Y Z Li

N Mangelinck-Noël

G Zimmermann

L Sturz

H Nguyen-Thi

Comparative Study of Directional Solidification of Al-7wt.% Si Alloys in Space and on Earth: Effects of Gravity on Dendrite Growth and Columnar-to-Equiaxed Transition

Keywords: B1. Alloys, A1. Directional solidification, A2. Microgravity conditions, A1

Directional solidification experiments of grain refined Al -7 wt.% Si alloy were carried out on Earth under normal gravity conditions (1g) and in the Material Science Laboratory on board the International Space Station in microgravity environment (µg), to investigate the impact of the gravity on the solidification microstructure and the columnar-to-equiaxed transition (CET). The increase of the dendrite growth velocity imposed by the processing conditions during the experiments leads to a size decrease of the dendrite microstructure and to a more homogeneous eutectic distribution under both 1g and μg conditions. A progressive CET is obtained in both samples implying the existence of an intermediate region after the inception position of CET defined as the end of growth of the columnar dendrites. However, a more progressive CET and longer dendrites aligned with the applied temperature gradient are observed in presence of gravity. This difference is attributed to the convective flow on Earth.

On the one hand, it carries the grains that nucleate ahead of the columnar front away into the bulk liquid phase. On the other hand, it sweeps the solute away from the dendrite tip zone.

Consequently, the blocking effect is diminished, allowing extended continuous growth of the elongated dendrites.

Introduction

The understanding and as a further step the control of the morphological development during solidification remains of tremendous interest in order to master the quality and performance of materials because of the relationship between the microstructures and the properties of the final materials. In metallic alloys, the solidified dendrite microstructure can be either elongated columnar or equiaxed, according to the solidification conditions [START_REF] Dantzig | Solidification[END_REF].

Columnar-to-equiaxed transition (CET) is an important and common morphological transition, which frequently occurs during industrial processes such as ingot casting, welding and additive manufacturing. CET occurs when the amount and/or the size of equiaxed grains that grow ahead of the columnar front become sufficient to block the continuous columnar dendrite growth [START_REF] Jung | Columnar to equiaxed transition during directional solidification in refined Al-based alloys[END_REF][START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF]. The competition of dendrites at the solidification front is a complex topic, which involves mechanical effects as well as thermal and solutal interaction [START_REF] Hunt | Steady state columnar and equiaxed growth of dendrites and eutectic[END_REF][START_REF] Martorano | Predicting the columnar-to-equiaxed transition for a distribution of nucleation undercoolings[END_REF].

The first analytical model to predict the conditions for CET was proposed by Hunt [START_REF] Hunt | Steady state columnar and equiaxed growth of dendrites and eutectic[END_REF]. In this model, equiaxed grains are assumed to form by heterogeneous nucleation ahead of the dendritic columnar front in the undercooled liquid and to grow in this region. The extension of the undercooled zone and the maximum value of the undercooling depend on the thermal gradient and pulling rate. In Hunt's model, a steady-state criterion is added to predict the CET: fully equiaxed growth occurs when the equiaxed volume fraction is large enough to block the columnar growth. This criterion is often referred to as mechanical blocking. Despite some model hypothesis which can be discussed, this model agrees qualitatively well with experimental observations, in particular that fully equiaxed growth is dominant at low temperature gradient and high pulling rate. However, the model predictions strongly depend on two parameters: the nucleation undercooling (undercooling above which the particles become active) and the nucleus density. These parameters are not easily determined during experiments.

Wang et al. [START_REF] Wang | A unified solute diffusion model for columnar and equiaxed dendritic alloy solidification[END_REF] proposed a model where the solutal interaction between equiaxed grains was taken into account. However, the solutal interaction between the equiaxed microstructure and the columnar front is neglected, which implies to keep the mechanical blocking criterion to predict the CET. Martorano et al [START_REF] Martorano | A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification[END_REF] extended this approach and developed a model where the solutal interaction between the equiaxed microstructure and the columnar front is successfully treated. The solute concentration ahead of the columnar front gradually increases due to the solute rejection from columnar and equiaxed grains and, consequently the columnar front undercooling decreases. If the reduction is sufficient to annihilate the columnar front undercooling completely, the columnar dendritic microstructure is stopped and CET takes place. In this approach, CET is a direct consequence of the solutal interaction between the equiaxed microstructure and the columnar front, so that it is referred as solutal blocking. Like in Hunt's analysis, this model depends on the two key parameters of refining particles, namely nucleation undercooling and nucleus density. Experimental evidences of both solutal interaction and mechanical blocking were brought by Reinhart et al [START_REF] Reinhart | In-situ observation of transition from columnar to equiaxed growth in Al-3.5 wt% Ni alloys by synchrotron radiography[END_REF], by means of synchrotron X-radiography to follow the dynamics of CET in situ and in real time.

During ground-based solidification, another crucial issue to be clarified is the role of gravity on the microstructure evolution, because gravity can affect all the factors linked to the above issues: thermal field, solute distribution and position and amount of new grains [START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF][START_REF] Dupouy | Effects of gravity on columnar dendritic growth of metallic alloys: flow pattern and mass transfer[END_REF][START_REF] Rerko | Effect of melt convection and solid transport on macrosegregation and grain structure in equiaxed Al-Cu alloys[END_REF].

However, the solidification is a multi-scale and multi mechanisms process so that it is very difficult to deconvolute the different effects. Accordingly, microgravity experiments are the unique way to be able to study the effect of gravity by comparison with ground condition experiments [START_REF] Nguyen-Thi | On the interest of microgravity experimentation for studying convective effects during the directional solidification of metal alloys[END_REF]. Indeed, the two key ingredients in microstructure evolution during the solidification on Earth are the natural convection and grain motion due to buoyancy forces [START_REF] Bogno | Growth and interaction of dendritic equiaxed grains: In situ characterization by synchrotron X-ray radiography[END_REF][START_REF] Wang | A multiphase solute diffusion model for dendritic alloy solidification[END_REF]. The natural convection, induced by any density differences in the melt in both horizontal and vertical direction [START_REF] Burden | Macroscopic stability of a planar, cellular or dendritic interface during directional freezing[END_REF][START_REF] Gomes | On the Natural Convection in the Columnar to Equiaxed Transition in Directionally Solidified Aluminum-based Binary and Multicomponent Alloys[END_REF], is present in the liquid ahead of the solidification front as well as in the interdendritic region [START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF][START_REF] Hui | Primary dendrite distribution and disorder during directional solidification of Pb-Sb alloys[END_REF][START_REF] Steinbach | The influence of fluid flow on the microstructure of directionally solidified AlSi-base alloys[END_REF], significantly modifying the solute and thermal fields [START_REF] Nguyen-Thi | On the interest of microgravity experimentation for studying convective effects during the directional solidification of metal alloys[END_REF][START_REF] Spinelli | Influence of melt convection on the columnar to equiaxed transition and microstructure of downward unsteady-state directionally solidified Sn-Pb alloys[END_REF]. Consequently, convection is responsible for both micro-and macro-segregation [START_REF] Shevchenko | Investigations of fluid flow effects on dendritic solidification: Consequences on fragmentation, macrosegregation and the influence of electromagnetic stirring[END_REF][START_REF] Flemings | Our understanding of macrosegregation: past and present[END_REF][START_REF] Beckermann | Modelling of macrosegregation: applications and future needs[END_REF][START_REF] Guillemot | Modeling of macrosegregation and solidification grain structures with a coupled cellular automaton-finite element model[END_REF]. Furthermore, the gravity can significantly affect the CET by two effects. First, the liquid flow ahead of the solidification front can dramatically modify the heat and solute conditions, leading to a significant modification of the undercooled region ahead of the columnar dendrites responsible for nucleation and dendrite growth [START_REF] Griffiths | The influence of bulk liquid natural convection on the formation of the equiaxed regions in Al-Cu and Al-Si alloys[END_REF]. Second, the interdendritic flow can favor the fragmentation by secondary branch neck remelting due to solute pile-up or transport of hot liquid at the level of the secondary branch neck [START_REF] Zimmermann | Fragmentation-driven grain refinement in directional solidification of AlCu10wt-% alloy at low pulling speeds[END_REF][START_REF] Ruvalcaba | In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy[END_REF].

Such fragments can participate to the CET if they are transported from the columnar front into the undercooled region where they can continue to grow and possibly stop the advancement of the columnar front [START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF][START_REF] Spittle | Columnar to equiaxed grain transition in as solidified alloys[END_REF][START_REF] Hellawell | Dendrite fragmentation and the effects of fluid flow in castings[END_REF]. In the case of grain refined alloys, the liquid flow might also lead to the transportation of the grain refiners and therefore can affect the CET [START_REF] Bedel | A model study of the impact of the transport of inoculant particles on microstructure formation during solidification[END_REF][START_REF] Tveito | Numerical study of the impact of inoculant and grain transport on macrosegregation and microstructure formation during solidification of an Al-22%Cu alloy[END_REF][START_REF] Heyvaert | Modeling of the Coupling of Microstructure and Macrosegregation in a Direct Chill Cast Al-Cu Billet[END_REF].

Finally, the newly nucleated equiaxed grains ahead of the columnar front are subjected to buoyancy force. Depending on the density difference between the grains and the surrounding liquid, they can either sediment, which can favor the blocking of the columnar front [START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF][START_REF] Wu | Modeling equiaxed solidification with melt convection and grain sedimentation-II. Model verification[END_REF], or float and be transported from the columnar front into the bulk liquid where they can be remelted [START_REF] Nguyen-Thi | Investigation of gravity effects on solidification of binary alloys with in situ X-ray radiography on earth and in microgravity environment[END_REF]. In the latter case, the buoyancy force can inhibit the columnar to equiaxed transition [START_REF] Nguyen-Thi | Investigation of gravity effects on solidification of binary alloys with in situ X-ray radiography on earth and in microgravity environment[END_REF][START_REF] Kumar | Grain Floatation During Equiaxed Solidification of an Al-Cu Alloy in a Side-Cooled Cavity: Part I-Experimental Studies[END_REF][START_REF] Salloum-Abou-Jaoude | Characterization of motion of dendrite fragment by X-ray radiography on Earth and under microgravity environment[END_REF].

Within this context, solidification experiment under microgravity conditions can provide unique benchmark data by effectively suppressing the gravity-driven phenomena and we can expect to achieve nearly diffusive conditions [START_REF] Jansen | Solidification under microgravity[END_REF][START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Akamatsu | In situ observation of solidification patterns in diffusive conditions[END_REF]. Within the ESA project CETSOL (Columnar to Equiaxed Transition in SOLidification processes), directional solidification experiments under both gravity (1g) and microgravity conditions (µg) [START_REF] Zimmermann | Investigation of columnar-to-equiaxed transition in solidification processing of AlSi alloys in microgravity-The CETSOL project[END_REF][START_REF] Zimmermann | Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project[END_REF] have been carried out on selected aluminum-based alloys. Solidifications were carried out in the Material Science Laboratory (MSL) that was made available by the European Space Agency (ESA) on board the International Space Station (ISS), providing a platform for microgravity solidification investigations to clarify major scientific issues in solidification. The comparative study of directional solidification of Al-7wt.% Si alloys in Space and on Earth is ideal to deepen the understanding of the formation of the solidification microstructure and of CET. The eutectic and the dendritic structure as well as the CET main features are quantitatively evaluated and compared in both 1g and µg conditions to enlighten the influence of gravity.

Experimental

Experiment details

Within the framework of the CETSOL project, several microgravity experiments (µg) and one reference experiment on Earth (1g) have been conducted. In this paper, a comparative study is presented between the only 1g experiment labelled GM (GM for Ground Module) and the corresponding µg experiment B1FM5 (B1 for Batch1, FM for Flight Module, and noted as FM hereafter) processed with identical solidification parameters. Both the GM and FM samples here were elaborated using the Low Gradient Furnace (LGF), which was described in details in our previous studies [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The LGF is a Bridgman-type furnace, which consists of two heating zones separated by an adiabatic region. The cold zone and the hot zone are constituted of three (H1-H3 in Fig. 1) and four (H4-H7 in Fig. 1) separated heating elements, respectively. The temperature of each heating element can be adjusted independently during the solidification to achieve the required temperature profile along the solidification direction.

For the ground experiment, the LGF pulling direction is vertical upward along the fixed mounted sample, opposite to the gravity direction, leading to an upward solidification direction.

The sample cartridge assembly (SCA) is schematized in Fig. 1. The alloy sample is mounted inside a protective Al 2 O 3 tube crucible with Shapal plugs at both bottom and top ends. Twelve N-type thermocouples (labelled TC1-TC12), spaced by 10 mm, are located in four machined external axial grooves at the outer surface of the crucible to record the temperature evolution profiles along the sample. 1.

The solidification procedure consists of three successive stages:

-Stage I: The initial temperature gradient (G) is about 0.9 K/mm. The solidification is initiated by the furnace motion at a low pulling velocity (v 1 = 0.01 mm/s) for 20 mm.

-Stage II: The second stage is triggered by a cooling down of the hot zone at a cooling rate of 0.067 K/s, which yields to a continuous decrease of the temperature gradient. The furnace motion length is 20 mm for this stage and the pulling rate is identical to the stage I (v 1 = 0.01 mm/s).

-Stage III: A furnace pulling at a velocity of 3 mm/s is applied to complete the solidification.

During this final stage, the temperature gradient and the cooling rates are no longer controlled, but the temperature profiles are still recorded, which enable us to determine these two important experimental parameters.

Microstructure characterization

After solidification, both samples are cut in the same manner into transverse and longitudinal sections and prepared for metallographic analysis, the sketch of the cutting sections are shown in Fig. 2. Longitudinal sections are cut close to the centerline. The samples were mechanically polished with diamond suspension to identify the dendritic microstructure. Then, electrolytic etching was performed to distinguish dendrites with different crystallographic orientations in different colors using an optical polarized light microscope (OM) and thereby to reveal the grain structure. The OM images of the longitudinal sections located at the level of the transition from the stage I to the stage II for both the GM and FM samples are first segmented into binary images using a threshold to separate the two phases: dendrite and eutectic phase. Based on those binary images, the eutectic percentage (E%) maps are determined to display the distribution of the eutectic phase, using a box-averaging method with a box size of 0.875 mm in length, along the sample axis direction, and 0.656 mm in width, along the sample diameter direction.

The size of the averaging box is indicated in Fig. 4 in comparison to the sample size. From the binary images revealing dendrites and eutectic, a linear intercept method is applied to determine the dendrite arm spacing (DAS) [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. For each data point of DAS, thousand lines are randomly generated in each measuring box to increase the result statistics and reliability.

It is worth to mention here that this measured DAS is not equal to the primary or secondary dendrite arm spacing but is a useful average characteristic to display the scale of the dendritic structure as described before [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Han | Microstructure Prediction in A356 Alloy Castings[END_REF]. Moreover, DAS and E% profiles along the solidification direction, i.e. along the main cylindrical sample axis are determined by averaging within boxes of 0.875 mm in length and including the whole sample diameter in width.

Results

Analysis of the processing parameters

The recorded temperature profiles during the solidification for both samples are shown in Fig. 3a andb, respectively. Based on the temperature profiles, the temperature gradient ahead of the liquidus isotherm (T L = 891 K for Al-7 wt.% Si) G L and the velocity of the liquidus isotherm v L of both samples are calculated, as shown in Fig. 3c andd, respectively. Based on the linear interpolation method, the temperature gradient ahead of the liquidus isotherm is calculated at the time when the liquidus isotherm reaches a thermocouple T N , by the temperature difference and the known distance 10 mm between T N and its neighboring thermocouple T N+1 . Then, the velocity of the liquidus isotherm can be deduced by the liquidus isotherm positions at this instant and next time-step. The temperature gradient and velocity of the liquidus isotherm are calculated for each stage and are gathered in Table 2 as average value for stage I and as Minimum/Maximum values in stage II. The procedure, described in details in our previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF], is similar to the method used by Gandin [START_REF] Gandin | Experimental study of the transition from constrained to unconstrained growth during directional solidification[END_REF].

The transition position between stages, as indicated by the vertical blue dashed lines in Fig. 3, are also deduced from the cooling curves delimited by the transition time at which the furnace started to move for every stage. The calculation details of these positions were explained in our previous work [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. The transition positions between stages I and II are 133. The curves in Fig. 3 show similar temperature profiles and also G L and v L profiles of GM and FM for the entire calculated range, indicating that the influence of the gravity on the detected thermal field during the solidification process is not significant here. The calculated values of G L are almost constant in stage I, whereas the calculated values of G L gradually decrease and the calculated v L increases in stage II, as can be seen in Fig. 3. Table 2 As shown in Fig. 4a1 and4b1, a columnar structure is revealed in stage I for both samples.

Close to the transition position from the stage I to the stage II, the growth of the columnar grains issued from the initial dendrites zone are blocked by other grains indicated by the different colors and stem growth directions for both samples as highlighted by the white dash lines in Fig. 4a1 and4b1. For the FM sample, according to previous studies [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Gandin | From constrained to unconstrained growth during directional solidification[END_REF], this position defines the CET inception (i.e. end of the fully columnar growth) and is noted as CET min in Fig. 4b1, as indicated by smaller and equiaxed dendrite grains after this position.

The CET could be recognized as progressive mode when considering the elongation factor (EF) of the grains after CET min [START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF]. In such case of progressive CET, an intermediate region with elongated equiaxed grains (EF>2) exists between CET min and the fully equiaxed region limit defined as the position for which the average grain elongation is lower than two, according to Hunt's criterion. However, for the GM sample, the new nucleated grains after this position are still columnar as shown in Fig. 4a1, although the initial columnar dendrites 2. The results in Fig. 5 and Table 2 suggest that, in the GM sample, the E% is constant from the stage I to the stage II (black squares in Fig5a), whereas the DAS slightly decreases (black dots in Fig. 5b). However, both the E% and DAS decrease from the stage I to the stage II in the FM sample (red symbols in Fig. 5a and Fig. 5b). Moreover, the average E% is higher in the FM sample compared to the GM sample in the stage I whereas the values are comparable in the stage II. Besides, the average DAS values are comparable for both samples in the stage I (131 µm and 134 µm)

whereas the average DAS is much lower in the FM sample (95 µm) compared to the GM sample (117 µm) in the stage II. This difference is ascribed to the gravity which will be discussed later. It was mentioned in Section 2.2 that the DAS shown in Fig. 5 is only an average characteristic of the dendritic structure. However, the microstructure of the transverse section could be used to measure the average grain size of the dendritic structures [START_REF] Mccartney | Measurements of cell and primary dendrite arm spacings in directionally solidified aluminium alloys[END_REF] as

λ = �𝐴/𝑛
where λ is the average grain size, A is the analyzed area, and n is the number of grains in this area. Microstructures of the transverse sections corresponding to the positions shown in Fig. 2 are displayed for both samples in Fig. 6. According to Fig. 4, the sections at 127 mm and 157 mm are in the stages I and II, respectively. Therefore, these sections could be used to estimate the average grain size in the stage I and II, respectively. By counting the number of the grains in the sections shown in Fig. 6, the λ values in the stage I are 4.1 mm and 2.1 mm for GM and FM, respectively, and in the stage II are 1.5 mm and 1.3 mm for GM and FM, respectively.

This shows that in both cases (GM and FM), lower λ values were obtained due to the higher solidification velocity in the stage II, as shown in Fig. 3 and Table 2. Specifically, larger λ values in the GM sample compared to the FM sample in both the stages I and II could be observed, especially in the stage I under a lower solidification velocity.

Particular observation of a long columnar dendrite in stage II of the GM sample

Microstructures of the longitudinal sections of the GM sample are displayed in Fig. 7. It can be seen that the two large dendritic grains in the start region of stage II, almost occupy the whole sample width as shown in Fig. 7a and Fig. 4 above. At higher solidification length, the grain size decreases, with a more equiaxed characteristic in the following solidification steps.

These observations are related to the increasing growth velocity and decreasing temperature gradient as mentioned in Section 3.1. Nevertheless, a long dendrite growing close to the sample axis, i.e. the direction parallel to the temperature gradient, is observed in the same region, as indicated by the white arrows in Fig. 7a. The maximum length of this dendrite is up to 62 mm. Fig. 7b and Fig. 7c show the zoomed images of the largest dendrite outlined in yellow. For this dendrite, the secondary arms are almost perpendicular to the primary trunk, which indicates that the primary trunk growth direction of this dendrite corresponds to the cutting section displayed in Fig. 7, the <100> direction being the prior crystal orientation of α-Al dendrite growth in this alloy. Thereby, the growth direction of this dendrite is almost parallel to the thermal gradient and anti-parallel to gravity i.e. vertical. The start position of this longest dendrite is just located in front of the two big dendrites in the beginning of the stage II.

Finally, the growth of this dendrite is blocked by numerous and finer dendritic grains in the region close to the transition position from the stage II to III, which was estimated by the length of the mushy zone.

Discussion

Effect of the thermal conditions (G, v) on the microstructure and CET

The growth velocity of the dendrite tips is approximated by the liquidus isotherm velocity v L during the solidification. In stage I, large solute-enriched liquid pockets in the interdendritic region form and later transform into large eutectic zones because of the large size of the dendrites. These large dendrites are due to the low growth velocity in the stage I, as shown in Fig. 3b. In the stage II, the continuous increase of the growth velocity triggers the dendritic branching and consequently decreases the typical size of dendrite structure. Accordingly, a more homogeneous eutectic distribution is observed in the stage II compared to the stage I.

Moreover, in a refined alloy as the one used in the experiments, the origin of equiaxed grains is dominated by the nucleation on added refining particles [START_REF] Greer | Modelling of inoculation of metallic melts: application to grain refinement of aluminium by Al-Ti-B[END_REF][START_REF] Mohanty | Mechanism of grain refinement in aluminium[END_REF]. The enhanced undercooling in front of the columnar dendrites due to growth velocity increase results in an increasing amount of nucleation of equiaxed grains on refiners ahead of the columnar front.

These newly nucleated grains ultimately block the initial columnar grains, leading to the inception of CET in stage II for both the GM and FM samples and defining the position CET min . The progressive CET observed for both samples means that the final applied temperature gradient and pulling rate are located in the solidification parameters range of columnar and equiaxed mixed region [START_REF] Jung | Columnar to equiaxed transition during directional solidification in refined Al-based alloys[END_REF][START_REF] Liu | Structures in directionally solidified Al-7 wt.% Si alloys: Benchmark experiments under microgravity[END_REF][START_REF] Pineda | Columnar to equiaxed transition in directional solidification of inoculated melts[END_REF].

Effect of the gravity on the microstructure

The natural convection flow and its effect on CET 20

The significant differences of the solidification microstructure observed between the GM and the FM sample indicate that the gravity significantly affects the solidification process, which also has been reported previously [START_REF] Nguyen-Thi | Investigation of gravity effects on solidification of binary alloys with in situ X-ray radiography on earth and in microgravity environment[END_REF][START_REF] Dupouy | Natural convection in directional dendritic solidification of metallic alloys-I. Macroscopic effects[END_REF][START_REF] Jung | Columnar to equiaxed transition in nonrefined Al-based alloys during directional solidification in microgravity and on earth[END_REF]. According to calculated G L and v L , as shown in Fig. 3 and Table 2, no significant variation of the thermal field is observed between the two samples. Therefore, the distinction of the microstructure and CET features between the GM and the FM sample can only be attributed to the different gravity conditions between the two experiments.

It has to be discussed, whether the amount or distribution of the grain refiner (GR) we used in this study can be different in the GM and FM samples. Before starting the solidification stage I, a temperature adjustment and thermal homogenization phase of about 110 min existed in both experiments. In this initial state about 2/3 of the samples lengths was melted and a similar and nearly stable distribution and amount of the active GR would be expected both in GM and FM samples [START_REF] Karagadde | 3-D microstructural model of freckle formation validated using in situ experiments[END_REF]. As shown in the study of Reinhart et al. [START_REF] Murphy | XRMON-SOL: Isothermal equiaxed solidification of a grain refined Al-20 wt%Cu alloy[END_REF], the amount and distribution of the active GR always remained similar even after several times of remelting of the aluminum alloy on Earth, which indicated that the sedimentation of the GR could be neglected during the solidification under the 1g condition. Therefore, also the amount and distribution of the active GR will be considered the same for the GM and FM samples.

On Earth, natural convection or fluid flow is induced by instable density gradients from the constitutional and thermal gradients in the liquid phase. Then, natural convection in general changes the thermal and solutal conditions ahead of the dendrite front and also in the mushy zone [START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF][START_REF] Dupouy | Effects of gravity on columnar dendritic growth of metallic alloys: flow pattern and mass transfer[END_REF]. Based on previous results [START_REF] Gomes | On the Natural Convection in the Columnar to Equiaxed Transition in Directionally Solidified Aluminum-based Binary and Multicomponent Alloys[END_REF][START_REF] Shevchenko | Investigations of fluid flow effects on dendritic solidification: Consequences on fragmentation, macrosegregation and the influence of electromagnetic stirring[END_REF][START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF][START_REF] Karagadde | 3-D microstructural model of freckle formation validated using in situ experiments[END_REF], from both experiments and simulations, the qualitative liquid flow patterns induced by the gravity in the mushy zone and ahead of the dendrite front during the solidification can be estimated in this experiment. In practice, solutal convection dominates in the case of metallic alloys owing to their large Lewis number defined as the ratio of the thermal diffusivity to the solutal one (Le = D th /D), typically of the order of 10 3 to 10 4 .

Generally speaking, in presence of gravity and depending on the alloy (partition coefficient k and respective densities of alloy elements), the convection flow is different in the two regions illustrated in Fig.8 [START_REF] Gomes | On the Natural Convection in the Columnar to Equiaxed Transition in Directionally Solidified Aluminum-based Binary and Multicomponent Alloys[END_REF][START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF][START_REF] Karagadde | 3-D microstructural model of freckle formation validated using in situ experiments[END_REF]: within the mushy layer (generally considered as a porous medium) and in the region ahead of the mush/liquid interface. In the latter case, the characteristic length scale may vary from several times the solutal length D/V (V being the solidification velocity) up to the sample size far from the S/L interface.

Moreover, convection liquid flow can exist in the interdendritic region due to the solutal effects (rejection of solute during the phase transition) and volume shrinkage. It is worth mentioning that the former convection is gravity-dependent, whereas the latter effect is not gravity-dependent. Accordingly, shrinkage flow becomes dominant in the mushy zone and in the close vicinity of the columnar front in microgravity experiments as recently revealed by in situ observation during equiaxed growth in isothermal conditions [START_REF] Murphy | XRMON-SOL: Isothermal equiaxed solidification of a grain refined Al-20 wt%Cu alloy[END_REF], as well as during directional solidification [START_REF] Abou-Khalil | Influence of gravity level on Columnar-to-Equiaxed Transition during directional solidification of Al-20 wt.% Cu alloys[END_REF]. In the case of Al-7wt%Si, it is expected that the solutal induced flow has a rather low velocity because of the weak density difference between Al and Si. But the convection induced by the radial temperature gradient also existed, which would enhance the liquid flow [START_REF] Reinhart | Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure[END_REF][START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF]. As mentioned by Jung [START_REF] Jung | La transition colonnaire equiaxe au cours de la solidification dirigee d'alliages metalliques[END_REF], under the solidification parameter G=0.5 K/mm and v=0.002 mm/s, the maximum convection velocity for Al-7wt%Si (2.3 μm/s) was much higher than that for Al-3.5wt%Ni (0.9 μm/s), even though the density difference between Al and Ni is much larger. In the zone ahead of the tip of the large dendrite, the convection liquid flow pattern is drawn in black dash cyclo-streamlines, labelled (1), in Fig. 8, and can extend from the solidification front to far away in the liquid region. As a possible scenario, the flow directions are downward in the center and upward at the edges, according to the simulation results reported by Zhou et al. [START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF]. Newly nucleated equiaxed grains are present in the undercooled zone delimitated by the dendrite tips and the liquidus temperature isotherm (T L ). The liquid flow ( 1) is assumed to be stronger than the liquid flow inside the mushy zone because of the decreasing permeability when going down towards the eutectic isotherm. Besides, there is a liquid flow in the close vicinity of the large dendrite tip, indicated by the dashed red box in Fig. 8, as reported respectively by Zhou [START_REF] Zhou | Comparative study of the influence of natural convection on directional solidification of Al-3.5wt% Ni and Al-7wt% Si alloys[END_REF] and Karagadde [START_REF] Karagadde | 3-D microstructural model of freckle formation validated using in situ experiments[END_REF]. Indeed, minor flow rolls, at the scale of the primary spacing, were described by Karagadde in this region and adhering to the dendrites, both between two dendrites and in front of the tip of one single dendrite [START_REF] Karagadde | 3-D microstructural model of freckle formation validated using in situ experiments[END_REF]. In FM sample under µg condition, the new nucleated grains and solute rejected from the equiaxed and columnar growing dendrites are not submitted to flow and sedimentation phenomena so that equiaxed grains accumulate in the undercooled region and solute builds up triggering CET. On the contrary, in the GM sample, the bulk convective flow ((1) in Fig. 8) carries part of both the new grains and of the solute away from the columnar tip zone towards the upper liquid region where the temperature is higher and the Si concentration is lower.

Consequently, the transported equiaxed grains are most likely remelted as in situ observed by Nguyen-Thi et al. during the solidification of Al-20wt.% Cu alloy [START_REF] Nguyen-Thi | Overview of in situ X-ray studies of metal alloy solidification in µg conditions -The XRMON project[END_REF]. It is worth noting that the transport of the dendritic grains far into the liquid where they are remelted inhibits or delays the columnar-to-equiaxed transition. Additionally, the lower extent flows in the tip region can participate to the removal of new grains and of the solute away from the columnar tip zone. In summary, due to gravity effects, the blocking of the columnar front is alleviated or diminished and the growth of the columnar dendrite and of the remaining equiaxed grains is promoted, leading to a more progressive CET and much larger dendrites in the GM sample.

The long dendrite growth in GM

As shown in Fig. 4a1 and Fig. 7b, several dendrite grains nucleate and grow in the GM sample after CET min . During dendrite growth, the growth direction of the primary trunk is controlled by the initial grain orientation when no seed is used, by the direction of the temperature gradient at low velocity and by crystallographic effects at high velocity. In some cases, the dendrite primary trunk is well aligned with the temperature gradient direction as for example the long dendrite in Fig. 7b in the GM sample. Fig. 9 illustrates the dendrite tip motion of two dendrites with different misorientations relatively to the temperature gradient direction during upward solidification: (1) 0° and (2) θ.

The growth competition of these two dendrites could be explained by the classical model proposed by Walton and Chalmers [START_REF] Walton | The origin of the preferred orientation in the columnar zone of ingots[END_REF][START_REF] Tourret | Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study[END_REF][START_REF] Tourret | Growth competition of columnar dendritic grains: A phase-field study[END_REF]. During the steady-state dendrite growth, grains at the solidification front should grow at the same velocity in the direction of the temperature gradient, so that v 1 = v 2 ' for the two dendrites in Fig. 9. Consequently, the tip growth velocity of the dendrite (2) would be higher than that of the dendrite (1), i.e. v 2 >v 1 . Since the tip growth velocity is linked to the undercooling [START_REF] Koss | Dendritic Growth tip velocities and radii of curvature in microgravity[END_REF][START_REF] Schwarz | Dendritic growth velocity and diffusive speed in solidification of undercooled dilute Ni-Zr melts[END_REF][START_REF] Chen | A Modified Cellular Automaton Model for the Quantitative Prediction of Equiaxed and Columnar Dendritic Growth[END_REF], the undercooling is higher at the level of the tip of the dendrite (2) compared to the dendrite (1): △T 2 >△T 1 . Therefore, the tip of the dendrite (2) lags behind the one of the dendrite (1). Thus, as the one observed in Fig. 7, the growth of the dendrites aligned with the temperature gradient is expected to be favored in the growth competition process. The growth of this particular dendrite in Fig. 7 is stopped by equiaxed grains close to the transition position from the stage II to the stage III. This is attributed to the blocking effect of the large amount of new nucleated grains due to the increase in pulling velocity and cooling rate in the stage III.

4.2.3

The gravity effect on E% and DAS Additionally, the quantitative microstructure differences between the GM and the FM samples, as mentioned in Section 3.2, are also attributed to the influence of the gravity induced convection, considering the identical solidification parameters. As mentioned in Table 2 and Fig. 5, the E% is lower in the GM sample compared to the FM sample. In the FM sample, the accumulation of the denser solute in the mushy zone results in large E%. In the GM sample, the lower E% is the signature of the upward motion of the rejected solute Si due to the intra-dendritic fluid flow, which consequently alleviates the large amount of solute accumulation and leads to smaller eutectic pockets in the GM sample. Due to the bulk liquid flow, the number of equiaxed dendrite grains in the GM sample is lower than in the FM sample, with a much larger grain size, as discussed above. As mentioned in Section 2.2, the DAS measurement takes into account all the primary, secondary and higher order dendrite arm spacing. And the average grain size from transverse sections in the GM sample are larger than in the FM sample. As the DAS measurement includes all spacings (grain size, primary, secondary and eutectic pockets) in a selected zone, a larger DAS value is obtained in the GM sample.

Conclusion

A ground reference solidification experiment on Earth and a microgravity experiment in the Material Science Laboratory on board the International Space Station were carried out under the same solidification parameters. The influence of the solidification parameters and in particular of the gravity on the microstructure and on the CET have been studied.

(1) The increase of the dendrite growth velocity from the stage I to the stage II leads to finer dendrite structure under both 1g and µg conditions. Consequently, a more homogeneous eutectic distribution is achieved in stage II.

(2) The CET is obtained in both samples in a progressive mode. This is directly linked to the applied processing conditions, continuous decrease of thermal gradient but at a low furnace pulling velocity, resulting in low undercooling ahead of the columnar dendrite tips. As a consequence, no copious equiaxed nucleation on the refining particles above the columnar front can be expected implying a progressive CET.

(3) The gravity significantly influences the microstructure and the CET because of the existence of the convection liquid flow. Indeed, in the GM, the liquid flow ahead of the solidification front carries both the new grains and the solute away from dendrite tip zone, alleviating or diminishing the blocking effect and promoting the continuous growth of the columnar dendrites. Therefore, the CET is more progressive in the GM sample. Additionally, the E% is lower and the DAS is higher in the GM sample than in the FM sample.

(4) Newly nucleated dendrites with the primary trunk aligned with the temperature gradient direction can grow all along the sample until dramatic change of the processing conditions. This is ascribed to their more favorable growth conditions directly linked to their relative orientation to the temperature gradient.

Fig. 1 .

 1 Fig.1. Sketch of a CETSOL Batch 1 cartridge MSL-SCA integrated in the MSL-LGF furnace

Fig. 2 .

 2 Fig.2. Photograph of the processed GM sample with identification of cross-section positions.

  3 mm and 132.1 mm for the GM and the FM sample, respectively. The transition positions between stages II and III cannot be determined because the temperatures (below 867 K) at the level of the highest thermocouple TC12 (position of 182.5 mm) at the instant of the transition from stage II to III are already much lower than the liquidus temperature (891 K) as indicated from the temperature records.

Fig. 3 .

 3 Fig.3. (a) and (b) Temperature curves recorded by the thermocouples during the experiments

3 . 2 .

 32 gathers the main processing parameters in both stages. It should be mentioned that only the first 25 mm are considered in the analysis of G L and v L in stage II for comparison to the microstructure shown in Fig.4. The comparison is discussed in more details in Section 4. Table 2 summarizes the initial and final values of G L and v L within this interval and includes the average values of the microstructure analysis. The length of the mushy zone (L MZ ) during the solidification process, defined by the distance between the liquidus and the eutectic isotherms (T L =891 K and T E =850 K), was also calculated to estimate the transition position from stage II to III. The average value of the mushy zone length is estimated at about 50 mm in stage I and gradually increases in stage II for both the GM and FM samples, which is expected due to the decreasing G L in stage II. Analysis of the microstructure Microstructures of the longitudinal sections corresponding to the transition between stage I and stage II are displayed for both samples in Fig.4a1 and 4b1. Different electrolytical etching methods are applied resulting in different color maps. The bottoms of Fig.4a1 and 4b1 correspond to the start position of stage I. The blank regions between two sections for both samples represent the material loss during the sample cutting and the transverse section micrograph preparation. The solidification stages and the corresponding furnace pulling velocities are indicated on the left side of the figure, based on the transition positions from stages I to II determined in Fig.3.

Fig. 4 .

 4 Fig.4. Microstructure along longitudinal sections in the region of the transition from stage I to

Fig. 5 .

 5 Fig.5. (a) Mean eutectic percentage and (b) mean DAS vs. position along the longitudinal

Fig. 6 .

 6 Fig.6. Microstructure of the transverse sections at two different solidification positions for

Fig. 7 .

 7 Fig.7. Microstructure along longitudinal sections in the GM sample: (a) Section identical to

Fig. 8 .

 8 Fig.8. Schematic patterns of the liquid flow ahead of the dendrite front due to gravity during

Fig. 9 .

 9 Fig.9. Schematic tip growth velocity of two dendrites with different orientations relatively to

Table 1 .

 1 Control parameters for samples solidified under gravity (1g) and microgravity (μg): v n is the furnace pulling velocity, z n the solidification length under v n in stage n, G the initial temperature gradient und R the cooling rate in Stage II.

	Sample Gravity	Initial G, K/mm	Stage I v 1 , mm/s z 1 , mm v 2 , mm/s z 2 , mm R, K/s v 3 , mm/s Stage II Stage III
	GM/FM 1g/µg	0.9	0.01	20	0.01	20	0.067	3
	Both grain refined Al-7 wt.% Si (AlSi7) samples are prepared from a same batch provided by
	Hydro Aluminum GmbH. 0.5 wt% of master alloy AlTi5B was added to the sample for grain
	refinement. Samples have a cylindrical shape with a diameter of 8 mm and a length of 245
	mm. The main solidification parameters, identical for both samples, are summarized in Table

Table 2 .

 2 Processing parameters and average values of both the eutectic percentage (E%) and the dendrite arm spacing (DAS) in each stage of the GM and FM samples. In stage I, the calculated values of G L are constant and only one value of v L is obtained, whereas in stage II, for which an evolution is observed, minimum and maximum values are given.

	Sample	Stage	G L , K/mm	v L , mm/s	E, % DAS, µm
		I	1.0	0.01	44	131
	GM
		Initial part of II	From 1 to 0.6	From 0.01 to 0.06	45	117
		I	0.9	0.01	53	134
	FM
		Initial part of II	From 0.9 to 0.6	From 0.01 to 0.06	48	95

Acknowledgement

This research work is supported by the European Space Agency under the CETSOL (Columnar to Equiaxed SOLidification processes) ESA MAP project (project No.: AO_99_117 -Contract 14313/01/NL/SH), the French National Space Agency (CNES) and the German Federal Ministry for Economic Affairs and Energy (BMWi/DLR) (project No.: FKZ 50WM1443 and FKZ 50WM1743). The authors acknowledge Hydro Aluminium Rolled Products GmbH for providing the alloys used for the experiments.


Adel Thaljaoui
email: adel.thaljaoui@irit.fr

Damien Brulin
email: damien.brulin@laas.fr

Thierry Val
email: val@irit.fr

Nejah Nasri
email: nejah.nasri@isecs.rnu.tn

Real Time Acoustic Localization of Elderly Persons in a Smart Home

Keywords: Home-care, localization, sound, microphone, TDoA

Due to the growing number of elderly people during the last decade, new needs came out especially in term of healthcare, resulting in more demand for self-care and homebased services. The emergence of smart technologies and homebased care has made this possible. In fact, smart home technology is designed to provide a place where old people can live independently as they wish by maintaining a control of every aspect of their daily life. Locating an elderly person in his home at any moment is one of the most concerns of smart home designers. The use of acoustic information captured in the smart home is one of the axes that can bring more possibilities in term of localization. This paper focuses on developing a sound source localization system using microphone arrays. Time difference of arrival (TDoA) using correlation technique is used for estimating the delay between two signals captured by two different microphones. The direction of arrival of the sound source can be obtained using this delay. Finally the sound source is positioned by adopting the geometric location method. This system has been tested by a set of experiments and the results are satisfactory

I. INTRODUCTION

Auditory perception in animals is an innate process that enables them to locate the source of any sound with a precision that can reach ±1° for some species [START_REF] Harold | Auditory Computation[END_REF]. This process is based directly on the operation of animal ears. In the case of Humans, the localization of a coming sound is carried out by combining the slightly deferred acoustic signals that arrive to each ear. Scientific community has focused during the last decade on designing localization systems that could achieve high degrees of precision and reliability as offered by human auditory systems. Therefore, many studies have been performed especially on the field of robotics [START_REF] Valin | Localization of Simultaneous Moving Sound Sources for Mobile Robot using a Frequency-Domain Steered Beamformer Approach[END_REF] [3] [4] [START_REF]Continuous Sound Source Localization Based on Microphone Array for Mobile Robots[END_REF] and [START_REF] Li | Realtime Sound Source Localization for a Mobile Robot Based on the Guided Spectral-Temporal Position Method[END_REF].

One other concern of Scientifics was to build sound localization systems that could operate in indoor environments. Recent studies can be found in [START_REF] Bian | Sound source localization in domestic environment[END_REF] [8] [START_REF] Klee | Kalman filters for time delay of arrival-based source localization[END_REF] [10] [START_REF] Pertila | Acoustic Source Localization in a Room Environment and at Moderate Distances[END_REF] [START_REF] Vacher | Challenges in the processing of audio channels for ambient assisted living[END_REF] and [START_REF] Canclini | Acoustic source localization with distributed asynchronous microphone networks. Audio, Speech, and Language Processing[END_REF]. Many of these studies consider a set of two spaced microphones hooked to a computer and calculate the spatial location of an emitted sound using a set of mathematic methods. One of the most common methods is the estimation of the Direction of Arrival of a sound through the computation of Time Difference of Arrival (TDoA) [START_REF] Mandel | An EM algorithm for localizing multiple sound sources in reverberant environments[END_REF] [15] [START_REF] Woodruff | Binaural localization of multiple sources in reverberant and noisy environments[END_REF].

The aim of our works is to contribute on indoor localization by designing an hybrid localization system that combines acoustic, radio and light information in order to truck the position of an elderly person in a smart home at any moment.

To do so, we had to focus on every one of these three localization approaches as a standalone system (acoustic, radio and light indoor localization systems) in order to figure out the potentially useful signal parameters that we can exploit when designing our hybrid system.

Our first studies deal with the acoustic localization in indoor environments. They consist on the construction and the design of hardware as well as the implementation of an application that returns the location of an acoustic sound at any moment. As a first step, we had used a set of two microphones [START_REF] Thaljaoui | Localisation d'une source sonore par un réseau de microphones[END_REF] for the estimation of the angle of arrival of a sound source. The present paper introduces the second phase of our work on acoustic localization. We use a 4-microphone array for the determination of the geographic coordinates of an acoustic source based on the estimation of the Time Difference of Arrival (TDoA).

II. TIME DIFFERENCE OF ARRIVAL (TDOA)

Perception experiments conducted on humans and animals have been largely discussed and used by many researchers in the field of sound localization. As presented by Blauert [START_REF] Blauret | Spatial Hearing: The Psychophysics of Human Sound Localization[END_REF] and Yost and Dye [START_REF] Yost | Properties of Sound Localization by Humans[END_REF], the fundamental principles of sound localization combine both physics and geometry. Indeed, as the sound spreads out from its source, its power decreases. So, if the distances from the source to each receiver (ear) are unequal, an interaural level difference (ILD) will be noticed. Similarly, knowing the speed of sound in the air [START_REF] Lehrman | Foundations of Physics[END_REF], and considering two spatially separated receivers, sound will travel different distances to each receiver and, therefore, will arrive at different times. Time difference of Arrival (TDoA) is one of the indicators that has been largely used in many localization systems such as radar and sonar for positioning radiating sources.

Let's consider a source that is emitting a sound s(t) and an array of two spatially separated microphones array. Each one of the two microphones is receiving a signal (s 1 (t) for the first and s 2 (t) for the second). Due the distance between the two microphones (Fig. 1), a difference of time between the observations of the sound signal will be noted at each microphone, referred to as Time difference of Arrival. TDoA is computed using the spatial positions of the source and microphones.

III. PROPOSED METHOD AND SPECIFIC ASSUMPTIONS

The present paper introduces a method of localization of an acoustic source within a frequency spectrum of 22Hz to 22KHz using an array of two microphone pairs. By localization, we mean the determination of the spatial coordinates of the source in a 2D space. The first step consists on estimating the time difference of arrival (TDoA) of the signals captured by two separated microphones. Then, the direction of arrival of the sound with respect to the microphones array is computed using trigonometry specifications. This first step was presented in [START_REF] Thaljaoui | Localisation d'une source sonore par un réseau de microphones[END_REF]. The second step consists on localizing the acoustic source using a 4-microphone array. The process consists on merging the results obtained with each microphones couple in term of direction of arrival and then use a specific geometric positioning method in order to compute the geometric coordinates of the acoustic source in a 2D space.

Our method is designed under a set of assumptions: (1) only one acoustic source is located (2) We suppose that no Doppler shift will be detected meaning that there will be no obstacles that may change sound characteristics (3) Noise is White Gaussian (4) The set of microphones that we are using are Electret (5) we already know the spatial positions of microphones and (6) the distance between sound source and receivers is so big that we can consider that sound waves are planar.

IV. PHASE 1: ESTIMATION OF THE DIRECTION OF ARRIVAL OF

AN ACOUSTIC SOURCE This first step was published in [START_REF] Thaljaoui | Localisation d'une source sonore par un réseau de microphones[END_REF]. We considered a system of two microphones and a sound source placed outside the perpendicular plane to the line passing through these two microphones and crossing through their middle (Erreur ! Source du renvoi introuvable.). Therefore, the wavefront of the sound source reach the two microphones with a slight time difference or delay, depending on the arrival angle of the source. The maximum value that this delay can tell about a sound source located on the same line through the two sensors (0° or 180°).

Our aim was to find the angle θ corresponding to the direction of arrival of the wave emitted by the sound source. We assume that θ ∈ 0, π .  v = (331 + 0.6 × T) ms -1 ; where v is the speed of sound, in meters per second and T is the ambient temperature, in degrees Celsius. This approximation holds true for conditions near room temperature and pressure.

 TDoA also called τ..

In order to determinate the angle θ, we used trigonometry formulas for right triangle with d is the adjacent leg and D (distance between the two microphones) is the hypotenuse:

 cos 𝜃 = 𝑑 𝐷  
We know that for a distance d (Fig. 1), le speed of the acoustic wave is calculated using this formula:

𝑣 = 𝑑 𝜏 𝑑 = 𝜏 × 𝑣  (2) becomes: 𝑐𝑜𝑠 𝜃 = 𝜏×𝑣 𝐷 Therefore:  θ = cos -1 𝜏×𝑣 𝐷  
In order to find the direction of arrival (angle θ) of a sound wave, we proceed as follows:

 We first record the sound s(t), then we sample this signal according to a sampling frequency Fs (s(n)).

The two sampled signals corresponding respectively to each microphone (s 1 (t) and s 2 (t)) will be discerned.

 We then compute the cross-correlation between the two signals s 1 (t) and s 2 (t)

 We search the temporal position of the maximum of the cross correlation and therefore we identify the delay τ  We determine the angle θ

A. Acoustic sound recording

In this first step, we record the sound observed by the array of two microphones that we designed (Fig. 2). This signal is then sampled according to a sampling frequency Fe. The two microphones are connected to the computer through a stereo jack cable where left and right lane correspond respectively to the microphones 1 and 2. The two signals related to the two microphones are then returned.

B. Cross-corrélation & TDOA (τ) Estimation

There are many algorithms that can be used to calculate approximately the TDoA [START_REF] Carter | Coherence and time delay estimation: an applied tutorial for research, development, test, and evaluation engineers[END_REF]. The cross-correlation (CC) method is one of the basic keys of this problem.

The estimated delay is obtained by finding the time-lag that maximizes the cross-correlation between the two observed signals [START_REF] Omologo | Acoustic event localization using a crosspower-spectrum phase based technique[END_REF]. Indeed, the signals observed by the two microphones are time shifted versions compared to each other. Therefore, in order to determine the direction of arrival of the sound source we need to detect the temporal point at which the two captured signals are at their maximum correlation. In this point, the two signals are at their closest match when they are superimposed on each other.

When the signals are continuous, the cross-correlation function can be expressed by:

 𝐶 𝑠1𝑠2 (𝜏) = 𝑠 1 𝑡 𝑠 2 𝑡 -𝜏 𝑑𝑡 +𝑇 -𝑇

 

In our case, the observed signals are sampled, the expression that we use is as follows:

 C s1s2 (τ) = s 1 n s 2 n -τ N-1 n=0

 

where N is number of samples.

The idea is to scan the first captured signal according to an increasing time axis (i) while the second signal travels the time axis in the opposite direction (-i). That's why the two compared signals should have the same length. In MATLAB, the cross-correlation of two signals, x and y (length x = length(y)), is a vector of length= (2 × length x -1) [START_REF] Gu | A sound-source localization system using three-microphone array and crosspower spectrum phase[END_REF].

Once we have found the cross-correlation peak (delay τ between the two captured signals), we can deduce the temporal position of this maximum by applying the argument function on the maximized cross-correlation.

 𝜏 = 𝐴𝑟𝑔𝑚𝑎𝑥(𝐶 𝑠1𝑠2 )     V. PHASE 2: DETERMINATION OF THE SOURCE SPATIAL

COORDINATES

The aim of our acoustic source localization method is to be able to determine its 2D coordinates.

To do so, we consider the following layout: According to the assumptions we had already made, the spatial coordinates of the 4 microphones are known. Therefore, since we are able to estimate the angles θ 12 and θ 34 using the first step of our proposed method, we can calculate the spatial coordinates of the point of intersection of the two lines crossing the sound source with respectively microphone 2 and microphone 4 (D1 and D2).

Let's consider the two equations ( 7) and ( 8 To do so, we need to determinate the equations of these two straight lines. One of the mathematical solutions is to determine two points of each line and then compute their coefficients.

The coordinates of the acoustic source are than deduced through the resolution of the equation of intersection of the two equations above.

VI. EXPÉRIMENTATION

A. Performances of the proposed method

In order to evaluate the accuracy and the precision of the proposed method, we analyze the theoretic error E that we get while estimating the angle θ .

 E = θ -θ  

This error is calculated by varying the variance of the Additive White Gaussian Noise AWGN from 10dB to 10dB by 1dB steps. For more precision, we use the average of the error computed for 200 estimations of the angle θ.

Signal-to-noise ratio (SNR) is an indicator of the quality of information transmission by comparing the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power (dB): The theoretical average estimation error that we obtained is about 5°, which is considered a good result for our case.

B. 2-Microphone array MATLAB Programming

In order to test our method, we required a set of hardware including an array of microphones and a recording device (typically a sound card) as well as specific software to be used for recording and processing the acoustic signals observed by the microphones in order to discern relevant information.

Therefore, we designed a block of two microphones (D = 30cm) that we fixed as shown in Fig. 4. The sound source was a Smartphone emitting a continuous sound. We developed then a MATLAB application (Fig. 5) that estimates the angle θ for many theoretical arrival directions as well as different values of Ds (distance between the sound source and the microphones array). For more precision, we averaged the angle θ for 50 iterations(Fig. 6). For each one of the 50 estimations of the angle θ, we computed the standard deviation. According to the Nyquist Sampling Theorem, " If a timevarying signal is periodically sampled at a rate of at least twice the frequency of the highest-frequency sinusoidal component contained within the signal (in our case fmax=22Khz), then the original time-varying signal can be exactly recovered from the periodic samples". Thus, we chose a sampling frequency Fs = 44100Hz.

We varied Ds (0.5 -1 -1.5 -2 -2.5 -3 m). The estimations of the direction of arrival are obtained for five theoretical positions of the angle θ (0 ° -45 ° -90 ° -135 ° -180 °) with a mean error of 3°, which is considered a good result.

C. Two pairs of Microphone array experimentation

The aim of the second part of our method is to determine the spatial location of the acoustic source by calculating its geographic coordinates in a 2D space.

As mentioned above, in order to perform this phase, we consider an array of two pairs of microphones, two computers, one Smartphone emitting a continuous sound.

Every pair of the microphones is hooked to a computer. We place the Smartphone in a already known position as shown in Fig. 7. We then run simultaneously in the two computers the software we already prepared in the first step in order to determine for each microphone pair the angle of arrival of the sound emitted by the Smartphone. The obtained values of the two angles are automatically stored in two separated excel sheets for later use.

We performed a set of tests using the designed hardware as well as the developed application ( Fig. 8). This application reads the stored data from the two computers and returns the geographic position of the sound source using its estimated angles of arrival with the two pairs of microphones. This application works satisfactorily (Fig. 9). In fact, the error between the estimated positions and the real ones can be explained by the assumptions we had made (see Table 1).

VII. CONCLUSION AND FUTURE WORK

We have introduced in this paper, a method for positioning an acoustic source in a 2D space using an array of two pairs of microphones. We first computed for each pair of microphones the direction of arrival of the emitted sound (phase 1). Therefore, we estimated the time difference of arrival TDoA between the two sound signals observed by each microphone of the considered pair. In the second phase, we merged the results obtained simultaneously for each pair of microphones (in the first phase) in order to determine the spatial coordinates of the source.

In order to test our method, we carried out a set of experiments using the microphones array that we had already designed as well as a software that we developed using MATLAB. The results seem to be satisfactory.

Actually, as mentioned above, the method that we propose in this paper is based on a set of assumptions. One of these assumptions is that the environment we are working in represents no noise nor reverberations nor echoes. That is why, we used the cross correlation method to determine the delay τ which works good in such conditions. But, in real environment, this method is no longer suitable [START_REF] Valin | etourneau, Robust Sound Source Localization Using a Microphone Array on a Mobile Robot[END_REF]. One of the common solutions is to consider the Generalized Cross Correlation (GCC) instead of the CC. Indeed, GCC transforms the signals from time domain to the frequency domain using Fourier transformation.

For a better accuracy, a weighting function or filter can be used in order to sharpen the peak of correlation (Fig. 10). The most common weighting functions are the phase transform "PHAT", the maximum likelihood "ML", the least mean square adaptive filter "LMS", SCOT, ROTH, ... As a continuation to our work, we are planning to compare these methods in order to figure out which one suits more to our case of study.

Besides, we intend to work jointly on radio and light localization methods to propose an hybrid localization system exploiting radio (Ibeacon BLE), light (LiFi) and audio (this present work) relevant information, in order to take advantage of these systems depending on the position of the person to locate.

Fig. 1 .

 1 Fig. 1. Time Difference of Arrival (TDoA)

  We consider : D s = distance between S and Mic 2  D s -d = distance between S and Mic 1  v : speed of sound in air that can be approximated as (Laplace formula):

Fig. 2 .

 2 Fig. 2. Our designed 2-microphone array

Fig. 3 .

 3 Fig. 3. Two 2-microphone pairs array

  ) as the respective equations of D1 and D2:  𝑦 = 𝑎 12 𝑥 + 𝑏 12     𝑦 = 𝑎 34 𝑥 + 𝑏 34   Where (a 12 , b 12 ) and (a 34 , b 34 ) are the respective couple of coefficients of each line.

  P signal = Power of the original signal ang P WGN = power of the White Gaussian Noise.Let's consider WGNinit an initial White Gaussian Noise (mean=0 and variance=1). WGN init = randn(1, N est )  Here Nest is the number of estimations of the angle θ (In our simulations we considered Nest=200)The idea is to add to the original signal a White Gaussian Noise WGN with a null mean and a variance σ² : WGN = σ × WGN init P WGN = σ² × P WGNinit RSB = 10 ×

Fig. 4 .Fig. 5 .

 45 Fig. 4. First phase experimentations

Fig. 6 .

 6 Fig. 6. 50 estimations of the angle θ for different Ds

Fig. 7 .Fig. 8 .

 78 Fig. 7. Real positions of the acoustic source during the experimentation

Fig. 10 .

 10 Fig. 10. Estimation of TDoA using the GCC method

TABLE I

 I

		.	EXPERIMENTAL RESULTS
	Real angles	Real	Estimated angles	Estimated
	(°)	positions (m)	(°)	positions (m

) θ12 theo θ34 theo X theo Y theo θ 12 esti θ 34 esti X esti Y esti

	90	45	1	1.3	94.15	39.03	0.946	1.25
	90	135	1	2.3	95.9	135.048	0.831	2.132
	90	90	1	1.8	84.078	89.554	1.13	1.79
	45	45	1.4	0.9	44.61	41.77	1.35	0.84
	45	90	2.3	1.8	53.28	87.38	1.92	1.735

Fig. 9. Acoustic source estimated positions vs theoretical positions


Y Zhou

E Rupnik

P-H Faure

M Pierrot-Deseilligny

GNSS-assisted accurate corridor mapping with small UAV

Keywords: précision, automatisation, UAV, GNSS, point d'appui au sol accuracy, automation, UAV, GNSS, ground control point

Avec le développement des véhicules aériens sans pilote (UAV) et du système de positionnement par satellites (GNSS), les positions précises de la caméra à l'exposition peuvent être connues et l'approche ajustement de faisceau (BBA) assisté par GNSS est devenu possible pour l'orientation des images. L'estimation de multiples bras de levier dans la procédure BBA permet de fusionner des blocs d'images de différentes configurations telle que des images nadir et obliqueset ainsi obtenir une meilleure précision. En raison du coût substantiel de l'établissement d'un réseau de points d'appui (GCP), un nombre minimal de GCPs est attendu tout en maintenant la précision. En ajoutant un bloc d'images oblique au bloc d'images nadir ou en fusionnant des blocs d'images nadir de différentes hauteurs de vol, une précision de ∼ 5 cm est atteinte sans GCP sur une scène d'acquisition corridor de ∼ 600 m. Cette précision est également obtenue avec uniquement un bloc d'images nadir en fournissant une bonne calibration a priori de la caméra . Avec un GCP au milieu du bloc d'images, la précision verticale est significativement améliorée et une précision de ∼ 1.0 cm est atteinte.

Introduction

For traditional airborne photogrammetry with unmanned aerial vehicles (UAVs), the exterior orientation (EO) parameters are determined indirectly using the well-known method bundle block adjustment (BBA). The BBA method is effective and widely employed for photogrammetric production when the scene is well-textured and allows for automated tie point extraction.

3D point accuracy are strongly dependent on the geometry of acquisition field and the number of ground control points (GCPs) as well as their distribution within the image block [START_REF] Remondino | Uav photogrammetry for mapping and 3d modeling-current status and future perspectives[END_REF][START_REF] Vallet | Photogrammetric performance of an ultra light weight swinglet uav[END_REF]. Among different configurations of UAV acquisitions, the corridor mapping has a high potential in such as dike surveillance, highway planning and power line surveys. Nevertheless, it can also be challenging in many aspects. With the special geometry, a well-distributed GCP network is not easy to ensure. The acquired images are often in strips, which makes it difficult to have satisfying sidelaps and thus results in less accurate EO parameter determination. While the employment of a large number of GCPs prevents model distortion, the field work of ground control point establishment can be substantially expensive and time-consuming.

With the appearence and development of global navigation satellite system (GNSS), it is possible to know the accurate camera perspective center positions at exposure and thus to eliminate the requirement of GCPs within the image block [START_REF] Rehak | Fixed-wing micro aerial vehicle for accurate corridor mapping[END_REF][START_REF] Skaloud | Mapping with mav : Experimental study on the contribution of absolute and relative aerial position control[END_REF]. However, several GCPs are still used for the purpose of improving the redundancy and identifying possible bias in GNSS positioning [START_REF] Ackermann | Operational rules and accuracy models for gps-aerotriangulation[END_REF][START_REF] Heipke | Integrated sensor orientation : Test report and workshop proceedings[END_REF]. When coupling this GNSS-assisted bundle block adjustment approach to an inertial navigation system (INS), the EO parameters can be determined directly for each image without auxiliary information coming from the traditional AT procedure. For small UAVs, an accurate position and attitude aerial control remains challenging due to the limited availability of weight, power and volumn in the UAV payload.

Different researches have been carried out to mitigate errors in INS/GNSS system. The linear offset lever-arm can be determined indirectly by computing the difference between GNSS-derived positions of antenna reference point and camera perspective centers resulting from bundle block adjustment [START_REF] Ellum | Inexpensive kinematic attitude determination from memsbased accelerometers and gps-derived accelerations[END_REF]. This offset can also be estimated as an additional parameter during the bundle block adjustment whereas the accuracy is limited due to its correlation with camera interior orientation parameters [START_REF] Skaloud | High accuracy handheld mapping system for fast helicopter deployment[END_REF][START_REF] Lichti | On the calibration strategy of medium format cameras for direct georeferencing[END_REF]. While with classical methods (by a calliper or by photogrammetric approaches) the linear offset lever-arm can be determined, it is not possible for the boresight calibration to reach sufficient accuracy in the same way. Several boresight calibration methods have been proposed [START_REF] Skaloud | Exterior orientation by direct measurement of camera position and attitude[END_REF][START_REF] Kruck | Combined imu and sensor calibration with bingo-f[END_REF][START_REF] Cramer | System calibration for direct georeferencing[END_REF][START_REF] Mr Mostafa | Camera/imu boresight calibration : New advances and performance analysis[END_REF]. It can be performed either with "one-step" method (estimation within self-calibration process) or with "two-step" method (comparison of the INS/GNSS-derived attitude with that obtained by AT procedure). Moreover, taking into account the remaining temporal correlations within the navigation system can lead to a more realistic estimation [START_REF] Skaloud | Towards a more rigorous boresight determination : Theory, technology and realities of inertial/gps sensor orientation[END_REF]. Despite the possibilities of improving the INS/GNSS system accuracy, the INS system demands more effort to reduce errors and often needs accurate GNSS positions as constraints for error control. This demand on precision and thus on high quality of INS/GNSS sensors can be complicated given the limited UAV payload capability.

Therefore, for small UAV photogrammetric acquisitions, the assisted bundle block adjustment with GNSS data and GCPs seems to be a more interesting approach. Given the substantial inconvenience and cost of GCP establishment especially in areas with difficult access, the number of GCPs is needed to be reduced to a strict minimum.

The research results of V. Tournadre [START_REF] Tournadre | Métrologie par photogrammétrie aéroportée légère : application au suivi d'évolution de digues[END_REF] showed that for corridor mapping performed with small UAVs, by optimising the camera model and combining nadir and oblique images, a centimetric accuracy is attained with one GCP every 100 m. With embedded GNSS module on small UAVs, the GNSS-derived camera positions at exposure is used for integrated sensor orientation (ISO) of camera pose [START_REF] Daakir | Lightweight uav with on-board photogrammetry and single-frequency gps positioning for metrology applications[END_REF]. An accuracy of a few centimeters is reached with one single GCP.

Problem Formulation

With the development and increasing employment of UAVs in photogrammetric production as well as the possibility of knowing accurate camera perspective center positions with the aid of GNSS system, the need of well-distributed GCP network within the image block can be eliminated and only a few GCPs are required to improve the redundancy and to identify possible bias in GNSS positionning. Given the special geometry, corridor mapping has a higher demand on the quality of GCP network whilst the establishment can be expensive and time-consuming. In this paper, a UAV acquisition of a dike is presented and the accuracy of this corridor configuration that can be obtained with a small number of GCPs is investigated.

Paper Structure

The following part of this article gives brief introduction of the employed UAV system and sensors. In section 3 the nature of the acquisition field is described and the information of conducted flights are presented. The following section is devoted to the data processing pipeline with the focus on the integration of GNSS data and its improvement on tie point extraction efficiency. Finally, the results of conducted acquisitions are presented and the mapping accuracy is evaluated. Conclusions are drawn in the last section, as well as recommendations for further investigations.

System Design

UAV

The chosen UAV is a Copter 1B of SURVEY Copter which is robust and reliable. It has a wingspan of 1.82 m and a length of 1.66 m. Powered by a gasoline engine, the maximal payload capacity of the UAV is 4.1 kg and the endurance is up to 60 min.

Camera

The chosen camera for data acquisition, a home-made metric camera CamLight, is designed specifically to meet the needs of photogrammetric UAV acquisitions by laboratory LOEMI 1 of IGN 2 [START_REF] Martin | Réalisation d'une caméra photogrammétrique ultralégère et de haute résolution[END_REF]. The compact camera body without lens has a low mass of 160 g and is compatible with most commercially available lenses. Within the acquisition, the camera is equipped with a full frame sensor of 5120×3840 pixels and a 35 mm lens (140 g). The camera is triggered with an intervalometer every 2.5 s and powered by the onboard power system.

GNSS Receiver

The chosen GNSS receiver is a GPS monofrequency receiver with L1 GPS antenna and is integrated to the camera system. The GPS time of exposures is provided by the GPS module and is registered in the header file for The aforementioned hardwares are presented in Figure 1.

Flight Design

According to the flight autorization issued by the DGAC 3 , the distance between the telepilot and the UAV employed for the acquisition can not surpass 600 m. Therefore, the acquisition field is divided into 2 segments of 600 m and surveyed separately. The first segment of 600 m consists of the south part of the dike while the second segment consists of the rest of the dike including the turn on the north end. Figure 2 depicts the conducted flights and the information of flights are given in Table 1.

Synchronization of GNSS and Camera System

The GNSS data is post-processed using RTKLib in carrierphase differential mode with respect to a base station installed on the south end of the dike. The position of this base station is precisely determined by processing a ∼ 24 hour static observation session over two days with the service provided by IGN. With a sampling frequency of 1 Hz, one position is calculated every second. Nevertheless, the frequency of image acquisition is of 0.4 Hz, which introduces a desynchronization between GNSS and camera system. So as to determine the position of the camera at exposure, a parabolic interpolation is carried out taking into account the GNSS-derived position accuracy and velocity. Figure 3 depicts the desynchronization between the two systems ; circles in blue represent GNSS-derived positions and pyramids represent camera frames. For an image block of 395 images acquired with flight F1, the tie point extraction will be performed on 77815 image couples if no a priori information of camera positions is given, the computation procedure takes ∼ 5 h. While with the above-mentioned two iterations of tie point extraction, the computation only took 2h15min.

The IO/EO parameters in a relative scale are determined with a hybrid internal model coupling a high degree correction of radial distortion (up to R 15 ) and a general polynomial one for empirical distortion correction. Camera positions are then employed for transformation into an absolute scale. An absolute bundle block adjustment is performed with tie points, GNSS-derived camera positions and GCPs as observations.

The mathematical model of the performed absolute bundle block adjustment is presented as follows. The objectif is to minimize a global energy function :

E = L l=1 M m=1 (p l,m -ζ(π(R m (P l -C m )))) σ A im 2 (1)
+ Z z=1 K k=1 (R k (C k -C gnss,k ) -θ z ) σ gnss 2 (2)
+ N n=1 (P n -P gcp,n ) σ gcp 2 (3)
+ N n=1 M m=1 (p n,m -ζ(π(R m (P gcp,n -C m )))) σ H im 2 (4)
where : l is the index of tie points ; m is the index of images ; z is the index of image blocks defined by lever-arm ; The global energy function is composed of 4 parts : (1) the energy of tie points, (2) the energy of GNSS measurements, (3) the energy of GCPs and ( 4) the energy of image measurements of GCPs. The minimization problem is solved with Levenberg-Marquardt (L-M) method. The L-M is in essence the Gauss-Newton method enriched with a damping factor to handle rank-deficient Jacobian matrices [START_REF] Wright | Numerical optimization[END_REF].

k
Within the procedure, the lever-arm for each image block is determined as an additional parameter of the model. When flights of different configurations are merged and processed, one lever-arm per image block is estimated. This makes it possible to merge image block datasets acquired on the same acquisition field while having different configuration (e.g., nadir and oblique images, etc...)

The accuracy is evaluated with CPs and the root-meansquare (RMS) of check point residuals is used as the accuracy criteria. Figure 4 depicts the aforementioned data processing pipeline.

Combination of Flights

Several combinations of flights are investigated to benefit the presence of different configurations. The information of different flight combinations is given in Table 2.

With the combination C1, a better sidelap and a greater angle of perspective ray intersections are provided with the existence of oblique images, which is recommanded

Segment Flight C1 S2 F2 + F4 C2 F2 + F3 + F4 C3 S1 F1 C4 S1 + S2 F1 + F2 + F3 + F4 TABLE 2 -Information of flight combinations
for acquisition scenes of little height difference [START_REF] Clives Fraser | Limiting error propagation in network design((in photogrammetry))[END_REF][START_REF] Triggs | Autocalibration from planar scenes[END_REF]. By comparing the obtained accuracy of combination C1 and C2, the impact of including images of different heights is investigated. For combination C3 with only nadir images, the results with and without a priori camera calibration are compared. Combination C4 gives an indication of how accuracy varies when the length of acquisition field changes and the achievable accuracy with a few GCPs. Results for each flight combination is given in Table 3 For C1 and C2, the only GCP used is point C as shown in Figure 2 and the rest are used as CPs to evaluate the accuracy. For C1, the bundle block adjustment is performed with tie points, GNSS-derived camera positions (with and without point C as GCP) as input. For C2, a bias on vertical component is observed on GNSS-derived camera positions for F3 and a proper estimation of the lever-arm for this flight is not feasible. Therefore these GNSS-derived camera positions are eliminated from the following bundle block adjustment. The differences on accuracy between V1-V2 and V3-V4 show that, with only tie points and GNSS-derived camera positions the model is less accurate on vertical component than on horizontal one. This is mainly due to the small height difference on acquisition scene. Adding at least one GCP will improve the accuracy especially on vertical component. By investigating the difference on accuracy between V1-V3, an improvement is observed on vertical component after including tie points from flights of different heights. It can be explained by the fact that the IO/EO parameters are better de-correlated. However, the difference of accuracy between V2-V4 shows that the accuracy declines slightly by only adding tie points of different flight heights without adding the corresponding GNSS-derived camera positions.

The newly added images are not perfectly oriented under the constraints of tie points and one GCP, which also reflects the impact of GNSS-derived camera positions on 3D point accuracy.

Point A is used as GCP for C3 dataset. V5 and V6 are processed without the self-calibration step, i.e., IO parameters are not determined a priori. V7 and V8 are processed with the IO parameters coming from V2 and the IO parameters are fixed during the determination of EO parameters. In the configuration of V5 only tie points of nadir images and GNSS-derived camera positions are used for bundle block adjustment and no a priori camera calibration is provided, the addition of oblique images (V1) does not have great impact on horizontal accuracy whereas improves considerably the vertical accuracy since the inclusion of oblique images enhanced the sidelap and increased the intersection angle between perspective rays. The inclusion of point A as GCP (V6) in the bundle block adjustment renders better determination of the focal length and then a better vertical accuracy compared to V5. The difference between V5 and V7 indicates the importance of a good camera calibration.

For C4, point B is used when one GPS is included in bundle block adjustment whilst point A and C are used for two GCPs configuration. The camera calibration of V2 is provided and fixed during the bundle block adjustment. For a corridor configuration of ∼ 1200 m, a 3D point accuracy of 2cm is reached with one GCP by performing the GNSSassisted bundle block adjustment.

Conclusion

The GNSS-assisted bundle block adjustment makes it possible to eliminate the requirement of GCPs for EO parameter determination. The use of a few GCPs improves the redundency and identifies possible bias in GNSS positionning. Due to the substential cost of field work, the number of GCPs is expected to be a minimum while maintaining the accuracy.

Several flights are conducted on a dike of ∼ 1200 m of which the corridor geometry and the little height difference remain challenging for photogrammetric acquisitions. By investigating results of different image block configurations, the following conclusions are drawn.

When performing the GNSS-assisted bundle block adjusment without GCPs to a nadir image block, the vertical accuracy is not ensured mainly due to the little height difference of the acquisition field. The inclusion of oblique images enhanced the sidelap and increased the intersection angle between perspective rays. The addition of images of different height flights rendered a better de-correlation of IO/EO parameters. Both these two strategies mitigated the vertical inaccuracy and the 3D point accuracy is ∼ 5.0 cm. Given a good camera calibration, the 3D point accuracy of ∼ 5.0 cm is achieved with solely nadir images. To further improve the accuracy (especially on vertical component), one GCP located in the center of the image block is used and the 3D point accuracy reached ∼ 1.0 cm. For the corridor acquisition scene of ∼ 1200 m, the 3D point accuracy is 2 cm with one GCP in the middle and 1.2 cm with 2 GCPs.

Because of the observed bias on vertical component for F3, the GNSS-derived camera perspective positions are not exploited during the bundle block adjustment procedure. In further studies, the impact when adding images of different flight heights and corresponding GNSS measurements should be investigated thoroughly.

1 .

 1 Laboratoire d'Opto-éléctrique et de Métrologie et d'Instrumentation 2. Institut National de l'Information Géographique et Forestière each image. Within the acquisition, the GPS module works at 1Hz frequency.

FIGURE 1 -

 1 FIGURE 1 -CamLight (left), camera set-up on UAV (middle), UAV (right)

FIGURE 2 - 1 TABLE 1 -

 211 FIGURE 2 -An illustration of executed flights The segment 1 (S1) is surveyed with one nadir flight of 3 strips at 50 m (F1) while the segment 2 (S2) consists of 3 flights (F2-F4). F2 (nadir) and F4 (oblique) share the same configuration with F1. F3 is a nadir flight of 2 single strip at different heights (30 m and 70 m) to better de-correlate IO/EO parameters.3. Direction Générale de l'Aviation Civil

FIGURE 3 -

 3 FIGURE 3 -An illustration of the desynchronization between GNSS (blue circles) and camera (pyramid) system

FIGURE 4 -

 4 FIGURE 4 -Data processing pipeline

  is the index of images with GNSS measurements ; n is the index of GCPs ; ζ is the camera model ; π is the projection function ; p l,m is the 2D position of tie point l in image m ; (R m , C m ) is the pose of image m ; P l is the 3D position of tie point l ; C k is the camera perspective center of image k ; C gnss,k is the phase center of GNSS antenna of image k ; R k is the world to camera rotation ; θ z is the lever-arm of image block z ; P n is the pseudo-intersection position of GCP n ; P gcp,n is the ground measurement of GCP n ; p n,m is the image measurement of GCP n in image m ; σ A im is the weight of tie points in images ; σ gnss is the weight of GNSS measurements ; σ gcp is the weight of GCPs ; σ H im is the weight of image measurements of GCPs ;

  .

		Comb GCP GNSS	RMS (cm) horizontal vertical 3D
	V1 V2 V3 V4	C1 C2	0 1 0 1	F2 + F4	1.7 0.6 2.0 0.8	8.5 0.7 4.5 0.9	8.7 0.9 4.9 1.2
	V5		0		1.6	20.2	20.3
	V6 V7	C3	1 0	F1	1.4 1.3	1.5 4.8	2.0 5.0
	V8		1		1.2	0.7	1.4
	V9		0	F1	1.4	5.4	5.5
	V10	C4	1	+	1.4	1.4	2.0
	V11		2	F2+F4	1.0	0.7	1.2

TABLE 3 -

 3 Residuals on check points