency when compared to the ITRF2000 and ITRF2005. The resulting scale improvements in discrepancy before and after the switch were 0.35 to 0.15 ppb for IGS00 TRF and 0.24 to 0.04 ppb for IGS05 (Fig.2-20).[START_REF] Herring | Impact of Absolute Phase Center Models on GPS Reference Frames[END_REF] has arrived to the same conclusion for the scale with an additional remark on the dependence of the GPS frame translation origin on the Z-direction from the SRP parameters.

Fig. 2 -

 2 Fig. 2-21 : Non-tidal loading displacements from MOG2D model at GPS stations between 47°-50°N on the shelf of Brittany. (J. Marty personal communication)

  PPP then the non-tidal loading displacements should be taken into account. The last conclusion agréés with the recommended révision on chapter 7 of the IERS conventions bipm.org/utils/en/events/iers/Conv PP1 .txt).2.4.2 Center of the mass corrections due to océan tidesAccording to § 2.1.2.2 the position of the center of mass of the System of solid Earth, fluid and atmosphère undergoes periodically motions due to the extemal forces acting upon it, such as océan tides. The geodetic stations which are fixed on the solid Earth will be subject to the counter-motion of the center of mass which takes place in order to counterbalance the displacement of masses.Space geodesy techniques such as Satellite Laser Ranging (SLR)[START_REF] Watkins | Observations of Tidally cohérent diumal and semidiumal variations in the geocenter[END_REF], and the Global Positioning System (GPS) are fixed in space and are in principle able to detect this centre of mass motion of the solid Earth(Scherneck et al. 1999).

2. 4 . 3

 43 Effects of the solid Earth tides It is well known that the position of a point on the Earth's surface varies over a range of temporal scales due to the elastic response of the crust to the external tide generating potential (sun, moon and planets) (Melchoir 1983). The resulting response is called the solid Earth tide and can account for displacements up to 0.4 m. The most prédominant signais are located in the semi-diumal and diumal bands. As previously shown by Watson et al. (2006), mis-modelling of the solid Earth tides can propagate into coordinates and troposphère parameters of the level of annual amplitudes of ~1.6 mm in the vertical component and -2 mm of diumal signais in ZTD parameters.

Fig. 2 -

 2 Fig. 2-22 : Océan loading, atmospheric loading (ECMWF), Polar tides and solid Earth tides displacements in mm over GRAZ (47.061°N and 15.4934°E, Austria) and KOUR (5.2521°N and 307.1940°E, French Guyana) GPS stations over doy 03 2006.

Fig. 2 -

 2 Fig. 2-23 : (Left) Equivalent water height (mm/10-day) trend over 2002-2006 from the GRACE 10-day GRGS gravity field and (right) hydrological loading displacements from GRACE and GPS in BRAZ (station) situated at the Amazonian basin (the satellite image is from google map)

  to deal with them were examined. Examples with real data from different GPS receivers hâve demonstrated the advantages and disadvantages of current algorithms at the preprocessing level. Receiver clock drifts and cycle slips présent a serious aspect for précision and accuracy in kinematic and static positioning by GNSS. Fligher order ionospheric delay terms not eliminated by classical linear combinations of the carrier phases can introduce important systematic effects especially when sub-mm level accuracy is required during absolute (PPP) or relative positioning of huge global networks. The effect of the troposphère on the GNSS observables dépends on the mapping function used. From previous studies it has been demonstrated that different mapping functions will introduce different levels of discrepancies in the coordinate time-series. The exact position of the antenna's phase center

  2 : Summary of the 4 software strategies applied3.2.1.2 Comparison resultsThe inter-comparison is basée! on the analysis of each estimated coordinate time-series component. The station time-series compared are: Brest (BRST), Cherbourg (CHER), Coutances (COUT), Le Diben (DIBE), Le Mans (MANS), Rennes (RENN), Paimpol (PAIM), Saint Ygeaux (YGEA), and Trévignon (TREV). The geographical location of these stations can be seen in Fig.4-2 of Chapter 4.

Fig. 3 - 2 :

 32 Fig. 3-2 : Extract of 7 days of the 3D position time-series (in mm) for a représentative campaign station (CHER) from the four solutions: red circle for Bemese, black triangle for GAMIT, green diamond for GIPSY, and blue square for GINS

  Fig. 3-3 : 3D RMS scatters (in mm) for each station time-series solution in North, East and Vertical directions

Fig. 3

 3 Fig. 3-4 : Phasor plots of the intra-software solutions in North, East and Vertical, (red) Bemese, (Green) GIPSY, (Blue) GINS, (Black) GAMIT

Fig. 3

 3 Fig. 3-5 : The GNSS attittude models XYZ and XYD

  Fig.3-6. The four aforementioned SRP models are applied in each case and the total RMS misfit to the IGS orbits is extracted. Furthermore an SRP scale factor, a Y-bias and its drift are adjusted. The nominal attitude is at the DYX System.

Fig. 3

 3 Fig. 3-7 : 3D RMS misfits to the IGS sp3 orbits for different SRP models

  -7. The different colour illustrations represent the four different dynamic parameterisations for ail GPS Blocks. • Yellow represents the adjustment for one SRP scale factor and Y-bias plus its drift / arc ; • Purple represents the adjustment for one SRP scale factor plus 2 periodic coefficients (sin and cos) per révolution and an Y-bias plus a drift / arc ; • Red represents the adjustment for one SRP scale factor, an Y-bias and 2 harmonie accélérations in the X and D System per révolution per arc ; • Light-blue represents the adjustment for one SRP scale factor, an Y-bias and 2 harmonie accélérations in the T and N System per révolution per arc.

Fig. 3 Fig

 3 Fig.3

Fig. 3 -

 3 Fig. 3-11 : Internai vs extemal 3D-RMS misfits for GINS GPS orbits with the UCL SRJP model in four different parameterisations. Units are in meters.

Fig. 3 -

 3 Fig. 3-12 : Post-fit residuals of the scale factor with the adjustment of forces in the X and D directions for the B-W SRP model.

Fig. 3 -

 3 Fig. 3-13 : Post-fit residuals of the scale factor with the adjustment of forces in the T and N directions for the B-W S RP model.

Fig. 3 -

 3 Fig. 3-12 represents the post-fit residuals of the scale factor with the adjustment of harmonie accélérations in the X and D directions. Fig. 3-13 illustrâtes the post-fit residuals when periodical forces in the T and N directions are estimated. By comparing the erratically changing variations of the scale factor in Fig. 3-13 with respect to the more cohérent one in Fig. 3-12 we immediately understand that errors in the SRP of the B-W model are better absorbed when forces are included in the solar oriented XYD directions than when defined

Fig. 3 -

 3 Fig. 3-14 : Mean SLR observed range biases (m) for PRN 05/06 wrt IGS (in red) and GINS (in black) microwave orbits in year 2005.

  extends from June 5 to November 25 2006. The orbit validation is based on internai overlaps of fitted SLR orbits of 5-days having a 2-day common segment and on the comparison of the pre-fit and post-fit station residuals. The attitude model used for GIOVE s/c is illustrated in Fig. 3-5 and corresponds to the XYD coordinate frame. For GIOVE-A, I implemented in GINS a new B-W SRP model including respectively 16 surface sections with approximate reflectivity and specularity coefficients. The following GIOVE-A dimensions are used in the B-W model: • Total mass : 614 kg (source ES A); • Main body dimension : 1.3 m * 1.8 m * 1.65 m (Height x Width x Length) (source ESA); • Wing dimension : 0.98 m * 1.74 m * 4 (in total 4 surface sections) (source ESA);

  Fig. 3-16 : The GIOVE-A global SLR network

Fig. 3 -

 3 Fig. 3-17 : Station-specifïc SLR residuals for the periods of June 5 to November 25 2006

Fig. 3 -

 3 Fig. 3-18 : (a) RMS misfit residuals between successive 5-day SLR arcs overlapped over 2 central days. (b) The amount of normal point observations during the period June 5 to November 25 2006. (c) The total Post-fit residuals for the saine period.

Finally

  the SLR-orbits for GIOVE-A were evaluated by internai RMS misfits comparisons together with the performance of a new B-W model specially implemented for this satellite. The radial accuracy of the SLR-only GIOVE-A orbits in a period from June 5 to November 25 2006 varies from 5 to 10 cm. The analysis of the global post-fit residuals and the RMS misfîts has revealed periods of unannounced manoeuvres or un-modelled perturbations for which a spécial stochastic parameterization is needed. The first implémentation steps for the POD of the future Galileo System were accomplished.

4. 2

 2 Océan tide loading (OTL) displacements from global and local grids: comparisons to GPS estimâtes over the shelf of Brittany, France. Advances in space-geodetic positioning techniques in recent years hâve made it possible to acquire direct geodetic measurement of many of the non-tidal phenomena associated with the dynamics of the Earth's crust, including postglacial rebound, tectonic deformation, polar motion and atmospheric mass movements (Lambert et al. 1998). Apart from the non tidal part of the Earth's deformations, geodetic techniques are very efficient in monitoring deformations caused by transport of masses in the océans which in close distance from the coasts can provoke significant loading displacements.

  Canada and northern US (Hudson Bay and Gulf of Alaska) (Schrama 2005, Khan and Scherneck 2003, Lambert et al 1998) as well as Antartica (King and Padman 2005).

  model; T/P, TOPEX/Poseidon altimetry data assimilated; ERS, ERS altimetry data assimilated; T/G, tide gauge data assimilated; T-UGOm, Toulouse Unstructured Grid Océan model (follow-up of MOG2D/3D); LSA, loading and self attraction potential.

  atlas has been analyzed from a one year-long tidal simulation, carried out with the Toulouse Unstructured Grid Océan Model (T-UGOm) in a 2D barotropic, shallow water mode (Pairaud I. personnal communication). T-UGOm (which is the follow-up of MOG2D/3D a modelled estimate of the sea surface response to both the atmospheric pressure and wind forcing) is based on an unstructured mesh that permits to increase the resolution of the shorelines. It ranges from 20 km over the deep océan to less than 1 km along the coastlines. Here we use an interpolated regular grid that cornes to the highest resolution possible from that mesh. The boundary conditions in élévation hâve been extracted from the FES2004 global model, which allows us to nest this high resolution régional grid into the global FES2004 model in order to hâve a better refinement of the tides, especially near the complex coasts of Brittany, as shown in Fig. 4-1 for the M2 tidal wave. The local NEA2004 model covers the area from -20°to 14°in east-longitude and from 30°to 61°i

Fig. 4

 4 Fig. 4-1 : Effect of the resolution: (left) The M2 surface amplitudes from the FES2004 grids with resolution of 0.125°x 0.125°and (right) the M2 surface amplitudes from the NEA2004 grids with the highest resolution of 0.016°x 0.016°.

  highly energetic with water height variations in the Bay of Mont St-Michel in excess of 14 m during the equinoxes, as well as important shallow-water tides (Le[START_REF] Provost | Tidal spectroscopy of the English Channel with a Numerical Model[END_REF]. The four main semi-diumal constituents M2, S2, N2, and K2 provide the most significant contribution to the tide signal and provoke displacements of several cm of the crust along the coasts. The semi-diurnal M2 constituent is the largest single contributor to the tides in this région. It causes the low-tide high-tide cycle, and its modulation with the mean solar semi-diurnal wave S2 produces the spring-tide neap-tide cycle. M2 surface élévation amplitude ranges from 1 m above the abyssal plain to 1.7 m at the Atlantic coasts with a fast increase over the shelf where it reaches 4.3 m in the Mont St-Michel bay (see Fig.4-1).

  positions of the GPS campaign stations in a 24-hour straightforward solution are estimated. At the pre-processing level data editing, cycle slips, clock-drift and millisecond jumps corrections are performed. The synthetic observable of doubledifference (DD) baselines of the ionosphere-free (L3) combination is used. Their formation is based on a common station pass criterion of the GPS satellites. The satellite and receiver docks are eliminated. We use the IERS 2003 conventions for solid

Fig. 4 -

 4 Fig. 4-4 displays the GPS OTL time-series for three représentative selected stations DIBE, MALO and CHER in north, east and vertical directions. The diumal and

Fig. 4

 4 Fig. 4-3 : Amplitudes of the M2 (left) and S2 (right) vertical OTL displacement wave over the Brittany shelf and the campaign GPS stations (prédictions are from the FES2004 tide model)

Fig. 4

 4 Fig. 4-5 : Phasor diagrams of eastward OTL displacements at the three campaign GPS stations. Units are in meters. The GPS estimâtes are represented by a point sign along with their 95% error ellipse according to the error propagation law in the estimated amplitudes and phases. Olfg/olmpp OTL modelling for : FES2004, squares; TPXO.7.0, diamond; TPXO.6.2, downward pointing triangle; GOTOO.2, hexagram; NA099.b, asterisk\ CSR4.0, circle; GéochargeV3.0 OTL modelling for : FES2004, cross; NEA2004, right pointing triangle.

Fig. 4

 4 Fig. 4-6 : Phasor diagrams of northward OTL displacements at the three campaign GPS stations. Units are in meters. The GPS estimâtes are represented by a point sign along with their 95% error ellipse according to the error propagation law in the estimated amplitudes and phases. Olfg/olmpp OTL modelling for : FES2004, squares; TPXO.7.0, diamond; TPXO.6.2, downward pointing triangle; GOTOO.2, hexagram; NA099.b, asterisk; CSR4.0, circle; GéochargeV3.0 OTL modelling for : FES2004, cross; NEA2004, right pointing triangle.

  Fig. 4-7 : Phasor diagrams of up-ward OTL displacements at the three campaign GPS stations. Units are in meters. The GPS estimâtes are represented by a point sign along with their 95% error ellipse according to the error propagation law in the estimated amplitudes and phases. Olfg/olmpp OTL modelling for : FES2004, squares; TPXO.7.0, diamond; TPXO.6.2, downward pointing triangle; GOTOO.2, hexagram; NA099.b, asterisk; CSR4.0, circle\ GéochargeV3.0 OTL modelling for : FES2004, cross; NEA2004, right pointing triangle.

  Fig. 4-8 : Misfits of GPS OTL estimâtes compared to: (SC) Olfg/olmpp OTL modelling for: TPXO.7.0, TPXO.6.2, GOTOO.2, NA099.b, CSR4.0, FES2004; (OF&MA) GéochargeV3.0 OTL modelling for: FES2004, NEA-2004. MALO station is excluded. The misfit bars start respectively from left (black) to right (white).

a

  Set of 4 constituents M2, S2, N2, K[ without St MALO b Olfg/olmpp OTL web service provider cGéochargeV3.0 OTL program Second in misfit agreement with GPS/models are GOTOO.2 and CSR4.0. The models with the highest misfits are TPXO.7.0, TPXO.6.2 and NA099.b. The local NEA2004 grids are performing almost equivalently with the global FES2004 grids.

  Fig. 4-9 : (left) the EUREF-IGS network together with the estimated GPS stations (Black-box) and (right) the global IGS network used in this experiment.

  Fig.4-11 : Power spectra of the TZD time-series from 24-h solutions where OTL is corrected. Units in xaxis are in log (days-of-year) and in y-axis in log (m).

Fig. 4 -

 4 Fig. 4-12 : Vertical GPS time-series (in black) versus the TZD time-series (in red) obtained with océan loading and without océan loading corrections. Units are in (m) in y-axis and days-of-year in x-axis.

Fig. 4 -

 4 Fig. 4-12 shows the time-series of the TZD différences (OTL corrected -no OTL) (in red) estimated for DIBE and the vertical GPS displacement time-series due to OTL (in black). Both time-series are correlated indicating that an important part of the un-modelled OTL displacement is absorbed by the TZD parameters.

Fig. 4 -

 4 Fig. 4-13 : Corrélation diagram of the observed vertical site displacements due to OTL and of the différences of TZD parameters estimated. Units are in (m).

Furthermore, Fig. 4 -

 4 13 demonstrates the corrélation diagram for DIBE in order to quantify the quasi-linear relation between the différences of the TZD and the vertical site displacements. The corrélations for the other sites show the same quasi-linear behaviour. For DIBE a scaling factor (ratio) of the vertical displacements versus TZD of the order of 2.94 ± 0.03 and a corrélation of 75.9 % is obtained. At MALO the ratio is 2.70 ± 0.02 and the corrélation is 65.2 %.

  4.2.6 Aliased OTL signatures GPS satellites hâve a repeat orbital period almost of one sidereal day, 23.93447192 hours (23 hours 56 min 4.1 s), which is insufficient enough to adequately sample semidiumal and diumal tidal constituents. Penna and Stewart (2003) hâve shown that aliasing effects of the océan tides are also présent in the GPS data due to un-modelled residual OTL effects. Stewart et al. (2005) demonstrated that the combination of a moving reference point and un-modelled periodic displacements at the unknown point of interest (due to OTL) results in an output coordinate time-series containing longwavelength periodic terms when zéro and first-order Taylor expansion terms are used in the linearization of the functional model.

  figures the large discrepancies of M2 between predicted OTL constituents verify the same assumption. Previous studies refer to the significance of the extremely localized non-linear semidiumal and higher (such as M4) interactions in the région[START_REF] Provost | Tidal spectroscopy of the English Channel with a Numerical Model[END_REF]. As such, in areas like Mont St-Michel bay, non-linear and shallow water OTL displacement cannot be ignored. A suggestion for the océan tide modeling solutions would be the assimilation of these kinds of observed OTL constituents into the

Furthermore, we hâve

  evaluated and validated the performance of the updated load89[START_REF] Francis | Global charts of océan tide loading effects[END_REF] géochargeV3.0 OTL program, by cross-comparing to the OTL estimâtes of Onsala's web-based olfg/olmpp algorithm with respect to the FES2004 model and to the GPS estimâtes. Ail predicted OTL constituents hâve a good agreement in height with the GPS estimâtes and sub-mm agreement in the horizontal.

I

  own my gratitude to N. Florch and M. Llubes the Pis of the océan tide loading Brittany campaign performed in 2004, as well as the GDR G2 (Geodesy-Geophysics) that financed the campaign. The valuable contribution from P. Collard, J. Kieffer océan surface dynamic topography, seastate, and derived parameters.This part of my Thesis embraces two domains of the Earth Sciences, geodesy and oceanography.It first involves a complex geodetic GPS technique to provide a précisé real-time 3D positioning of a floating tracer (e. g. boat, buoy) with respect to distant fixed reference geodetic points. This technique was used and demonstrated previously but over close distances to fixed reference stations, especially in the altimétrie calibration sites of Senetosa in Corsica[START_REF] Bonnefond | Levelling Sea Surface using GPS-Catamaran[END_REF], Bass Strait, in Australia[START_REF] Watson | TOPEX/Poseidon and Jason-1 Satellite Altimeters : Absolute Calibration in Bass Strait, Australia[END_REF]), the T/P California offshore platform in the US (Haines

>

  To validate with respect to altimétrie data such a kinematic GPS technique for measuring the sea-state and the sea-surface topography over a baseline of few hundreds kilométrés in an especially rough area; > To combine the GPS derived sea-level data with altimétrie and gravimétrie data to détermine in the Drake passage the ACCt geostrophic mean current, its variability and associated absolute transport, and to validate these results with respect to climatology, model outputs and in-situ data when available; > To give recommendations for improving the demonstrated GPS technique in order to use it more systematically in many other régions during further dedicated or opportunity campaigns.

  Fig. 5-2 : The "Polarstem's" trajectory on Jason's-l 104 ground path (in red pointed line) and the bathymetry variations along the DRAKE Passage in (m)

  Fig. 5-3 : Satellite visibility for a reference station (in red) and a GPS buoy (in blue) at the bottom and middle panels respectively. The number of common passages of the baseline formed is shown in the upper panel.

Fig. 5

 5 Fig. 5-4 : The Puntas Arenas calibration campaign

Fig. 5

 5 Fig. 5-5 : Schematic view of the two configurations for the wave-rider GPS buoy, with the ARP above the mean SSH. (The graph was modified from the one of Watson 2005. The photograph was taken by Y.Ménard)

9. 2

 2 cm above the mean SSH for the case where one life préserver is used. In the open océan, where two life preservers were used, the position of the ARP above the SSH was 20.5 cm. This simple design of wave-rider buoys is inspired from the altimetry calibration campaigns at the Harvest platform(Key et al. 1998) and at the Corsica site undertaken in 1996/97[START_REF] Exertier | Calibration of Radar Altimeters in the Corsica Area: Recent Improvements in View of Jason-1 Mission[END_REF].The two géométrie représentations of the wave-rider GPS boy used during the two calibration periods of the FL inside the port and at the sessions in the open sea are illustrated in Fig.5-5. In the first configuration the GPS antenna platform is placed on a unique life préserver. This configuration was used during the calibration periods in the Port of Puntas Arenas. In the second configuration the antenna platform is placed on a double life préserver used in the open océan and at the O'Higgins sessions.5.3.2 Working at the cm-level during the calibration periodsA common strategy is used to estimate the position of a moving target during the calibration periods. Here a moving target refers to either the GPS buoy or the ship's antennas. The key steps of the positioning strategy are listed below: 1. Two stable reference stations are used (RIOG and PARC) to form independent baselines with the moving targets and also in between them. So three baselines are formed to estimate the dynamic position of the moving station as indicated below: baselines (a and b) with the moving station provide redundant solutions for the moving target. The third baseline (were ambiguities are fixed) between the two reference stations provides not only redundant, but more accurate solutions for parameters like TZD. When the individual solutions are cumulated, these more accurate estimations from the baseline between the reference stations positively influence the solutions for the other baselines. This configuration increases the accuracy and robustness of the solution. Fig. 5-6 gives the conceptual idea of the baselines involved. Fig. 5-7 shows the map of GPS stations involved during the lst and 2nd Calibration Periods.

Fig. 5

 5 Fig. 5-6 : The basic principle of position détermination during the DRAKE campaign

  Fig. 5-9 respectively. The mean uncertainties on the positions of the moving targets are illustrated in

Fig. 5

 5 Fig. 5-8 : SSH time-series of the lst calibration period at 3s time-steps for PAB1. Y-axis units are in meters and x-axis units are in minutes of day

Fig. 5 -

 5 Fig. 5-10 : The FL of the lst Calibration at Asmar Terminal. The RMS error is 14.6 mm. Y-axis units are in meters and x-axis units are in minutes of day

Fig. 5 -

 5 Fig. 5-11 : SSH time-series of the 2nd calibration period at 3s time-steps for PAB2. Y-axis units are in meters and x-axis units are in minutes of day

  Fig. 5-13 : Horizontal motion of the buoy during the lst Calibration period (left) versus the 2nd Calibration period (right). Units are in métrés

  Fig. 5-14 : The FL of the 2nd Calibration period at Gas Terminal. The RMS error is 42.2 mm. Y-axis units are in meters and x-axis units are in minutes of day

Fig. 5 -

 5 Fig. 5-16 : (Left) The long-lat time-series from POLB (antenna connected to the Ashtech receiver) and (right) the long-lat time-series from the POLT (antenna connected to the Trimble receiver).

(

  many thanks to C. Watson from the University of Tasmania and to J.-M. Lemoine from the CNES for providing me with the data). During this empirical validation process I compared two GPS-buoys SSH time-series with a collocated Tide Gauge (TG) for about 7 hours. This comparison is illustrated in Fig. 5-17. The two GPS SSH time-series (in blue and green) compared to the TG SSH time-series (in red) show a signiflcant corrélation. Their maximal and minimal différences are around 70 mm and 20 mm respectively. Consequently, the current GPS kinematic epoch-by-epoch approach reaches the relative accuracy of 20-70 mm compared to the TG SSH time-series. As such the same accuracy applies to the SSH time-series of the two sessions during the calibration of the vessel's FL.

Fig. 5 -

 5 Fig. 5-17 : The two GPS-buoy SSH (3 s) time-series ( in blue and in green) against the collocated TG SSH (1 min) time-series (in red) at Spring Bay, Tasmania.

  Error budget of the GPS SSH observations in Puntas Arenas. Expected uncertainties are referring to ail sessions including the whole cruise in the open océan and the Antarctic buoy sessions.

  6.1.1 Software Development and Validation (Part 1) More spécifie in matters of development and improvements of the software's capacities I concentrated in: • the development of a unified geodetic coordinate System more suitable for geophysical studies to an already implemented geocentric System ; • the possibility to create time dépendent partials of the station's positions for high-frequency positioning ; • the possibility to process high-frequency GPS kinematic data of 1 Hz ; • the development of new processing schemes that would allow me to proceed in my geodetic studies; • the implémentation of a new B-W SRP model for the GPS satellites as well as for the GIOVE-A, the first satellite of the Galileo constellation, • paving the way of intégration of the Galileo radio observables in the software. Ail modifications were then evaluated against a sériés of validation tests: • The comparisons of the estimated GPS stations' high-frequency coordinate time-series with respect to the ones originating from other well-established GNSS software in the geodetic community such as : GAMIT 10.21, GIPSY/OASIS II, Bemese 5.0 ; • The 3D-RMS misfit overlaps of GINS' POD of the GPS satellites to the précisé IGS sp3 orbits ; • The évaluation of the SLR POD précision of the first Galileo satellite, GIOVE-A;

  study for the ACCt variability and absolute transport using the GPSship -buoy and gravity data set from the 2006 DRAKE campaign was initialised.During this preliminary phase an epoch-by-epoch mode procedure was developed designated to calibrate the vessel's FL and détermine the MSSH from a GPS-buoy combination under calm conditions. The minimum and maximum précision reached in the estimation of the FL were 45 mm and 15 mm respectively. The relative accuracy of the current implémentation is between 20 mm to 70 mm compared to an independent TG and GPS-buoy collocated SSH data set from Spring Bay in Tasmania. The lst and 2nd calibration periods with the current modifications hâve shown that "reasonable" GPS MSSH détermination can be achieved depending on the dynamic States of the buoy and the ship.As a general conclusion, during these 3 years I managed to modify and validate new software designated to be used in studies of local and régional GNSS networks.The scientific objectives conceming the studies of a déformable network due to océan tide loading hâve been reached. I proved that GPS can be used as a validation technique for océan tide models in complex areas like Brittany at the N-W part of France very efficiently and not only. These GPS derived OTL estimâtes could be used for the further improvement of océan tide models accuracy in the région. This study enters into the nonlinear, temporal, geophysical and stochastic approaches for the establishment of Global Reference Frames through the direct observation of the displacements which relate the regularized positions of reference points to their instantaneous positions as referred in Chapter four and seven of the IERS 2003 conventions(McCarthy and Petit 2004). Additional software modifications hâve allowed me to develop for the First time at GRGS, a GPS kinematic processing scheme designated to embrace two domains of the Earth' sciences, geodesy and oceanography. The final objective is the observation of the Antarctic Circumpolar Current through a purely geodetic combination technique of GNSS maritime networks, spatial gravimetry and altimetry.

  in fonction with the expériences eamed during the last three years of my PhD are concentrated around: 1) The forther development of the GNSS kinematic technique dedicated to observe the ACCt; 2) Collocated TG networks with GNSS stations for the détermination of Vertical Land Motion Rates (VLMR) and the calibration of the altimeters' Global Sea Level Rise (GSLR). The first complétés what has been initiated in the last chapter of fois Thesis. It consists of: • Extending the kinematic GPS processing to the whole DRAKE data set; • Updating the GINS Global Navigation Satellite Systems (GNSS) software for addressing the ambiguity resolution issue in high State dynamics environment; • Determining GPS sea level profiles ail along the "Polarstem" trajectory and so along the Jason-1 104 ground track. Parameters, including instantaneous Sea Surface Height (SSH), significant wave height (SWH) and the mean sea level (MSL) will be extracted; • Comparing collocated SSH, MSL and SWH altimétrie profiles from Jason-1, ENVISAT (and GFO) with coincident GPS derived SSH, MSL and SWH profiles and analyzing the différences in terms of errors. Additional comparisons with in-situ SWH observations noted during the campaign and with sea-state models will be performed as well as with the future altimetry mission of Jason-2; • And finally, estimating the ACCt sea-level signature and derived parameters and their variability based on altimetry, GPS and on the derived geoid profiles from : a) GPS MSL estimâtes; b) altimétrie and gravimétrie measurements collected during the campaign; c) from Grâce geoid models EIGEN-GL05S (200 km resolution), the more refined model EIGEN-GL05C (55km resolution) gravity model and the future GOCE.

Table 1 -

 1 1 : The Galileo's signal caracteristics, modulations, channels, ranging codes and

	data encryption

Table 1 -

 1

6 : The tomorrow's and today's GNSS characteristics Table 2-1 : The GPS three frequency combinations. The M-Iono is the ionosphère amplification factor relative to Li and sigma-Lcomb is the final noise of the synthetic phase Table 2-2 : The GLONASS three frequency combinations. The M-Iono is the ionosphère amplification factor relative to L| and sigma-LCOmb is the final noise of the synthetic phase

Table 2 -

 2

3 : The Compass four frequency combinations. The M-Iono is the ionosphère amplification factor relative to L| and sigma-Lcomb is the final noise of the synthetic phase Table 2-4 : The Galileo five frequency combinations. The M-Iono is the ionosphère amplification factor relative to L| and sigma-LCOmb is the final noise of the synthetic phase

Table 2-5 : Observational model budget and the effects on GNSS parameters

Table 3 -

 3

1 : Ad-hoc dynamic and environment models for GNSS positioning with GINS.. Table 3-2 : Summary of the 4 software strategies applied

Table 3

 3

	-3 : 3D Corrélation coefficients between two solutions for different GPS
	stations. The 3D mean corrélation coefficients over ail stations are indicated
	in the last column

Table 3

 3

	-4 : GPS 35 10-day SLR arc overlap wrt. IGS sp3 final orbits
	Table 3-5 : GPS 36 10-day SLR arc overlap wrt. IGS sp3 final orbits

Table 3 -

 3

6 : Helmert transformation wrt. the IGS microwave orbits for GPS 35 JJULD 20610-20620 in mm 151 Table 3-7 : Helmert transformation wrt. the IGS microwave orbits for GPS 36 JJULD 20610-20620 in mm

Table 3 -

 3 8 : The GIOVE-A orbit estimation strategyTable 4-1 : Summary of selected Océan Tide Models Table 4-2 : The GPS data set of the 8 campaign stations Table 4-3 : The main harmonie constituents of the tides in the English Channel (Le Provost and Fornerino 1985) Table 4-4 : GPS OTL displacement estimâtes. One sigma uncertainties are inside parenthesis Table 4-5 : GPS frequency displacement estimâtes in integer multiples of the Kl wave....

Table 4 -

 4

6 : Table Chi-square per degree-of-freedom for GPS estimâtes of OTL displacements to modelled constituents

Table 4 -

 4 7 : Periods, Amplitudes and Admittances of the Long Wavelength Signais

arising from unmodelled M2 and N2 3D OTL

Table 4 -

 4

8 : Amplitudes of the long-wavelength signais arising from the FES2004 and TPXO.7.0 OTL displacement modelling errors

Table 5 -

 5

	calibration campaigns

1 : The GPS stations-buoys and code names used during the lst and 2nd

Table 5 -

 5 4 : Error budget of the GPS SSH observations in the Puntas Arenas. Expected uncertainties are referring to ail sessions including the whole cruise in the open océan and the Antarctic buoy sessions 225 Résumé L'équipe géodésique du GRGS, du Centre National d'Etudes Spatiales, a saisi l'importance des systèmes GNSS sur la détermination du système international de référence terrestre et la détermination des paramètres des mouvements du Pôle via le projet pilote des Centres de Recherche et des Combinaisons (CRC) de FIERS. L'observation des déformations surfaciques de la croûte Terrestre mesurée par des stations permanentes GNSS est un sujet que le CNES/GRGS voulait investiguer. L'impact de tels types de déformations sur les applications scientifiques de la géodésie de très haute précision ne peut plus être négligé comme c'est déjà mentionné dans les conventions de FIERS pour 2003. En parallèle les besoins en océanographie et en altimétrie pour des mesures indépendantes de variations du niveau des océans, ainsi que leurs validations et

comparaisons croisées à partir des traceurs flottants sur des bouées et des bateaux ou des marégraphes co-localisées avec des stations permanents GPS, ont imposé l'utilisation des récepteurs du système GNSS.

  In 1978 the Department of Defense (DoD) of the United States of America has launched GPS the first Global radio-positioning System in order to replace the old and limited in coverage Transit System. Its principle is based on calculating the distances between MEO satellites, and a receiver on the Earth's surface by comparing the departure and arrivai time of a radio signal. Nowadays GPS is vastly used for the détermination of 3dimentional coordinates of geodetic stations. Together with GPS the Russian Global Navigation Satellite System (GLONASS) is also operating. The later is based on the same principle as GPS. On the other hand, the European Community is developing its own global

• the GPS 35 and GPS 36 satellites of the Global Positioning System (GPS); • the first Galileo In Orbit Validation Elément (GIOVE-A). positioning System, Galileo, which will be fully operational by 2012. Recently the Chinese govemment has decided to enter the game of "public" global positioning by building its own navigation satellite System Compass/Beidou. Together ail four Systems form of what we call as the Global Navigation Satellite System, commonly GNSS.

  its mission statement currently reads as follows: "The International GPS Service is committed to providing the highest quality data and products as the standard for global navigation Systems (GNSS) in support of earth sciences research, multi-disciplinary applications, and éducation. These activities aim to advance scientific understanding of the Earth System components and their

interactions, as well as to facilitate other operational applications benefiting society."

2.2.2

GRGS as an analysis center of the IGS Since the 10th of July 2007 GRGS has entered an évaluation test period in order to become a future IGS AC. GRGS has been producing its own GNSS and reference frame products since 2005: orbits and clocks for GPS satellites, stations positions and velocities. The GNSS products are based on a global sub-network of ~70 GPS IGS stations. For a homogeneous

Table 2 -

 2 1 : The GPS three frequency combinations. The M-Iono is the ionosphère amplification factor relative to Li and sigrna-Lcomb is the final noise of the synthetic

	phase

Table 2 -

 2

	ni	n2	n3	^-comb (m)	M-Iono (cycles)	M-Iono	sigma-Lcomb (m)
	1	0	0	0,1863	1	1	0,0019
	0	1	0	0,2402	1,2893	1,6623	0,0024
	0	0	1	0,2502	1,343	1,8036	0,0025
					Wide Lanes
	1	-1	0	0,8302	-0,2893	-1,2893	0,0117
	0	1	-1	6,0098	-0,0537	-1,7315	0,0850
	1	0	-1	0,7295	-0,343	-1,3430	0,0103
				Narrow Lanes
	1	1	0	0,1049	2,2893	1,2893	0,0015
	0	1	1	0,1225	2,6323	1,7315	0,0017
	1	0	1	0,1068	2,3430	1,3430	0,0015

2 : The GLONASS three frequency combinations. The M-Iono is the ionosphère amplification factor relative to L] and sigma-Lcomb is the final noise of the synthetic phase

Table 2 -

 2

	ni	n2	n3	n4	^-comb (m)	M-Iono (cycles)	M-Iono	sigma-Lcomb (m)
	1		0	0	0,1886	1	1	0,0019
	0	1	0	0	0,1920	1,0183	1,0370	0,0019
	0		1	0	0,2363	1,2532	1,5706	0,0024
	0		0	1	0,2483	1,3169	1,7344	0,0025
					Wide Lanes
	1	-1	0	0	10,4676	-0,0183	-1,0183	0,1480
	0		-1	0	1,0247	-0,2349	-1,2762	0,0145
	1		-1	0	0,9333	-0,2532	-1,2532	0,0132
	1		0	-1	0,7836	-0,3169	-1,3169	0,0111
	0		0	-1	0,8470	-0,2986	-1,3411	0,0120
	0		0	0	0,1920	1,0183	1,0370	0,0019
	0		1	-1	4,8842	-0,0637	-1,6504	0,0691
					Narrow Lanes
	1		0	0	0,0951	2,0183	1,0183	0,0013
	0		1	0	0,1059	2,2716	1,2762	0,0015
	1		1	0	0,1049	2,2532	1,2532	0,0015
	1		0	1	0,1072	2,3169	1,3169	0,0015
	0		0	1	0,1083	2,3353	1,3411	0,0015
	0		0	0	0,1920	1,0183	1,0370	0,0019
	0		1	1	0,1211	2,5702	1,6504	0,0017

3 : The Compass four frequency combinations. The M-Iono is the ionosphère amplification factor relative to L] and sigma-Lcomb is the final noise of the synthetic phase

Table 2 -

 2 4 : The Galileo five frequency combinations. The M-lono is the ionosphère amplification factor relative to Li and sigma-Lcomb is the final noise of the synthetic phase

	ni	n2	n3	n4	n5	^comb (m)	M-Iono (cycles)	M-Iono	sigma-Lcomb (m)
		0	0	0	0	0,1903	1	1	0,0019
	0	1	0	0	0	0,2344	1,232	1,5178	0,0023
	0	0	1	0	0	0,2483	1,3051	1,7032	0,0025
		0	0	1	0	0,2515	1,3217	1,7468	0,0025
		0	0	0	1	0,2548	1,3391	1,7933	0,0025
						Wide Lanes
		-1	0	0	0	1,0105	-0,2320	-1,2320	0,0143
		1	-1	0	0	4,1865	-0,0731	-1,6079	0,0592
		0	-1	0	0	0,8140	-0,3051	-1,3051	0,0115
		0	0	-1	0	0,7819	-0,3217	-1,3217	0,0111
		0	0	0	-1	0,7514	-0,3391	-1,3391	0,0106
		1	0	-1	0	3,4558	-0,0897	-1,6283	0,0489
		1	0	0	-1	2,9305	-0,1071	-1,6498	0,0414
		0	1	-1	0	19,8014	-0,0166	-1,7249	0,2800
		0	1	0	-1	9,7684	-0,0340	-1,7477	0,1381
		0	0	1	-1	19,2793	-0,0175	-1,7699	0,2726
						Narrow Lanes
		1	0	0	0	0,1050	2,2320	1,2320	0,0015
		1	1	0	0	0,1206	2,5371	1,6079	0,0017
		0	1	0	0	0,1077	2,3051	1,3051	0,0015
		0	0	1	0	0,1083	2,3217	1,3217	0,0015
		0	0	0	1	0,1089	2,3391	1,3391	0,0015
		1	0	1	0	0,1213	2,5537	1,6283	0,0017
		1	0	0	1	0,1221	2,5711	1,6498	0,0017
		0	1	1	0	0,1250	2,6267	1,7249	0,0018
		0	1	0	1	0,1258	2,6442	1,7477	0,0018
		0	0	1	1	0,1266	2,6608	1,7699	0,0018
						Low Ionosphère
		-3	1	-4	2	0,1058	0,0007	0,0004	0,0078
		0	1	-3	-1	0,1088	0,0010	0,0006	0,0057
		0	0	-1	-2	0,1087	0,0001	0,0000	0,0050
		3	0	0	-5	0,1119	0,0003	0,0002	0,0073
						Big Wavelength
		-3	1	-3	4	3,9389	0,0006	0,0129	0,2363
		2	-5	-2	5	14,9522	-0,0091	-0,7145	1,1387
		1	-1	-4	4	31,8589	-0,0032	-0,5370	1,8577
		1	-2	-1	2	11,8168	-0,0216	-1,3394	0,3737

Table 2 -

 2

5 : Observational model budget and the effects on GNSS parameters software: updates and validations The GRGS Space Geodesy department of the CNES in France has been created in 1971.

Since that epoch the GRGS is developing the scientific software for space geodesy namely GINS.

Table 3

 3

	-1:

series estimation DYNAMO is used for inverting and stacking the normal équations provided by GINS. It is possible to eliminate and reduce un-necessary parameters, specify continuity and minimal constraints to the individual geodetic parameters for the datum définition (see § 2.1.2).

Table 3

 3

	-2:

Table 3

 3

	-3. The mean values are

Table 3 -

 3

3 : 3D Corrélation coefficients between two solutions for different GPS stations. The 3D mean corrélation coefficients over ail stations are indicated in the last column.

  .... . ..T..........T.....T...V.:...r...r7..........rr..

		rrr^rr"Ti"	:7':lfll:r1 : ;""1	» 11: : J _	:
		v i vr r v r i*f*r*v	•	r	1-1	• -; ïri r-r-l • ••• ri
		».	.	4.;.;.			* . . -. i	\	-
		.		4--	4.44 ; i ; 444 i;;-4 il 144 II-44 44.1 4444 1 4 444-
	5:	H i t i H H H* •frlfi -f : :*!*•*	J-î-44-* J-4444 J-.-444 J i-tl idiiFirildilfifljfiFîIflFflflif J 1 l ' 1 1 ' \ \
		*1				? î-t-î v? : t ? t > :-i-?	? |	! ' -i ~r v	|
							3 -? 4-•Y44-I-44YYI 7 ?4 ; 1	• •

••'• I :*4*?*î-. i..:. :. i.».;..;. i.i .1. i.i..1 i.i.l. i_ .

Table 3

 3

	-4 : GPS 35 10-day SLR arc	overlap wrt.
	IGS sp3 final orbits.
	GPS-36 RMS Misfits (cm)
	Earth Along (Tangential)	9.55
	Earth Normal	25.75
	Earth Radial	2.03

Table 3

 3

	-5 : GPS 36 10-day SLR arc overlap wrt. IGS
	sp3 final orbits.

  Table 3-6 and 3-7 summarize the statistics from this comparison.

	Tx (mm)	-7.8 +/-9.
	Ty (mm)	-.4 +/-.9
	Tz (mm)	59.8 +/-9.
	S (ppb)	.620124 x 10'9+/-.375 x 10J'
	S (mm)	16.5 +/-10
	Rx (arcmin)	-.33 x 10'3+/-.1 x 10'3
	Ry (arcmin)

Table 3

 3

	-6 : Helmert transformation wrt. the IGS
	microwave orbits for GPS 35 JJULD 20610-20620
		in mm.
	Tx (mm)	2.2 +/-5.3
	Ty (mm)	. 8 +/-5.3
	Tz (mm)	45.3 +/-5.3

Table 3

 3

	-7 : Helmert transformation wrt. the IGS
	microwave orbits for GPS 36 JJULD 20610-20620
	in mm.

Table 3 -

 3

8 : The GIOVE-A orbit estimation strategy

Table 4

 4

	-1 : Summary of selected Océan Tide Models

  . As a conséquence, I was able to analyze a set of four major OTL displacement constituents for the région, M2, S2, N2 and K|.

	Constituent	Angular velocity (deg h'1)	Period (days)	Period	(h)
		Diumal
	0!	13.942	1.078	25.819
	Pl	14.958	1.003	24.066
	Kj	15.041	0.997	23.935
	Qi	13.405	1.119	26.868
		Semidiurnal
	n2	28.439	0.5271	12.659
	k2	30.082	0.4986	11.967
	s2	30.000	0.4999	12.000
	m2	28.984	0.5175	12.421
	Table 4-3 : The main harmonie constituents of the tides in the English Channel (Le Provost and Fomerino
		1985)

  -3.

			M2		S2		N2		Kl
	GPS-site	f	Ab, mm	0e, deg	Ab, mm	0e, deg	Ab, mm	0e, deg	Ab, mm	0e, deg
			12	97.5	2.0	118.4	1.6	85.4	0.9	139.1
		P
			(0.2)	(2.2)	(0.7)	(9.1)	(0.3)	(8.8)	(0.2)	(12.5)
			6.2	27.3	2.3	52.4	1.3	25.0	0.2	22.9
	YGEA	N
			(0.2)	(2.2)	(0.2)	(6.0)	(0.2)	(10.4)	(0.2)	(56.4)
			23.2	304.6	6.1	16.2	4.6	296.0	9.45	322.55
		U
			(0.7)	(1.6)	(0.6)	(7.2)	(0.8)	(9.4)	(0.7)	(4.2)
			8.6	98.7	2.7	124.2	1.7	74.6	0.5	188.1
			(0.3)	(2.0)	(0.2)	(5.2)	(0.2)	(8.6)	(0.2)	(22.5)
			7.1	11.9	2.8	49.4	1.2	10.0	0.7	359.2
	DIBE	N
			(0.2)	(1.8)	(0.2)	(4.7)	(0.2)	(11.0)	(0.2)	(14.4)
			32.8	311.9	10.3	23.5	7.5	296.7	7.9	288.9
		U
			(0.8)	(1.4)	(0.7	(3.8)	(0.8)	(5.5)	(0.6)	(4.5)
			8.0	94.7	2.7	120.8	1.7	74.7	0.4	196.2
			(0.3)	(1.6)	(0.2)	(5.1)	(0-2)	(7.0)	(0.2)	(24.7)
			6.9	18.4	2.6	44.8	1.4	19.2	0.1	39.8
	PAIM	N
			(0.2)	(2.0)	(0.2)	(3.7)	(0.2)	(9.3)	(0.1)	(73.7)
			29.3	320.2	8.7	27.0	5.7	308.1	6.69	307.1
		U
			(0.6)	(1.2)	(0.6)	(3.8)	(0.6)	(6.7)	(0.62)	(4.6)
			8.0	109.4	2.0	138.4	1.5	92.1	0.7	155.5
			(0.2)	(1.8)	(0.2)	(6.1)	(0.2)	(8.9)	(0.2)	(15.1)
			6.7	21.5	2.4	44.2	1.4	30.1	0.4	124.3
	LAMB	N
			(0.2)	(1.9)	(0.2)	(4.7)	(0.2)	(7.9)	(0.2)	(23.9)
			22.0	314.3	5.9	29.9	5.0	305.3	7.5	333.9
		U
			(0.7)	(1.7)	(0.6)	(6.7)	(0.7)	(8.3)	(0.6)	(4.5)
			7.8	151.5	2.7	173.9	1.6	145.7	0.3	31.2
			(0.2)	(1.7)	(0.2)	(4.8)	(0.2)	(9.2)	(0.2)	(28.9)
			7.1	55.8	2.8	68.5	1.4	65.1	0.4	146.5
	MALO	N
			(0.2)	(2.0)	(0.2)	(4.8)	(0.2)	(9.5)	(0.2)	(27.7)
			23.3	357.6	5.8	79.0	5.8	355.7	2.8	187.1
		U
			(0.9)	(2.0)	(0.8)	(7.2)	(0.8)	(8.6)	(0.8)	(15.4)
			8.0	127.8	2.1	157.5	1.5	112.1	1.0	170.6
			(0.2)	(1.4)	(0.2)	(5.3)	(0.2)	(7.9)	(0.2)	(11.7)
			4.3	47.7	1.8	61.7	1.0	54.4	0.4	320.9
	DUCE	N
			(0.2)	(2.6)	(0.2)	(5.9)	(0.2)	(12.1)	(0.2)	(22.5)
			14.7	315.9	5.7	45.6	3.1	305.7	4.9	309.1
		U
			(0.6)	(2.2)	(0.6)	(5.7)	(0.6)	(H.4)	(0.5)	(6.8)
			10.4	133.3	2.8	173.8	1.9	119.0	0.4	201.1
			(0.2)	(1.21)	(0.2)	(4.6)	(0.2)	(6.2)	(0.2)	(24.6)
			3.7	92.3	0.8	165.9	1.0	79.5	0.4	332.7
	CHER	N
			(0.2)	(3.0)	(0.2)	(13.2)	(0.2)	(11.0)	(0.2)	(21.2)
			15.4	342.7	6.9	60.1	3.2	323.5	6.4	328.7
		U
			(0.7)	(2.17)	(0.6)	(4.9)	(0.7)	(11.2)	(0.5)	(4.8)
			7.6	133.1	2.2	175.0	1.3	115.1	0.6	206.5
			(0.2)	(1.8)	(0-2)	(5.2)	(0-2)	(9.2)	(0.2)	(18.6)
			5.1	90.4	1.1	120.7	1.3	86.8	0.4	350.8
	BAYE	N
			(0.2)	(2.1)	(0.2)	(9.3)	(0.2)	(8.6)	(0.2)	(24.1)
			7.0	340.6	4.7	76.9	1.8	346.1	6.1	325.1
		U
			(0.5)	(4.1)	(0.6)	(7.2)	(0.6)	(17.9)	(0.5)	(4.9)

Table 4 -

 4 4 : GPS OTL displacement estimâtes. One sigma uncertainties are inside parenthesis Horizontal amplitudes are not negligible for M2, S2, N2 and K|. The highest one reaches 10.4 mm at CHER (Cherbourg) for the M2 wave in the eastward direction. As for the other two major constituents, S2 and N2, their maximum horizontal amplitudes are 2.8 mm and 1.9 mm, respectively, situated at CHER in eastward direction. Kl gets it highest horizontal displacement of 1 mm at DUCE (Ducey) in the eastward direction.

  Table 4-5 for ail stations (only shown for the first two frequencies) are calulated. Additionally, Table 4-5 demonstrates that the amplitudes of these signais are important enough to introduce biases in the signatures of shallow water OTL

	constituents such as the combinations of SK3, MK3, 2MK5, 2SK5 or constituées very
	close to them, such as M3 and M4.
		K3	K4
	GPS-site f	Ah, mm	Ab, mm

Table 4

 4

	-5 : GPS frequency displacement estimâtes in integer
	multiples of the Kl wave
	a U, Upwards; b A, Amplitude

Table 4 -

 4 6 : Table Chi-square per degree-of-freedom for GPS estimâtes of OTL displacements to modelled constituents

Table 4 -

 4 7 shows the level of admittances with which the un-modelled M2 and N2 displacements propagate into the GPS height time-series. The predicted OTL displacements are not applied to ail three directions in order to provide a more realistic assessment of the spurious effects in the real data. It is obvious that the un-modelled

	periodicities are significant and cannot be ignored. For example in D1BE the input
	height amplitude for M2 is 35.5 mm and the spurious effect of un-modelled 3D OTL
	displacements of around 6.7 mm propagates with an admittance of 18.8 %. At CF1ER,
	the unmodeled 3D OTL effect propagates at 13.66 days with a 7.6 mm height signal and
	an admittance of 38.8 %. The N2 un-modelled 3D effect can be substantial as well. At
	YGEA the unmodeled amplitudes resuit in a spurious signal of 2.6 mm in height at
	-9.13 days period with an admittance of 47 %. At CHER the spurious signal of
	unmodeled OTL results in an amplitude of 3.4 mm propagated with an admittance of
	89.5 %. It is obvious that the admittance, with which the unmodeled OTL constituents
	propagate into the GPS height time-series of the campaign sites, grows for stations with
	smaller input vertical amplitude. This demonstrates that there is a signifïcant
	propagation of spurious signais also from the horizontal unmodeled OTL constituents
	which usually hâve amplitudes considerably less (often by a factor of 3) than the height
	amplitudes.
	While the 13.66 and 9.13 days signatures are apparent for ail stations Table 4-8
	demonstrates the effect if FES2004 or TPXO.7.0 (from olfg/olmpp) OTL model
	prédictions are applied.
		-13.6 Day Period (M2)	-9.13 Day Period (N2)
		FES2004	TPXO.7.0	FES2004	TPXO.7.0
	Site	(mm)	(mm)	(mm)	(mm)
	DIBE	0.5 ±0.3	4.55 ±3.0	0.5 ±0.8	4.2 ±2.9
	YGEA	0.9 ±0.4	4.2 ±3.1	0.3 ±0.8	4.0 ±3.0
	PAIM	0.2 ±0.4	5.7 ±3.0	0.6 ±0.5	4.4 ±3.0
	LAMB	1.4 ±0.4	3.4 ± 3.1	0.5 ±0.4	5.5 ±3.0
	MALO	1.3 ±0.4	1.3 ±0.4	0.6 ±0.3	5.8 ±3.0
	DUCE	1.4 ±0.4	3.6 ±3.2	0.5 ±0.4	5.5 ±3.1
	CHER	1.4 ±0.4	4.4 ± 3.1	0.2 ±0.4	5.2 ±3.0

Table 4 -

 4

8 : Amplitudes of the long-wavelength signais arising from the FES2004 and TPXO.7.0 OTL displacement modelling errors.

Table 4

 4

	-7 when the

So by comparing the amplitudes at the predicted periodicities arising when the OTL prédictions are applied thus provide an alternative mean to test the validation of océan tide models. A limitation of this method for testing OTL displacement estimâtes is that the method cannot discem between M2 and Oi model quality if substantial amplitudes are présent for Oi for example. Fortunately this is not the case for this région.

Table 5 -

 5 1 : The GPS stations-buoys and code names used during the lst and 2nd calibration campaigns. . Attitude variations observed in the ship's positions may generate a significant noise in the final position estimâtes (see § 5.3.3).

During the second calibration period I also evaluated the position time-series for 2 antennas on-board the Polarstem in order to analyze the corrélation in motion between them

Table 5

 5

		-2. Ail time-series are relative to ITRF2000 and
	expressed in the GRS80 ellipsoid (semi-major axis 6378137 m and inverse flattening of
	278.25722210).
		RMS error (mm)
	Moving
		North	East	Up
	targets
	PAB1	9.4	9.3	10.6
	POLA	9.6	7.7	10.1
	Table 5-2 : RMS errors for PAB1 and POLA at 3s time-steps

  Table 5-1), which is significantly smaller compared to the first calibration period. The main reason for this is that the GPS buoy during this period suffers from frequent loss-of-lock events, and long durations of adéquate satellite visibility were difficult to obtain. Coupled with this, the Ashtech receiver has important data-gaps in the R1NEX raw files attributed to the more rough conditions during this period.

		RMS error (mm)
	Moving
		North	East	Up
	targets
	PAB2	24.0	85.2	41.3
	POLB	5.4	11.7	8.5
	Table 5-3 : RMS errors for PAB2 and POLB at 3s time-steps
	10.5
	10.4
	10.3

  -16.

			Lamda vs Phi
	£ 0.7	*
	û.
	0.4	'	'	1	*
	-6.7	-66	-66	-6.4	-6.3	-6.2
			Larctoda (meters)

Table 5

 5

-4.

in implémentation stage and

at shutdown stage. 1.1.4.2 The modernization Plan On December 25 2006 from Baikonour launch site, three modemized satellites, GLONASS-

Acknowledgments

Usually some words are not enough for ail the people to be thanked for contributing both professionally and personally during this Thesis.

(Montpellier University), and J. Cali (ESGT/L2G) for the installation of the GPS sites must be mentioned. This research project was greatly supported by my PhD fellowship award of the French Minister of Superior Education, and Research (MESR).

B-W-Box-and-Wing

During the past 3 years of this PhD study and in order to be able to accomplish my research on the régional and local terrestrial and maritime GNSS networks, the following improvements in the software code hâve been added:

•

Introduction of a unified local geodetic System in the position time-series ;

• Ambiguity resolution by applying the QIF method (see § 2.3.2.6) the same as applied in the Bernese software [START_REF] Hugentobler | Bemese GPS software Version 4.2[END_REF]) ;

• Possibility to hâve position time-series in higher frequencies (hours, minutes, seconds) than of a 1-day or 1-week solutions ;

• Implémentation of new processing strategies for local geodetic networks ;

• Modifications of scripts and table dimensions inside the GINS' code ;

• Implémentation of new SRP models for POD of the GNSS satellites including GIOVE-A, the first satellite of the future Galileo European global positioning System.

Processing GNSS data inside GINS

The up-to-date GNSS data processing with GINS software is implemented in the following steps:

• The formation of a coordinate file containing GNSS stations from a local, régional or dedicated campaign network ;

• The concentration of ail necessary data files (RINEX, SINEX, satellite ephemerides, clocks) in a pre-defined directory ;

• The data-editing : clock jump corrections, cycle slips corrections ;

• The formation of synthetic observables: un-differenced or double-differenced data of the iono-free combinations ;

• The processing scheme implémentation by the GINS ' Directory-File (GDF) ;

• The output screening of the processing in the GINS' Listing-File (GLF);

• For stacking and manipulation of normal équations, use of the DYNAMO software package in order to apply minimal constraints for the datum réalisations, reduce or eliminate un-necessary parameters ;

Finally, for the east component, the corrélation coefficient is 80 % and 69 % with

Bemese's and GAMIT's solutions respectively. The worst corrélation coefficient in East cornes from the comparison to GIPSY's solution which results about 49 %.

The three solutions of Bemese, GAMIT and GINS présent a mean 3D corrélation coefficient of about 82 % and 52 % when GIPSY's solution is included.

To conclude, GINS' solutions are validated with respect to the régression analysis performed.

4.

Comparisons of the in-phase and out-of-phase 3D displacement coefficients in the semidiumal band (Fig. 3-4) at the 9 GPS campaign stations are realised.

Conceming the phase on the horizontal components, a good agreement is observed (différences lower than 40°) for GAMIT, GINS, and GIPSY solutions, except in BRST station which présents the highest discrepancies (-100°) for the east component.

Bemese's solution generally represents an important phase shift which can reach at complété phase opposition for some stations (MANS, PAIM, and YGEA). The four solutions are in a very good agreement at CHER, COUT, and RENN stations. For the vertical component, the phase discrepancies are lower than 15-20°between the 3 solutions of GAMIT, GINS and GIPSY.

The phase shift of Bemese's solutions at certain stations could be related to a "bug" in the solid earth tides displacement corrections présent in versions 4.2 and 5 (Hugentobler, personal communication). From the same Fig. 4-10 we can observe that the solutions with "tight constraints" (in red) on the positions of a set of IGS-EUREF stabilisation sites give results (in terms of précision and accuracy) for the selected 6-GPS network of stations équivalent to the "loose constraints" approach of the global set of IGS-stabilisation sites which makes use of a similarity transformation of 7 parameters for the datum définition.

The régional "loose constraint" stabilisation approach seems to perform less well in précision and accuracy with respect to the two others strategies. In general terms the The dominant aliasing period for S2 yields a signal at 182.63 days. Additionally, M2

should yield a secondary spectral peak at 14.77 days which is the aliasing period obtained from the équation according to [START_REF] Jacobs | The global structure of the annual and semiannual sea surface height variability from Geosat altimeter data[END_REF]: f = abs /~^int(/'A + 0-5)

Eq. 4-12

Where: f is the aliased frequency; / is the original frequency; À is the sampling interval. Again in this case, due to the limited time-span of the data-set this peak will not be easily separated from the dominant 13.66 days signal.

With the présent scénario we can also not examine the aliasing signais for the less important diumal OTL waves of Oi and K| (with period close to the GPS orbital révolution) at 14.19 days and 364.26 days respectively.

Harmonies of the GPS height time-series spectral analysis are presented in Fig. 4-14 for four représentative campaign stations: DIBE, YGEA, MALO and CHER. For ail stations the dominant aliasing periods of M2 and N2 yield signais with amplitudes of several millimétrés. Considering first M2, the prominent spectral peak at 13.66 days and most probably the one at 14.76 days are detected since the lobs are rather large in that band. Similarly N2 shows a pronounced spurious signal around 9.13 days period which is detected for ail sites.

The above results stress the importance of modelling ail periodic systematic errors as accurately as possible.

Arm Effect (LAE) (Melachroinos 2004). These offsets may hâve any value from 0 to 150 m. The longer the offset the bigger will be the LAE.

Il Vertical at