Christophe Roche
email: christophe.roche@univ-savoie.fr

Luc Damas
email: luc.damas@univ-savoie.frwww

Julien Roche

Multilingual Thesaurus: The Ontoterminology Approach

Making collections accessible to users speaking different languages raises several issues among which the multilingualism problem. Finding equivalent terms as well as mapping thesauri require a common conceptualisation or at least "compatible" conceptualisations.

In that context, ontology of the knowledge engineering, defined as a formal specification of a domain conceptualization, is one of the most promising perspectives for the concept system of thesaurus and terminology. By distinguishing the two conceptual and linguistic dimensions, such an approach enables a more comprehensive understanding of the domain, and a more precise description of collections in relation to the domain knowledge. It also enables to improve search functionalities by using both the linguistic relationships between terms and the logical properties of the relationships between concepts. At last, mapping thesauri can gain benefits from works on ontology alignment.

Dans ce contexte, l'ontologie au sens de l'ingénierie des connaissances, définie comme une spécification formelle d'une conceptualisation, constitue une des voies les plus prometteuses pour la représentation du système conceptuel des thesaurus et des terminologies. En distinguant les dimensions conceptuelle et linguistique, elle permet une meilleure compréhension du domaine amenant à une description plus précise des contenus au regard des connaissances du domaine. Elle permet d'exploiter pour la recherche d'information aussi bien les relations linguistiques entre termes que les propriétés logiques des relations entre concepts. Enfin, elle fait bénéficier la mise en relation de thesaurus des résultats des travaux menés sur l'alignement d'ontologies.

L'approche ontoterminologique des thesaurus (une ontoterminologie est une terminologie dont le système notionnel est une ontologie formelle) a été mise en oeuvre dans le cadre d'un 1 er projet européen de gestion de contenus multilingues (ASTECH). Elle est aujourd'hui utilisée au sein de projets liés au secteur culturel (Linked Heritage, Athena Plus) et au partage de connaissances multilingues (SIERA, Université de Liaocheng).

L'article est illustré avec l'environnement OTe-for-Thesaurus qui permet, sur la base du modèle ontoterminologique, l'import et l'export de thesaurus au format d'échange SKOS, la création, l'édition et l'alignement de thesaurus dans le respect des normes ISO 25964-1 et -2.

The ontoterminology approach of thesaurusan ontoterminology is a terminology whose conceptual system is a formal ontologyhas been deployed in the framework of a first European project for multilingual document management system (ASTECH). It is now involved into different European projects dedicated to cultural heritage (Linked Heritage, AthenaPlus), to multilingual knowledge sharing (SIERA) and to multilingual terminology (University of Liaocheng). This approach is illustrated with OTe-for-Thesaurus, a thesaurus editor based on ontoterminology. In accordance with the ISO 25964-1 and 25964-2 Standards on Thesaurus, the OTe-for-Thesaurus provides functionalities for creation, editing, and mapping thesauri. Based on the SKOS interchange format, it also allows importing and exporting thesauri. The TMP2, stands for Thesaurus Management Platform version 2, is the version of OTe-for-Thesaurus developed for the AthenaPlus European project.

Résumé:

Rendre accessibles des collections à des utilisateurs parlant d'autres langues soulève entre autres le problème de la prise en compte du multilinguisme. La recherche d'équivalents linguistiques tout comme la mise en relation de thésaurus supposent une conceptualisation du domaine commune ou du moins des conceptualisations "compatibles".

Introduction

Opening and linking data in a global and multilingual world are among the most important challenges of the new century [Linked Data] [ [START_REF] Hyvonen | Publishing and Using Cultural Heritage Linked Data on the Semantic Web[END_REF]]. From a thesaurus point of view, they raise several issues among which multilingualism management and mapping thesauri. Making collections accessible to users speaking different languages require a shared conceptualization -or at least "compatible" conceptualisationsof the domain. The notion of concept is become the core element of thesaurus as the last versions of the ISO Standards highlight it [ISO 25964-1], [ISO 25964-2].

In that context, Ontology coming from Knowledge Engineering and defined as a "formal specification of a domain conceptualization" [Gruber 92], i.e. a set of concepts linked by logical relationships, is one of the most promising perspectives for Thesaurus. By distinguishing the two conceptual and linguistic dimensions, such an approach enables a more comprehensive understanding of the domain, and a more precise description of collections in relation to the domain knowledge. It also enables to improve search functionalities (precision and recall) by using both the linguistic relationships between terms and the logical properties of the formal relationships between concepts. At last, mapping thesauri can gain benefits from works done on ontology alignment. But an ontology is not a thesaurusneither a terminologyeven if ontology can be used for information management and information retrieval [START_REF] Kiryakov | Semantic Annotation, Indexing, and Retrieval[END_REF]] [Fernandez et al. 2011]. Ontology does not include a linguistic dimension: a concept is an extra-linguistic knowledge. It means that a concept cannot be reduced to terms that designate it. As a matter of fact, the conceptual system does not match with the lexical system [START_REF] Roche | Saying is not Modelling[END_REF]].

It remains to combine Ontology and Terminology in one paradigm for thesaurus purposes. This leads to the notion of Ontoterminology (a terminology whose conceptual system is a formal ontology) whose application to Thesaurus opens new perspectives both for information retrieval and mapping thesauri.

The structure of the article is fourfold. The next section focuses on the notion of concept as it is specified by the ISO Standards on Thesaurus and Terminology. The second section is about ontology from the Knowledge Engineering point of view. The third one is dedicated to ontoterminology, its principles, and its application to thesaurus. The article ends with the presentation of OTe-for-Thesaurus, an ontoterminology-oriented thesaurus environment.

Concept in Thesaurus and in Terminology

Concept in Thesaurus

The "Overall objective" section of the ISO 25964-1 Standard on Thesaurus starts by these first sentences: "The traditional aim of a thesaurus is to guide the indexer and the searcher to choose the same term for the same concept. In order to achieve this, a thesaurus should first list all the concepts that might be useful for retrieval purposes in a given domain. The concepts are represented by terms, and for each concept, one of the possible representations is selected as the preferred term." The concept is therefore the core element of thesaurus: "a thesaurus should first list all the concepts […] in a given domain".

Such an importance given to the concept finds its roots in its extra-linguistic nature. A concept is an abstract entity independent of terms that designate it. Indexing on concepts enables information retrieval on the meaning of terms rather than on the terms themselves; i.e. on concepts not on keywords. Hence, multilingualism can be easily managed insofar users share the same conceptualization. It means that different terms in different languages can be attached to the same concept (figure 1). Focusing is done on understanding of the domain, rather than on the way one speaks about it.

Figure 1. Different vocabularies sharing a common conceptualisation

Although the concept is the central element of Thesaurus, it is simply defined as a "unit of thought" without specifying its characteristics. The notion of "definition" in the literal sense 1 does not exist in ISO 25964-1the DEF (for definition) note is only a linguistic explanation.

In Thesaurus, a concept finds its meaning through its relationships with the other concepts. The hierarchical relationships (generic, whole-part, instance) allow to express a subordination level between concepts. The generic relationship links two concepts whose one is more specific than the other, e.g. <Wrist Watch> is a kind of <Watch>, when the whole-part relationship links two concepts whose one is a part of the other considered as a whole, for example <Mechanical Movement> is a part of <Mechanical Watch>. The instance relationship links a concept to one of its individual instances, like /Longines/ is an example of <Watch Brand>. These three kinds of hierarchical relationships are not always distinguished, gathered under the same BT/NT tags (Broader Term/Narrower Term), under the pretext that "The extra work and complexity required in doing so should be balanced against the benefits for the application anticipated" [ISO 25964-1]. Nevertheless, it is important to distinguish them using the BTG/NTG tags (Broader Term Generic/Narrower Term Generic) for the generic relationship, the BTP/NTP tags (Broader Term Partitive/Narrower Term Partitive) for the whole-part relationship, and at last BTI/NTI tags (Broader Term Instancial/Narrower Term Instantial) for the instance relationship. And this for two main reasons. The first one is for understanding the domaina generic relationship is not a partitive relationship neither an instance relationship, and an instance is not a conceptthe second one concerns the precision criterion 2 in information retrieval: for example, looking for a concept does not mean looking for its parts. At last, the associative relationship enables to express associations between concepts which are not related hierarchically.

There is not a clear distinction between concepts and terms in Thesaurus, when they belong to different semiotic systems 3 , which should not be confused. Even if "The traditional aim of a thesaurus is to guide the indexer and the searcher to choose the same term for the same concept" [ISO 25964-1], the information retrieval relies on concepts and not on terms designating them: "The prime application for a thesaurus is in information retrieval, where the aim is to search for concepts" [ISO 25964-1]. Agreement must be reached on the concepts whatever the languages and whatever the termsa concept, as a unit of thought, is language independent 4 . Furthermore, some concepts are necessary only for understanding the domain and do not require any descriptors (or terms). For example, management contents about economic information by country require descriptors on concepts representing countries and cities, e.g. Germany and Berlin, but not on the Country concept itself.

1 A definition of conceptwhich must not be confused with definition of wordspecifies the characteristics, either essential or descriptive, of the concept which uniquely identify it. 2 Precision in information retrieval is the ratio of the number of relevant retrieved contents to the total number of retrieved contents. 3 A concept, a "unit of thought", is an extra-linguistic knowledge, when a term, a "word or phrase used to label a concept", belongs to linguistics. Even if strictly speaking a descriptor is for indexing and retrieval purposes, it is not necessary a lexical unit belonging to the vocabulary of the domain. 4 It is clear that is not so simple. A concept depends on cultural background which can lead to different categorizations which are themselves not completely independent of languagesit is the famous Sapir-Whorf's hypothesis which states that the category of thought depends on category of language [Kay and [START_REF] Kay Und Willett Kempton | What is the Sapir-Whorfhypothesis?[END_REF].

The confusion between concepts and terms is maintained when the relations between concepts are named as being relations between terms5 : BT (Broader Term) instead of a more appropriate BC (Broader Concept), BTI (Broader Term Instancial) instead of a more appropriate Instance-Of, etc.

Concept in Terminology

As in Thesaurus, the couple "concept-term" plays a central role in Terminology. Their definitions in ISO Standards looks quite similar: a concept is a "unit of thought" for Thesaurus when it is defined as a "unit of knowledge" in Terminology [ISO 1087-1], and a term is a "word or phrase used to label a concept" for Thesaurus when it is a "verbal designation of a general concept" in Terminology [ISO 1087-1]. In a similar way, concepts in Terminology are structured into a concept system linked by hierarchical relationships, either generic or partitive, and associative relations. It is the reason why thesaurus and terminology are sometimes confused. For examples, English Heritage6 defines a thesaurus as "a structured wordlist used to standardise terminology" and the software environment for thesaurus management developed during the Linked Heritage7 European project was called TMP for Terminology Management Platform. But, a terminology is not a thesaurus and vice versa, a thesaurus is not a terminology. The main goal of terminology is not indexing contents for retrieval information but to aim to a "clarification and standardization of concepts and terminology for communication between humans" [ISO 704]. The main activities of Terminology include identifying concepts and concept relations, analysing and modelling concept systems, establishing representations of concept systems, defining concepts, and at last attributing designations (predominantly terms) to each concept in one or more languages [ISO 704]. A concept is then defined as a "unit of knowledge created by a unique combination of characteristics" [ISO 1087-1], and a definition is defined as a "representation of a concept by a descriptive statement which serves to differentiate it from related concepts". The concept definition relies on a typology of characteristics8 whose delimiting characteristics, which are essential characteristics used for distinguishing a concept from related concepts. To sum up, the concept is not defined in Thesaurus whereas the definition of concept is a central activity in Terminology.

Concept system versus Term systems

To conclude this section, it is important to bear in mind that there are two different semiotic systems, a concept system and one or more term systems (one per language). The concept system represents the domain knowledge; a language-independent representation shared by users whatever their mother language. It relies on a precise definition of concept, i.e. on a specification of the characteristics of the concept, either essential or descriptive, which uniquely identifies it and distinguishes it from the other concepts. The concept system is structured according to different conceptual relationships, mainly generic, partitive and associative. On the other hand, a term system gathers, for a given language, the words designating the concepts. Even if a term can be considered as a concept label, the term systems do not necessary match with the concept system9 since there can be concepts without designations as well as some terms can be polysemic (figure 2). Furthermore, the linguistic relationships between terms cannot be reduced to a linguistic translation of conceptual relationships. For examples, hyperonymy allows multi-hierarchy when subsumption defined by specific difference only allows simple hierarchy.

Ontology

In its Introduction section the ISO 25964-1 Standard states that "today there is a demand […] for vocabularies that enable inferencing by machines". Operationalizing thesaurus for IT applications require a computational representation of the conceptual system. It is the definition of ontology from the Knowledge Engineering point of view [START_REF] Gruber | A Translation Approach to Portable Ontology Specifications[END_REF]] [Staab et al. 2004].

Definition

In the context of knowledge representation, an ontology is defined as "a specification of a conceptualization" [START_REF] Gruber | A Translation Approach to Portable Ontology Specifications[END_REF]], that is a shared description of concepts of a domain and their relationships expressed in a formal and computer readable language. In other words, an ontology is a system of concepts linked by relationships like "a kind of" (or "is-a"), "part of", and "associative" relationships; and where each concept is defined in a formal language specifying its characteristics, either essential or descriptive. The two following figures are examples of ontologies. The first one is a domain ontology where concepts are defined by specific differences 10 , e.g. a <Watch> is a 'portable' <Timepiece> ('portable' is a specific difference).

Figure 3. A domain ontology

The second one, Mikrokosmos [START_REF] Mahesh | A situated ontology for practical NLP[END_REF], is a top ontology, which aims to describe everything. The representation language is a frame-based language 11 where every concept (more often called class) is defined by a set of attributes common to all instances of the class. The classes are structured according to the hierarchical subclass relationship (the subclasses inherit the structure (the set of attributes) of its superclasses). 11 Also called schema-oriented language, coming from Artificial Intelligence

Formal languages

Building an ontology requires a formal and computational language for concept definition. Not all formal languages are of equal merit. They offer neither the same functionalities nor the same guarantees. Languages coming from Artificial Intelligence (see the previous example of Mikrokosmos), in a human readable form, offer interesting characteristics both from an epistemological 12 and computational point of view [START_REF] Minsky | A Framework for Representing Knowledge[END_REF]], [START_REF] Wright | SRL/1.5 Users Manual[END_REF], [START_REF] Brachman | Readings in Knowledge Representation[END_REF]]. On the other hand Logic-based languages occupy a special position. More than anything else, it is the definition of concept and relation that makes logic an important language. A concept is a unary predicate, like 'WristWatch (x)' 13 , and relations are many-place predicates. With their clear, precise syntax and semantics, logic-based languages guarantee coherent and objective definitions as well as sound inference mechanisms. Furthermore, their universal formalism makes them an ideal exchange format. "Description Logic" [START_REF] Franz | The Description Logic Handbook[END_REF]], based on the notions of individual, concept (a set of individuals) and role (binary relation between individuals) is an example of such languages, is at the core of the Protégé ontology editor [Protégé].

Ontoterminology

An ontology is neither a thesaurus nor a terminology. Nevertheless, ontology constitutes one of the more promising approaches for the representation of the conceptual system of thesaurus and terminology [START_REF] Roche | Terminologie et ontologie[END_REF]].

Definition

Combining ontology and terminology into a single paradigm leads to the notion of ontoterminology [START_REF] Roche | Ontoterminology: How to unify terminology and ontology into a single paradigm[END_REF]], a terminology whose conceptual system is a formal ontology. A double semantic triangle specifies the different involved notions and their relations. So, terms are separated from concepts as well as term definitions written in natural language are separated from concept definitions written in a formal language. It becomes possible to manage the two dimensions, conceptual and terminological, which compose every terminology and thesaurus.

Figure 5. The double semantic triangle 12 Where objects are described by a set of valued attributes. 13 Concepts are well-formed formulas (wff) defined using the logical operators. For example the WristWatch predicate (concept) is defined by the following wff:

WristWatch(x) ≝ Watch(x) ⋀ Wrist(x).

Ontoterminology for indexing and information retrieval

By separating the conceptual dimension from the linguistic dimension, ontoterminology allows a new approach for indexing and retrieval information. Terms are used to describe the contents which will be classified (indexed) under the corresponding concepts. Insofar concepts are extra-linguistic knowledge, i.e. language-independent, it becomes possible to manage multilingualism. The search in a given language returns all the contents that have been classified under the concepts corresponding to the request, whatever the language used for indexing these contents. Figure 6. Ontoterminology for indexing and searching Furthermore, taking into account the logical properties of the relationships between concepts enables to improve the recall and precision14 criteria.

Ontoterminology for mapping thesauri

Looking for information among vast collections is one the big challenges today (especially in a linked and opened data world), hence the need for semantic interoperability between thesauri. It is the scope of the second part of the 25964-2 ISO Standard on "Interoperability with other vocabularies" [ISO 25964-2]. The approach remains vocabulary-and languagedependent: "the principal aim of interoperability between vocabularies is to enable an expression formulated using one vocabulary to be converted to (or supplemented by) a corresponding expression in one or more other vocabularies" [ISO 25964-2]. Ontoterminology mapping enables to take into account the two dimensions, linguistic and conceptual, and to benefit from results on ontology alignment. Regarding ontology matching, two kinds of methods are distinguished. The linguistic methods compare concept names, based on the principle that the more the concept names are similar, the more they denote the same concept 15 . The semantic methods relies on either an extensional approach, i.e. taking into account the sets of items subsumed by concepts (extensions of concept), or an intensional approach relying on the definition of concepts (attributes) and/or their relationships (Figure 7).

OTe-for-Thesaurus

The ontoterminology approach has been used in different projects in Knowledge Management, Multilingual Encyclopaedias and Information Retrieval. OTe-for-Thesaurus is one of them.

Principles

OTe-for-Thesaurus is a Thesaurus editor environment based on OTe, the OntoTerminology Engine developed by the Condillac Research Group on "Ontology and Terminology" of the University of Savoie. Concepts and individuals, as well as terms and proper names, are explicitly represented in thesauri built with OTe-for-Thesaurus. The concepts are structured according to the "is-a", "part-of" and associative OTe relationships whose formal properties 16 guarantee the logical consistency of the conceptual system of thesauri.

In order to be in accordance with the ISO Standards, the OTe-for-Thesaurus interfaces use the terminology of Thesaurus. So, the "is-a" relation is called BTG (versus NTG), "part-of" is named BTP (versus NTP), and the instantiation relationship named BTI (versus NTI) (figure 8).

The display layout takes up the double dimension of the ontoterminology. The concept pane displays information about the selected concept (broaders, narrowers, and related concepts); when the term pane displays the preferred term and non-preferred terms for the selected number of necessary single-character edits to change one word into the other (insert, delete, substitute). 16 For examples, the is-a relationship is a strict-order binary relation (i.e. irreflexive, asymmetric, and transitive), and the is-a and part-of are acyclic relations. language (figure 9). The bottom pane displays the notes and external resources linked to the concept (e.g. information from Wikipedia). Figure 8. OTe-for-Thesaurus

Interchange Format

The internal representation of a thesaurus in OTe-for-Thesaurus is an ontoterminology, a more general representation than thesaurusa thesaurus is a particular case of ontoterminology.

The external representation of thesaurus in OTe-for-Thesaurus (for importing and exporting) relies on a web standard format, in this case SKOS. SKOS (Simple Knowledge Organization System) provides a model for expressing in RDF (Resource Description Framework) the basic structure and content of concept schemes such as thesauri, classification schemes, taxonomies, folksonomies, and other similar types of "controlled vocabulary". Concepts are labeled with strings in one or more natural languages. It thereby enables a simple form of multilingual labelling.

It is important to notice that OTe-for-Thesaurus is independent of SKOS, which is only used as an interchange format. As a matter of fact, SKOS is not a modelling language neither a formal knowledge representation language. It does not guarantee any logical properties about relations. So, the skos:broader is not defined as irreflexive in order to enable import ontologies written in OWL 17 . Furthermore the skos:broader relationship does not distinguish between the is-a relationship and the part-of relationship, two fundamental relations in ontology building.

Conclusion

The notion of concept has become the central element in Thesaurus as the ISO Standards highlight it. Multilingualism management and mapping thesauri are examples that rely on sharing conceptualization. In this context, ontology of Knowledge Engineering forms one of the most promising pathways for Thesaurus.

By distinguishing and linking the two conceptual and linguistic dimensions, ontoterminology a terminology whose conceptual system is a formal ontologyenables to take into account multilingualism and allows a concept-oriented indexing and search. It also enables to improve the information retrieval criteria of precision and recall, based on the logical properties of the formal relations between concepts. At last, mapping thesauri gain benefits from works done on ontology alignment.

Figure 2 :

 2 Figure 2: Concept system versus Term systems

Figure 4 .

 4 Figure 4. The Mikrokosmos ontology

Figure 7 .

 7 Figure 7. Ontology matching methods

Relations between terms are linguistic relationships, e.g. hyponymy, when relations between concepts are formal relationships like the subsumption. It is important to bear in mind that these relations do not belong to the same system and that hyponymy cannot be reduced to a linguistic translation of the subsumption relationship.

http://thesaurus.english-heritage.org.uk/newuser.htm

http://www.linkedheritage.org/

A characteristic is an "abstraction of a property of an object or of a set of objects" [ISO 1087-1].

Although it is not the purpose of this article, it is important to bear in mind that a term is not a concept name as well as the signified (meaning of a term) is not a concept[START_REF] Roche | Saying is not Modelling[END_REF]].

In information retrieval, precision is the ratio of the number of relevant retrieved contents to the total number of retrieved contents; and recall is the ratio of the number of relevant retrieved contents to the total number of relevant contents.

Using, for example, string-based techniques. One of the most popular measures of similarity between strings of characters is the Levenshtein distance defined as the minimum

Ontoterminology is the heart of the OTe-for-Thesaurus software, a Thesaurus editor environment, deployed in different European projects among which AthenaPlus for Culture Heritage and SIERA for Multilingual Knowledge Sharing.


Alizé Guilbert

Non-Nominal Troposphere Reassessment for Meeting CAT II/III with MC/MF GBAS

In Civil Aviation, to meet the long term goal of greater capacity, services must be expanded to provide more reliable, robust approach and landing operations in all weather conditions. This could be achieved globally by using modernized navigation systems. This paper relates to the development of the Multi-Constellation (MC) and Multi-Frequency (MF) Ground Based Augmentation System (GBAS) within the SESAR Framework Work Package 15.3.7. It deals also with the performance improvements obtainable for CAT II/III precision approaches, the most stringent operation currently defined.

Several challenges and key issues must be solved including those related to atmospheric modelling. Previous work principally undertaken at Ohio University [1] [2] [3] highlighted the need to consider the troposphere as a possible source of failure. GBAS activities in Europe have followed the approach of validating the protection levels, which includes treating the combined threat relating to ionospheric and tropospheric gradients. Therefore the tropospheric failure should be bounded by validating that the combination of atmospheric errors does not exceed the assumed models.

However, there are a number of arguments for revisiting this topic and specifically addressing the tropospheric threat. Firstly, recent observations [4], reported at last ICAO NSP (International Civil Aviation Organisation -Navigation System Panel) meeting, showed unexpected atmospheric behavior. The source could be related to a non-modelled behavior of the troposphere. Even if the range errors induced by this phenomenon are not significant compared to those due to ionospheric gradients, the combination of these "tropospheric" gradients with ionospheric gradients could impact integrity and continuity.

Secondly, in the advent of dual-frequency GBAS, the ionosphere may feasibly be removed through the Ionosphere-Free (I-Free) smoothing technique. In this case, the main contributor to the atmospheric error will come from the tropospheric delay. Under such a scenario, the troposphere threat model must be defined and a means for bounding the potential errors derived. This paper presents an initial analysis with the aim of evaluating the impact of non-nominal troposphere on VPL for different scenarios. The goal of this comparison is to ascertain the extent to which the proposed tropospheric bounding methodology increases the VPLs used at the aircraft.

Finally, this paper has initiated the process of assessing the impact of modelling the non-nominal troposphere on GBAS VPLs. Indeed a new methodology is proposed and seems to improve performance in terms of availability while respecting some constraints on a low data requirements for the VDB transmission.

INTRODUCTION

In the scope of the SESAR Work Package 15.3.7 several research threads are being undertaken to improve the performance of MC/MF GBAS to support CAT II/III precision approaches.

Several challenges and key issues must be solved including those related to atmospheric modelling. Previous work undertaken at Ohio University [START_REF] Diggle | An investigation into the use of Satellite Based positioning systems for flight reference/autoland operations[END_REF] [2] [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF] highlighted the need to consider the troposphere as a possible source of failure. GBAS activities in Europe have followed the approach of validating the protection levels, which includes treating the combined threat relating to ionospheric and tropospheric gradients. Therefore the tropospheric failure should be bounded by validating that the combination of atmospheric errors does not exceed the assumed models.

However, there are a number of arguments for revisiting this topic and specifically addressing the tropospheric threat. Firstly, recent observations, reported at last ICAO NSP meeting [START_REF] Ken | ICAO/NSP/WGW WP16, Observed Nominal Atmospheric Behavior using honeywell's GAST D Ionosphere Gradient Monitor[END_REF], showed unexpected atmospheric behavior. These observations have been confirmed by the FAA (Federal Aviation Administration) and Boeing and have shown that significant spatial gradients with no link to ionosphere activity are likely to appear mainly during warm and sunny days. The source could be related to a nonmodelled behavior of the troposphere. Even if the range errors induced by this phenomenon are around 9 cm and are not significant compared to those due to ionospheric gradients, the combination of these "troposphere" gradients with ionospheric gradients could lead to missed detection or false detection of the ground subsystem's ionospheric monitor, thus impacting integrity and continuity.

Secondly, in the advent of dual-frequency GBAS, the ionosphere may feasibly be reduced significantly through the ionosphere-free smoothing technique. Under such a scenario, the troposphere threat model must be defined and a means for bounding the potential errors derived. One could argue that in all cases, each error source should be independently bounded and as such the possibility of gross errors due to the troposphere should be evaluated further, at least in the European region.

As a result of these needs, WP15.3.7 contains a task to analyze European meteorological data and models to better select and parameterize the threat model for the European region. In the initial study presented here, the threat as outlined in the U.S at Ohio University [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF] is taken as input and the impact upon availability is assessed, determining an ideal protection level bound under these assumptions.

After a first part dealing with a brief introduction of the Nominal Troposphere and in order to understand the impact of non-nominal troposphere this paper will present the bounding concept as the Stanford University did in [START_REF] Pervan | Sigma etimation, Inflation and Monitoring in the LAAS Ground System[END_REF] [6] [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF].

The model chosen for the non-nominal differential tropospheric delay is detailed in a dedicated part of this paper. Then simulations were run to check the impact of this delay on Vertical Protection Level (VPL) for several scenarios with the existing methodology. Different data will be analysed in this report with some comparison with results obtained by Ohio University.

Finally, in order to meet the requirements for the worst performing aircraft, lower Vertical Alert Limits (VALs) may be required which could impact availability. Under such conditions, it would be beneficial to utilize a tropospheric bounding methodology. That is why, the last part of this paper is dedicated to a new proposed methodology and its results analysis in terms of availability performances for both Single Frequency (SF) and Dual Frequency (DF) cases. The next steps of this study should focus on further developing a solution which requires low data transmitted for computing a smaller bound in the protection level domain and reassessing the model parameterization.

NOMINAL TROPOSPHERE

For both SF and DF with I-free smoothing technique, differential residual error due to the tropospheric delays are expressed as computed in [START_REF] Guilbert | Optimal Processing Scheme for meeting CAT II/III with MC/MF GBAS[END_REF] as follows:

𝛿𝐽 = 𝐽 𝐴 -(𝐽 𝐺 + 𝑡 𝐴𝑍 𝐽 𝐺 ̇) (1)
Where 𝐽 is the tropospheric delay, 𝑡 𝐴𝑍 represents the time between the modified time of correction generation 𝑡 𝑍 and the time of application at the airborne receiver. The notation ∎ 𝐺 is used for parameters relating to the ground receivers and ∎ 𝐴 for those relating to the airborne receiver and ∎̇ defines the linear derivative.

In order to address the 2 nd -order temporal effects of the nominal troposphere errors, they may be decomposed into spatial and temporal components.

𝛿𝐽 = 𝐽 𝐴 (𝑡 𝐴 ) -𝐽 𝐺 (𝑡 𝐴 ) ⏟ 𝑠𝑝𝑎𝑡𝑖𝑎𝑙 + 𝐽 𝐺 (𝑡 𝐴 ) -(𝐽 𝐺 (𝑡 𝐺 ) + 𝑡 𝐴𝑍 𝐽 Ġ) ⏟ 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑙 (2)
It is currently under investigation within SESAR WP 15.3.7 as to whether J Ġ can be considered as a constant over the period of three smoothing windows. If so the residual differential error due to the troposphere will contain only a spatial component.

It is expected that the tropospheric delay variation is likely to be very linear in which case the difference: 𝐽 𝐺 (𝑡 𝐴 ) -(𝐽 𝐺 (𝑡 𝐺 ) + 𝑡 𝐴𝑍 𝐽 Ġ) should be small, maybe negligible. So, only the spatial component remains which may be decomposed into horizontal and vertical components. The vertical component which arises from the height difference between ground station and aircraft is corrected using the standardized nominal model given in [START_REF]Minimum Operational Performance Standards (MOPS) for GPS Local Area Augmentation System (LAAS) Airborne Equipment -RTCA DO-253C[END_REF]. The horizontal component had been neglected within the standardized models. Horizontal gradients will be treated as nonnominal tropospheric events in this paper, even though minor such gradients have been observed more frequently than previously thought. [START_REF] Ken | ICAO/NSP/WGW WP16, Observed Nominal Atmospheric Behavior using honeywell's GAST D Ionosphere Gradient Monitor[END_REF]

OVER-BOUNDING AND INFLATION CONCEPTS

In order to understand the impact of non-nominal troposphere we have to present the bounding concept [6] [7]. It is not practical to completely remove all non-zero mean components (biases) in the pseudorange corrections. These error sources must be over-bounded and using Gaussian model with a standard deviation hypothesized to be conservative. That is why the concept of a 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 was introduced, where the bounded errors and noisy errors are treated separately:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 = 𝑉𝑃𝐿 𝑁 + 𝑉𝑃𝐿 𝐵 (3)
Where 𝑉𝑃𝐿 𝑁 is the VPL component that bounds the existing sources of error currently overbounded by a Gaussian distribution and 𝑉𝑃𝐿 𝐵 is the VPL component that arises from the non-zero biases, such as caused by nonnominal tropospheric error.

The previous formula (3) can be derived for each ranging sources i:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒,𝑖 ≈ 𝐾𝑓𝑓𝑚𝑑 × 𝑆 𝑣𝑒𝑟𝑡,𝑖 × 𝜎 𝑁,𝑖 + 𝑉𝑃𝐿 𝐵,𝑖 (4)
Where 𝑉𝑃𝐿 𝐵,𝑖 = |𝑆 𝑣𝑒𝑟𝑡,𝑖 𝜇(𝑖)|

With 𝜇(i) defined as the ranging bias for the satellite 𝑖 in meters (out of the N number of visible satellites), 𝑆 𝑣𝑒𝑟𝑡,𝑖 is the vertical component of the appropriate geometry matrix for the satellite i, 𝐾𝑓𝑓𝑚𝑑 is the fault-free missed detection multiplier and 𝜎 𝑁,𝑖 is the standard deviation of the error source i noise only in meters.

Then, VPL-B can be evaluated with the following expression:

𝑉𝑃𝐿 𝐵 = ∑ 𝑉𝑃𝐿 𝐵,𝑖 𝑁 𝑖=1 = ∑|𝑆 𝑣𝑒𝑟𝑡,𝑖 𝜇(𝑖)| 𝑁 𝑖=1 (6)
And so 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 can be approximated (as described in [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF]) for all ranging source as:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 ≈ 𝐾𝑓𝑓𝑚𝑑 × √∑|𝑆 𝑣𝑒𝑟𝑡,𝑖 2 × 𝜎 𝑁,𝑖 2 | 𝑁 𝑖=1 + 𝑉𝑃𝐿 𝐵 (7)
The equivalent bounding or inflated VPL may be expressed as:

𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 ≈ 𝐾𝑓𝑓𝑚𝑑 × × √∑|𝑆 𝑣𝑒𝑟𝑡,𝑖 2 * 𝜎 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑,𝑖 2 | 𝑁 𝑖=1 (8)
Where 𝜎 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑,𝑖 is the net sigma which includes the necessary inflation.

The 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 can be seen as the "ideal" VPL and the 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 as the user VPL or the current VPL.

Integrity is ensured by setting:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 ≤ 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 (9)
So that means that the inequality 𝜎 𝑁,𝑖 < 𝜎 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 is required

In order to be conservative, the assumption that 𝑉𝑃𝐿 𝐵 considers the worst case (conspiring biases in our case) is made.

So the maximum value for 𝑉𝑃𝐿 𝐵 is defined by:

𝑉𝑃𝐿 𝐵 𝑚𝑎𝑥 = ∑|𝑆 𝑣𝑒𝑟𝑡,𝑖 × 𝜇 𝑚𝑎𝑥 | 𝑁 𝑖=1 (10)
Where 𝜇 𝑚𝑎𝑥 is the maximum ranging bias on all satellites.

According to [START_REF] Diggle | An investigation into the use of Satellite Based positioning systems for flight reference/autoland operations[END_REF] [2] it has been shown that 𝑉𝑃𝐿 𝐵 can be bounded and so its maximum 𝑉𝑃𝐿 𝐵 𝑚𝑎𝑥 by:

𝑉𝑃𝐿 𝐵 𝑚𝑎𝑥 ≤ 𝜇 𝑚𝑎𝑥 √𝑁 𝑉𝐷𝑂𝑃 (11)
This 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 aspect can be explained in the position domain by the following Figure 1 for each ranging source i:

Figure 1 -VPL Composite concept

In order to have a clearer figure, 𝑆 𝑣,𝑖 represents the 𝑆 𝑣𝑒𝑟𝑡,𝑖 variable and 𝑉𝑃𝐿 𝐶,𝑖 refers to the 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 for the ranging source i.

The equation ( 9) explained above, expresses the need to define a protection level with an inflated standard deviation that is at least as large as the composite VPL.

EXISTING METHODOLOGY

Non-Nominal Troposphere Modelling

The model chosen for the non-nominal differential tropospheric delay, is the "Wall model" following [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF]. As noted above, validation of this choice and further investigation into the European tropospheric threat is planned within 15.3.7. After discussions with partners and colleagues at Ohio University [START_REF]Private Correspondence[END_REF], alternative models such as the wedge, duct or along-wall models were neglected. These assumptions will be verified as part of the planned real data analysis.

Figure 2 -Weather Wall Model to the right of the Ground Station

In Figure 2, when the signal to the GBAS ground facility leaves the weather wall (Path 1), it experiences different conditions (T0,P0,RH0) than the signal to the user that is located beyond the wall limit (Path 2) with conditions (Tw, RHw, Pw). In this case the wall is represented to the right of the aircraft but it could equivalently also be on the left with no loss of generality. This assumption is valid if the vertical tropospheric correction models both nominal and non-nominal vertical gradients.

Existing Proposition to Bound Non-Nominal Troposphere within GAST C/D framework

The existing proposal for dealing with non-nominal troposphere use the following methodology [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF] [3]:

 Bounding biases with Absolute Bias Approach (conspiring biases) [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF] That assumes the same bias for all satellites: 𝜇 𝑚𝑎𝑥  Converting this bound to a standard deviation. It represents the bounding for non-nominal tropospheric standard deviation 𝜎 𝑛𝑜𝑛_𝑛𝑜𝑚_𝑡𝑟𝑜𝑝𝑜 This can be achieved by using the formula [START_REF] Xu | GPS Theory, Algorithms and Applications[END_REF] explained above and by seeing 𝑉𝑃𝐿 𝐵 𝑚𝑎𝑥 ≈ 𝐾𝑓𝑓𝑚𝑑 × 𝑉𝐷𝑂𝑃 × 𝜎 𝑛𝑜𝑛_𝑛𝑜𝑚_𝑡𝑟𝑜𝑝𝑜 as it is also shown in details in [START_REF] Diggle | An investigation into the use of Satellite Based positioning systems for flight reference/autoland operations[END_REF] [2]

𝜎 𝑛𝑜𝑛_𝑛𝑜𝑚_𝑡𝑟𝑜𝑝𝑜 = 𝜇 𝑚𝑎𝑥 √𝑁 𝐾 𝑓𝑓𝑚𝑑 (12)
 Ensuring integrity with the Relative Inflation Concept [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF] In this case 𝜎 𝑣𝑖𝑔 is inflated with 𝜎 𝑛𝑜𝑛_𝑛𝑜𝑚_𝑡𝑟𝑜𝑝𝑜 which is transmitted to the A/C by making the root mean square between both values in order to form an inflated value :

𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 = √𝜎 𝑣𝑖𝑔 2 + 𝜎 𝑛𝑜𝑛_𝑛𝑜𝑚_𝑡𝑟𝑜𝑝𝑜 2 (13)
This Relative Inflation Concept is the simplest sigma inflation approach which makes the assumption that biases are proportional to the sigma for each ranging source. This concept is described in details in [START_REF] Rife | The Impact of Measurement Biases on Availability for CAT III LAAS[END_REF]  Implementing inflated 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 at the A/C into

𝜎 𝑖𝑜𝑛𝑜 = 𝐹 𝑝𝑝 × 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 × (𝑥 𝑎𝑖𝑟 + 2𝜏𝑣 𝑎𝑖𝑟 ) (14)
 Computing 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 at the A/C Protection Levels are computed with the new 𝜎 𝑖𝑜𝑛𝑜 by the "traditional" way (without modifying VPL computation)

ANALYSIS

The initial analysis assesses the following VPLs:

 The VPL computed without non-nominal troposphere component (without non-zero mean bias) that is to say 𝑉𝑃𝐿 𝑁  The 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 computed by adding the exact value of 𝑉𝑃𝐿 𝑁 and 𝑉𝑃𝐿 𝐵  The 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 which is the VPL computed with the inflation methodology

The goal of this comparison is to ascertain the extent to which the proposed tropospheric bounding methodology increases the VPLs used at the aircraft in case of SF.

Processing Options and Parameters

The following model parameters are utilized in this analysis:

 Model implemented using Modified Hopfield Model from [START_REF] Xu | GPS Theory, Algorithms and Applications[END_REF] (this differs from the studies by Ohio University [START_REF] Van Graas | Conspiring Biases in the LAAS[END_REF] [3] as it captures better the vertical profile of the troposphere)

 The maximum number of tracked satellites by the airborne receiver is N=12 for GPS (24 for GPS+GAL) [START_REF] Pervan | Sigma etimation, Inflation and Monitoring in the LAAS Ground System[END_REF] (this differs from the value N=6 (and 12 respectively) as selected by Ohio University [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF] in order to select the worst case N).

Results obtained for N=6 for GPS and N=12 for GPS+GAL are presented in the appendix.

 𝐷 𝑇𝐻 is defined as the distance between the Ground Station and the Runway threshold. Then, two tests were performed with regards to the Ground Facility siting of 𝐷 𝑇𝐻 =5km [START_REF]GBAS CAT II/III Development Baseline SARPs[END_REF] and 10km instead of 1km employed in [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF]  A worst case mapping function is determined when determining the inflation in 𝜎 𝑣𝑖𝑔 (not 5° as taken in [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF])

 The nominal weather conditions are defined with parameters: T0=15°C, P0=1023.25hPa and RH0=50%. The temperature lapse rate is set to -6.5K/km.

 The Wall weather conditions are defined with parameters: Tw=26°C, Pw=1023.25hPa and RHw=100%. The temperature lapse rate is also set to -6.5K/km.

Standard Deviations Determination

For determining the 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 , two curves were plotted on the same Figure 3: The lower one (in blue) represents the wall model non-nominal troposphere standard deviation from Equation ( 12) as a function of distance to the GBAS ground station. The upper curve (in red) represents the residual ionospheric uncertainty due to spatial decorrelation of the 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 value. The goal is to overbound the non-nominal troposphere standard deviation so the value of 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 is needed to be found numerically, selecting the minimum value which bounds the 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 curve in blue.

Figure 3 -Example of Bound of Non-Nominal Troposphere using the Residual Iono Uncertainty due to Spatial Decorrelation

In order to see the influence of the inflation of sigma on the VPL computation, Table 1 represents 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 and 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 as a function of N and 𝐷 𝑇𝐻 for comparison of different scenarios (Results obtained for N=6 for GPS and N=12 for GPS+GAL are presented in the Appendix).They were determined by using the Equation ( 13) with the nominal value of 𝜎 𝑣𝑖𝑔 = 4𝑚𝑚/𝑘𝑚 and the methodology explained by the Figure 3. The value obtained in [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF] an with the equation ( 13) is:

𝑫 𝑻𝑯 = 5km 𝑫 𝑻𝑯 = 10km
 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 = 5.0mm/km for GPS constellation and 𝐷 𝑇𝐻 =1km

 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 = 6,4031 𝑚𝑚/𝑘𝑚 So by taking the parameter assumptions defined in the previous section, 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 of 11.89 mm/km was found instead of 6.4031 mm/km (as presented in [START_REF] Van Graas | Tropospheric Delay Threats for the GBAS[END_REF]) with the 𝐷 𝑇𝐻 of 5km and the GPS constellation chosen. This has an important impact on availability and thus suggests the existing proposition from Ohio University is more conservative than first determined.

Results

Simulations were run to check the impact of non-nominal troposphere on VPL for the following scenarios: Simulations were processed over 24 hours in the case of GPS and 10 days in the case of GPS + GALILEO, with a time resolution of 10seconds. In this report, the results for Seattle Airport and for an altitude of Aircraft h=200ft, are presented.

On the Figure 4, Figure 5, Figure 6 Ultimately, if the tropospheric threat is considered significant enough to be bounded separately, the intention is to derive a means to bound the resulting error whilst keeping the data transmission load low.

For 𝐷 𝑇𝐻 = 5km

In Figure 4, the different VPLs presented above are represented for the GPS constellation only and with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 4 -VPLs with 𝐷 𝑇𝐻 =5km for GPS constellation only

By analyzing this Figure 4, the following inequality is verified:

𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 > 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 > 𝑉𝑃𝐿 𝑁 ( 15
)
Also by seeing the Vertical Alert Limit (VAL) (set to 10m), the remark that for some epochs 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 is above to VAL can be made and this can clearly impact availability.

In the Figure 5, the different VPLs presented above are represented for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 5-VPLs with 𝐷 𝑇𝐻 =5km for GPS + GAL constellations

In the previous Figure 5, same results and conclusions as for Figure 4 can be made.

For 𝐷 𝑇𝐻 =10km

In the Figure 6, the different VPLs presented above are represented for the GPS constellation only with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 10km. Furthermore, cases where 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 is larger than VAL are more numerous than for 𝐷 𝑇𝐻 =5km.That means that for a larger 𝐷 𝑇𝐻 , the availability is more impacted.

In Figure 7, the different VPLs presented above are represented for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 10km.

Figure 7 -VPLs with 𝐷 𝑇𝐻 =10km for GPS + GAL constellations

In Figure 7, the same conclusions as for the GPS constellation case (Figure 6) is made concerning the validity of the inequality (15) and the level of VPLs.

But in this case of Dual Constellation GPS and Galileo, the difference between the VPL inflated (in red) and the VPL composite (in black) is more important. This leads to the conclusion that the methodology used is too conservative and finding a closer bound in the protection level domain appears feasible.

Furthermore, in the case of DF with I-Free smoothing technique, this methodology cannot be used anymore for dealing with the troposphere threat because the ionosphere component will be completely removed and no sigma parameter will therefore exist.

PROPOSED METHODOLOGY

The proposed methodology relies on the Modified Hopfield Model (MHM) [START_REF] Xu | GPS Theory, Algorithms and Applications[END_REF] explained above to compute tropospheric delays and on the fact that that they depends on satellite elevations and distances from Ground Station to Aircraft. In this part of the work, the assumption that 𝐷 𝑇𝐻 = 5km according SARPs [START_REF]GBAS CAT II/III Development Baseline SARPs[END_REF] is made. This value defines the largest distance between Ground Station and runway threshold.

In fact, the first phase of the study was to compute a table representing tropospheric delays for sets of satellite elevations bin with a width of 5°, from 0° to 90° and for distances between ground station and aircraft varying from 300m up to 30km with different steps according to how far aircraft is. In this case, tropospheric delays are represented from 300m to 1km with a step of 100m then from 1km to 8km with a step of 500m and from 8km to 30km with a step of 1km.

The second phase was to take, for each elevation bin of 5°, the maximum value of tropospheric delays over distances. 18 values which can be called 𝜇 𝑚𝑎𝑥 are obtained. It differs from the existing methodology because there is not only one value of 𝜇 𝑚𝑎𝑥 .

Then, 𝑉𝑃𝐿 𝑃𝑀1 is computed the same way as the previous 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 as explained by the equation ( 7). Finally, several curves are plotted in order to compare this methodology with others as done in the previous section.

Results

Simulations were processed over 24 hours in the case of GPS and 10 days in the case of GPS + GALILEO, with a time resolution of 10 seconds. This analysis was realized for all the five key points along the approach, as presented previously in this paper.

But in order to compare with previous results presented on Figure 4 and Figure 5, results for Seattle Airport and for an altitude of Aircraft h=200ft, are presented.

On the Figure 8 and In Figure 8, the different VPLs presented above are represented for the GPS constellation with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 8 -VPLs with 𝐷 𝑇𝐻 =5km for GPS constellation only

In the previous Figure 8, integrity is ensured because the following inequality is verified:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 ≤ 𝑉𝑃𝐿 𝑃𝑀1 (16)
Furthermore, the availability is improved compared to the existing inflation methodology. Indeed the following inequality is obtained:

𝑉𝑃𝐿 𝑃𝑀1 ≤ 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 (17)
The level of VPL with this new methodology represented by the green line is closer to the 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 (black line) than with the inflation methodology (red line). That is why for the GPS constellation case, an improvement in term of performance is made.

In the Figure 9, the different VPLs presented above are represented for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 9-VPLs with 𝐷 𝑇𝐻 =5km for GPS + GAL constellations

In the GPS and Galileo constellations case, the same conclusions can be made as in the GPS case presented before and inequalities ( 16) and ( 17) are still verified.

The difference between 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 (red line) and 𝑉𝑃𝐿 𝑃𝑀1 (green line) is more important and the 𝑉𝑃𝐿 𝑃𝑀1 is closer to 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 (black line) compared to the GPS case presented in Figure 8.

By analyzing these results and because we found VPLs closer to the black line representing 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 , the conclusion that the new methodology to bound nonnominal troposphere provides a better availability and keeps the integrity ensured is made.

However, this methodology requires also to send 18 parameters (𝜇 𝑚𝑎𝑥 ).In order to reduce the number of parameters, this methodology was modified by fitting the curve representing the 𝜇 𝑚𝑎𝑥 over elevations by a "bounding" curve always above 𝜇 𝑚𝑎𝑥 . The following equation was found and verified this condition:

𝜇 𝑚𝑎𝑥 (𝑖) = 1.31 × exp (- 𝐸𝑙𝑒𝑣(𝑖) 14.21 ) + 0.28 (18)
Where 𝐸𝑙𝑒𝑣(𝑖) represents the elevation of the satellite i in degrees.

The Figure 10 represents 𝜇 𝑚𝑎𝑥 over elevations for both new methodologies: with the 18 parameters sent and with the equation (18). In the following Figure 11, the different VPLs presented above are represented for the GPS constellation with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km and 𝑉𝑃𝐿 𝑃𝑀2 is designated by the yellow curve.

𝑉𝑃𝐿 𝑃𝑀2 ≤ 𝑉𝑃𝐿 𝑃𝑀1 (19)
That means that availability is improved although the difference between both data is quite small.

In the following Figure 12, the different VPLs presented above are represented for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km and 𝑉𝑃𝐿 𝑃𝑀2 is designed by the yellow curve.

Figure 12 -VPLs with 𝐷 𝑇𝐻 =5km for GPS + GAL constellations

In the previous Figure 12, the same conclusion as for Figure 11 is made.

Furthermore, although the difference between 𝑉𝑃𝐿 𝑃𝑀2 and 𝑉𝑃𝐿 𝑃𝑀1 is small, availability is improved and integrity is still ensured. But this new methodology with the "bounding" fitting is preferred because it requires lower data transmitted. Indeed, the equation (18) can be directly applied at the aircraft instead of sending 18 parameters what reduces the VDB transmission requirements.

To complete this analysis and in order to be less conservative, an improvement was achieved by applying conspiring biases only to the selected "Worst subset of satellites" at one side of the wall model and for the worst geometry possible. This was done by searching for the azimuth of the wall and thus subset Q where the value∑ |𝑆 𝑣𝑒𝑟𝑡 × 𝜇 𝑚𝑎𝑥 | 𝑄 is maximum.

This subset is represented and explained in the following Figure 13 and Figure 14

IONOSPHERE-FREE ANALYSIS

In case of DF GBAS, I-free smoothing may be used to eliminate the ionospheric delay term from the pseudorange observables and corrections. But as it is already mentioned above in the paper, the differential residual error due to the tropospheric delays has the same form as for SF case. It is expressed through the equation (1).

To complete this study, the same simulations were performed in the DF case with I-Free smoothing technique. Several analyses with different smoothing constants were realized but in this paper only results for 100s smoothing constant are presented.

To clarify figures, only results for the last presented methodology are analyzed in this paper.

In the Figure 17, 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒-𝑏 , 𝑉𝑃𝐿 𝑃𝑀1-𝑏 and 𝑉𝑃𝐿 𝑃𝑀2-𝑏 are represented in black, light green and yellow respectively, for the GPS constellation with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 17-VPLs for I-free case with 100s smoothing constant with 𝐷 𝑇𝐻 =5km for GPS constellation only

By analyzing the previous Figure 17, integrity seems to be ensured because the following inequality is verified:

𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 ≤ 𝑉𝑃𝐿 𝑃𝑀1-𝑏 ≤ 𝑉𝑃𝐿 𝑃𝑀2-𝑏 (20)
In the following Figure 18, 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒-𝑏 , 𝑉𝑃𝐿 𝑃𝑀1-𝑏 and 𝑉𝑃𝐿 𝑃𝑀2-𝑏 are represented in black, light green and yellow respectively, for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km.

Figure 18 -VPLs for I-free case with 100s smoothing constant with 𝐷 𝑇𝐻 =5km for GPS+GAL constellations

In the previous Figure 18, the same conclusion as for Figure 17 is made.

These results show that these new methodologies are still applicable in the DF case by applying the I-Free smoothing technique.

SUMMARY

The results presented with the existing methodology show a significant inflation of the VPLs in order to bound the non-nominal troposphere using the methodology proposed by Ohio University. However, this is the simplest solution to implement given the GAST C/D message definition. It appears excessively conservative to apply this bound. Thus, further investigation is needed on the appropriate model to be taken.

Furthermore, in all cases, there is a notable difference between the 𝑉𝑃𝐿 𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 represented by the red curve and the 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 represented by black curve. This difference is larger in the dual-constellation case than in the case where only the GPS constellation is used. Furthermore, with a larger 𝐷 𝑇𝐻 , a greater difference between curves can also be observed.

In order to meet the requirements for the worst performing aircraft, lower VALs may be required. It is important to note that at some epochs VPL inflated is above the VAL of 10m. Clearly with lower VALs, availability could be impacted. Under such conditions, it would be beneficial to utilize a tropospheric bounding methodology which leads to VPLs closer to the black line (according figures plotted above in this paper).

That is why the last part of this paper deals with a new methodology which seems to improve the performance by having a better availability than with the existing methodology and this by keeping integrity ensured. This new methodology which can be also used in the DF case with I-free smoothing technique, can be seen as a "low data transmitted" solution which was a main issue in this study.

This paper has initiated the process of assessing the impact of modelling the non-nominal troposphere on GBAS VPLs.

The next steps of this study should include:

 Analyzing European meteorological data within the associated task in the SESAR WP15.3.7  Using these data to better select and parameterize the threat model for the European region and so to reassess the choice of model and the model parameterization.

These tasks should be performed by using 3D Numerical Weather Models (NWM) such as HARMONIE provided by KNMI (Royal Netherland Meteorological Institute) and AROME provided by Meteo France. Both models are Non-Hydrostatic Models and are usually used for weather forecasting and analysis. They have a 2.5 km horizontal resolution and counts 60 vertical levels. HARMONIE which runs 4 previsions per day and 8 update analysis per day (3-hourly), covers an area around Netherland and AROME which as 5 previsions per day and 8 update analysis per day covers an area around France. Data extracted from these models could be used to complete our analysis.

Then further works could be realized for:

 Developing a low data solution to compute a closer bound in the protection level domain, and investigate if it is possible, without modification of the VPL computation at the Aircraft side.  Examining a greater range of 𝐷 𝑇𝐻 such as 7, 8 or 10km should be realized in view of future constraint relaxations concerning the maximum value of 𝐷 𝑇𝐻 as proposed by NSP in [START_REF] Ken | ICAO/NSP/WGW WP16, Observed Nominal Atmospheric Behavior using honeywell's GAST D Ionosphere Gradient Monitor[END_REF].

 4

 4 locations: Seattle Airport, Anchorage Airport, Miami Airport and an Airport located at a Latitude 0.  GPS and GPS + GAL constellations  𝐷 𝑇𝐻 =5km and 𝐷 𝑇𝐻 =10km  Five key points along the approach o Distance from A/C to Runway Threshold : D=20NM, o D=10NM o Altitude of A/C h=200ft, o h =100ft and o h=0ft.

  and Figure 7, different results are represented:  𝑽𝑷𝑳 𝒊𝒏𝒇𝒍𝒂𝒕𝒆𝒅 with non-nominal troposphere computed with the inflation methodology  𝑽𝑷𝑳 𝑪𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒆 computed by adding the exact value of 𝑽𝑷𝑳 𝑵 and 𝑽𝑷𝑳 𝑩  𝑽𝑷𝑳 𝑵 representing VPL without non-nominal troposphere

Figure 6 -

 6 Figure 6 -VPLs with 𝐷 𝑇𝐻 =10km for GPS constellation only By looking at Figure 6, the inequality (15) is still verified. The level of VPLs appears more important for 𝐷 𝑇𝐻 =10km than 𝐷 𝑇𝐻 =5km.

Figure 9

 9 different results are represented:  𝑽𝑷𝑳 𝒊𝒏𝒇𝒍𝒂𝒕𝒆𝒅 with non-nominal troposphere computed with the inflation methodology  𝑽𝑷𝑳 𝑪𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒆 computed by adding the exact value of 𝑽𝑷𝑳 𝑵 and 𝑽𝑷𝑳 𝑩  𝑽𝑷𝑳 𝑵 representing VPL without non-nominal troposphere  𝑽𝑷𝑳 𝑃𝑀1 computed with the new proposed methodology

Figure 10 -

 10 Figure 10 -𝜇 𝑚𝑎𝑥 with the 2 new methodologies Then, a new VPL named 𝑉𝑃𝐿 𝑃𝑀2 based on calculation of µmax according to (18) is represented in the same figure as the Figure 8 and Figure 9 in order to compare performance results.

Figure 11 -

 11 Figure 11-VPLs with 𝐷 𝑇𝐻 =5km for GPS constellation only By analyzing the previous Figure 11, the following inequality between the 𝑉𝑃𝐿 𝑃𝑀1 represented by the green line and 𝑉𝑃𝐿 𝑃𝑀2 represented by the yellow line is verified:

Figure 13 -

 13 Figure 13 -Representation of the Worst subset Q

Figure 15 -

 15 Figure 15 -VPLs with 𝐷 𝑇𝐻 =5km for GPS constellation onlyBy analyzing the previous Figure15and by comparing with previous case represented in Figure11, this new methodology implies a translation to the bottom of VPLs curves so in fact VPLs are reduced through this methodology except for 𝑉𝑃𝐿 𝐼𝑛𝑓𝑙𝑎𝑡𝑒𝑑 and 𝑉𝑃𝐿 𝑁 where this new methodology has no impact. Then as expected with less conservative assumptions, an improvement of the availability is observed.In the Figure16, the different VPLs introduced above are represented for the GPS and Galileo constellations with a distance from ground station to runway threshold (𝐷 𝑇𝐻 ) of 5km. The new 𝑉𝑃𝐿 𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒-𝑏 , 𝑉𝑃𝐿 𝑃𝑀1-𝑏 and 𝑉𝑃𝐿 𝑃𝑀2-𝑏 are represented in black, light green and yellow respectively.

Figure 16 -

 16 Figure 16-VPLs with 𝐷 𝑇𝐻 =5km for GPS+GAL constellations In the Figure 16, the same conclusion as for Figure 15 is made.

Table 1 -

 1 𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜 and 𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 for different cases

	N=6	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜
		= 8.0mm/km	= 9.9mm/km
		𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑	𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
		= 8.94𝑚𝑚/𝑘𝑚	= 10.68𝑚𝑚/𝑘𝑚
	N=12	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜
		= 11.2mm/km	= 13.8mm/km
		𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑	𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
		= 11.89𝑚𝑚/𝑘𝑚	= 14.37𝑚𝑚/𝑘𝑚
	N=24	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜	𝜎 𝑛𝑜𝑛-𝑛𝑜𝑚-𝑡𝑟𝑜𝑝𝑜
		= 15.9mm/km	= 19.5mm/km
		𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑	𝜎 𝑣𝑖𝑔_𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
		= 16.40𝑚𝑚/𝑘𝑚	= 19.91𝑚𝑚/𝑘𝑚

ACKNOWLEDGMENTS

The author would like to thanks the DSNA and NLR and more particularly Pierre Ladoux and Henk Veerman for their help and advice during this work. Also the author wants to thanks all partners of the SESAR WP 15.3.7.

"©SESAR JOINT UNDERTAKING, 2013. Created by ENAC for the SESAR Joint Undertaking within the frame of the SESAR Programme co-financed by the EU and EUROCONTROL. The opinions expressed herein reflects the author's view only.

The SESAR Joint Undertaking is not liable for the use of any of the information included herein. Reprint with approval of publisher and with reference to source code only."

Alizé GUILBERT is a French PhD student. She received in 2012 an Engineer Diploma from the Ecole Nationale Aviation Civile (ENAC) in Toulouse, France with a specialization in Aeronautical Telecommunications. She is currently doing a PhD in the SIGNAV laboratory at the ENAC for the SESAR (Single European Sky Air traffic management Research) project (WP15.3.7) since

APPENDIX

For 𝐷 𝑇𝐻 = 5km

For GPS constellation with N=6 For GPS+GAL constellations with N=12

For 𝐷 𝑇𝐻 = 10km

For GPS constellation with N=6

For GPS+GAL constellations with N=12


Michael Felux

Simona Mihaela

Boubeker Circiu

Michael Belabbas

Mirko Meurer

Carl Stanisak

Yiping Milner

Alizé Jiang

Andreas Guilbert

Philipp

Mirko Meurer

Stanisak

Concept

Mihaela-Simona Circiu

Boubeker Belabbas

Michael Meurer

Carl Milner

Yiping Jiang

Alize Guilbert Enac

Eurocontrol Andreas Lipp

Concept for a Dual Frequency Dual Constellation GBAS

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The Ground Based Augmentation System (GBAS) is a landing system for aircraft. It is built around a differential architecture for Global Navigation Satellite Systems (GNSS) and provides integrity information and thus enables safe, precise and reliable guidance for aircraft on the approach and in the near future also during landing and roll-out. Currently, an ever growing number of GBAS installations is in operation throughout the world including the airports of Frankfurt, Zurich, Houston, Newark and Sydney. All current stations offer only the GBAS approach service type (GAST) C which supports CAT I approaches, i.e. approaches with a minimum decision height of 200 ft. Current research and development effort is focused on providing a GBAS service to support also CAT II and III approaches (GAST D). In all those service types corrections are provided for single frequency measurements only. However, relying on only one frequency, unmitigated ionospheric disturbances can cause significant differential positioning errors. Thus, either very conservative error bounding or a significant amount of sensitive monitoring is required which might influence the availability especially in equatorial and auroral regions significantly [START_REF] Yoon | Multidimensional Verification Methodology of Ionospheric Gradient Observations during Plasma Bubble Events in the Brazilian Region[END_REF][START_REF] Fujiwara | GBAS Availability Assessment and Modelling of Ionospheric Scintillation Effects[END_REF]. With the growing Galileo and Beidou constellations and an improving GLONASS constellation, together with the introduction of a second usable frequency for aviation in the L5 band on all new GPS satellites multiple GNSS with at least two frequencies are potentially available for navigation. The use of a second frequency allows the calculation of an ionospheric free (Ifree) position solution and might be able to mitigate most of the ionospheric threat. However, the large number of possible new signals to be included in GBAS corrections provides a significant amount of possible combinations of frequencies, constellations and smoothing time constants, and thus in the end many possible processing modes. Each mode comes with different advantages and disadvantages. Therefore a difficult trade-off has to be made when deciding on supported modes and corrections to be transmitted. This paper proposes one possible scheme how such an architecture could look like. It is, however, not to be seen as an agreed draft for processing from SESAR, but should rather serve as basis for illustrating some of the most important constraints and the associated difficulties and trade-offs necessary in the definition phase of multi frequency multi constellation GBAS services.

CONSTRAINTS ON A DUAL FREQUENCY DUAL CONSTELLATION GBAS ARCHITECTURE

When defining a new GBAS architecture a large number of navigational and practical constraints have to be met. A significant constraint results from the requirement to be backward compatible to existing GAST C/D systems. There will be a significant amount of users equipped with GAST C/D avionics until a new GBAS service type will be defined, standardized and implemented. By January 2015 Boeing sold more than 1100 aircraft equipped with a legacy GBAS Landing System (GLS) and as of June 2015 Airbus reported that 30 of their customers also selected the GLS option [8,9]. A new service therefore requires provision of GPS L1 corrections and integrity parameters for GAST C and GAST D through the current VDB broadcast as specified today without impacting existing GLS users. Any additional corrections and parameters have to be accommodated in the very limited remaining capacity of the VDB. This is a very tough requirement since it might require sending corrections at a lower update rate than the currently used 2 Hz. This has an impact on integrity and could cause difficulties to meet the stringent time to alarm requirements.

Furthermore, a new architecture should not be too complex and include too many different processing modes. Many modes would mean a long and expensive development and certification process for the manufacturers and thus complex and expensive user equipment. Additionally, for each mode compliance with the appropriate requirements has to be demonstrated. Furthermore, all mode changes have to be investigated which would result in an enormous validation effort. Another important issue is the international acceptability of a proposed scheme. The developed concept should support different constellations and combinations of them. It would not make sense to limit the usability to specific systems. This might lead to problems (e.g. in case of mandates to use a certain constellation) and would probably not find support in a standardization process at ICAO level. Finally, of course all existing requirements have to be met also by the new processing modes while providing significant advantage over the legacy systems. This is also somewhat of a challenge since several assumptions, such as the failure rate of a satellite for example, are derived from experience with the systems. Introducing new GNSS constellations, such information might not yet be available and relevant failure modes might not yet be known. The details of a chosen architecture will still require a significant amount of further investigations, however at least the aforementioned requirements have to be fulfilled in any cases.

POSSIBILITES FOR SIGNAL USE IN DIFFERENT SCENARIOS

The more constellations and frequencies are potentially available the larger the number of possible combinations of navigation data. This section discusses the most important modes which will then be evaluated in the following sections. The first and most obvious set of modes are the legacy GAST C and GAST D modes supporting CAT I and CAT II/III approaches, respectively. As extension it is also possible to include signals from a second constellation on the same frequency, e.g. the Galileo E1 signals. The processing of the signals (e.g. 100 seconds / 30 seconds smoothing) and integrity monitoring (inflating sigmas for ionospheric threat mitigation) would be accomplished in the same way as with current systems if ground and airborne GBAS equipment can use the same second constellation. These modes would benefit from an improved geometry associated with typically much smaller protection levels and thus improved availability of the GBAS landing system. This is especially beneficial at airports with significant required masking angles for the ground station due to suboptimal sites for the reference antennas. It could potentially also bring benefits during increased ionospheric activity which often only affects a part of the sky. Even when monitors exclude individual satellites a good geometry could in many cases still be available. As the single and dual constellation cases are similar in processing and integrity monitoring (not so much in performance though), we regard them as only one mode for the rest of the paper.

In a similar way as in the other modes, positioning could be based on the signals from L5 / E5a instead of L1. It is possible to either offer a CAT I or a CAT II/III service based on the single frequency L5/E5a signals (again, either from one or two constellations with the same advantages of improved performance for the dual constellation case). The CAT I mode would have to provide inflated sigmas such that the ground stations completely protects a user from the ionospheric threat. For this service type we use the designator GAST E in this paper. Furthermore, a CAT II/II mode is possible which we call GAST F SF (single frequency) in this paper. Integrity could be provided in a similar way as in current systems with uninflated sigmas. However, the ionospheric threat mitigation needs to be handled in a different way. In this work we propose to base positioning on L5/E5a only but include the information on L1/E1 for ionospheric monitoring purposes. This makes GAST F SF not a true single frequency mode anymore and might be not optimal. However we regard the possibility to lose L1/E1 signals while having L5/E5a signals available as rather small and less significant than the gain resulting from better noise and multipath performance. In case of a loss of L1/E1 CAT II/III capability would be lost and a switch to GAST E would have to occur. With the ionosphere being the main reason for the significant monitoring required in GBAS, a natural candidate for a new service type is of course a dual frequency solution which allows forming an ionospheric free (IFree) combination such that the ionospheric delay is eliminated almost completely. This mode shall be called GAST F DF (dual frequency). Again, it is possible to base processing on measurements from a single constellation or from two constellations. Of course also in this service type, the larger number of satellites available in the dual constellation scenario improves navigation performance by a decrease in protection levels.

The scenarios under consideration in this paper are thus four single frequency positioning modes (GAST C, D, E and F SF) and one dual frequency mode (GAST F DF). All of them can be used either with a single GNSS constellation or in a dual constellation processing mode. The single constellation case is relevant in case of either a constellation outage or if the ground station provides corrections for constellations "A" and "B", whereas the airborne equipment supports constellation "B" and "C". In this case only the common constellation "B" could be used for navigation.

PERFORMANCE MEASURES

In order to assess the performance of the different service types mentioned in the previous section a metric is necessary. Of course it is desirable that the new processing modes should support operations without visibility limitations (i.e. CAT III conditions) including automatic landings. In order to support automatic landings it is assumed that the same methodology for airworthiness assessment as in GAST D is followed, namely the demonstration of a safe landing in the touchdown box with a very high probability. The detailed requirements are defined in [START_REF]Certification Specifications for All Weather Operations[END_REF] and [START_REF] Faa ; Landing | CRITERIA FOR APPROVAL OF CATEGORY III WEATHER MINIMA FOR TAKEOFF[END_REF]. While GAST D, F SF and F DF are going to meet these performance requirements it is not entirely clear how the performance in terms of availability for each mode will look like. The availability is impacted by epochs where the protection levels exceed the alert limits, but also by triggering of low-level monitors, such as the airborne code-carrier divergence monitor or the ionospheric gradient monitor in the GBAS ground system.

The vertical protection level VPL for the H0 case according to [START_REF]Minimum operational performance standards for GPS local area augmentation system airborne equipment[END_REF] in GAST C and D is defined as

22 , 0 , , 1 N Apr H ffmd Apr vert i i v i VPL K s D       (1)
         (2)
with contributions from residual ionospheric and tropospheric errors, as well as errors from the measurements of the airborne receiver (mainly noise and airframe multipath), and a small contribution coming from the corrections from the ground system. The ionospheric uncertainty would only be relevant in case of single frequency processing, whereas the tropospheric uncertainty is not frequency dependent and thus persists for all processing schemes. However, both uncertainties become smaller as the aircraft approaches the destination airport and the GBAS station. The receiver noise and multipath from the ground station are of course independent of aircraft positions and thus remain unchanged in one service type. The , pr gnd



are derived from at least 24 hours of measurements from the ground station and represent very well the actual performance of the station [START_REF]Minimum Operational Performance Standards Specification for Global Navigation Satellite Ground Based Augmentation System Ground Equipment to Support Category I Operations[END_REF]. The airborne noise and multipath, however, are bounded by the , pr air  parameter, which is

given in an elevation dependent model. This model has to be conservative in order to cover all aircraft installations with sufficient confidence. The airborne noise and multipath is much larger than the contribution from the ground system since no multipath limiting antennas and highly protected antenna sites are available on the airframe. Furthermore, the measurement errors increase especially during the last phase of the approach and during roll-out because signal reflections from the ground impact the receiver. First results about the airborne performance of the new signals are presented in [START_REF] Circiu | Evaluation of GPS L5, Galileo E1 and Galileo E5a Performance in Flight Trials for Multi Frequency Multi Constellation GBAS[END_REF]. However, the work presented here is based on the observed performance of , pr gnd



. The measurements used to derive these models were taken from DLR's GBAS test bed located in Braunschweig in northern Germany. The test bed uses Leica AR-25 choke ring antennas and Javad Delta 3 receivers. The reference locations and especially the antennas do not fulfil the requirements for actual GBAS stations. However, the results give a good indication as to what can be expected from the new signals and the different processing schemes. As the noise and multipath performance drive the protection levels they have a very close relationship to the availability of the system and are thus used within this work as metric to assess GBAS performance.

PRELIMINARY PERFORMANCE ASSESSMENTS OF THE DIFFERENT MODES

In GAST C only GPS L1 measurements are used. The position is calculated using a smoothing time constant of 100s. In GAST D also only GPS L1 measurements are used, however with a smoothing time constant of just 30 s. The reduction in smoothing time brings a significant increase in the residual noise and multipath in the pseudoranges used for navigation. This increase between the two smoothing time constants is clearly visible in Figure 1(the black and the blue curve) which shows an evaluation of the DLR GBAS test bed from a 40 day period. In a dual constellation case a combined GPS/Galileo GAST C/D-like scenario is also possible. In that case Galileo E1 signals would be used in the same way as GPS L1 signals with the same monitoring and error bounding strategy. The respective curves for Galileo are also depicted in Figure 1. Again a significant decrease in noise and multipath can be seen between the 30 s and 100 s smoothed pseudoranges. In general the Galileo performance seems to be somewhat better than the performance of GPS.

Figure 1 Sigma pr_ground from GBAS test bed in

Braunschweig for GPS L1 and Galileo E1 with a 100 s and 30 s smoothing time constant.

Another feasible processing scheme is the use of L5/E5a measurements only. Figure 2 shows the same evaluations for the signals from GPS L5 and Galileo E5a with a smoothing time constant of 100 s. As will be explained in the next section it is unlikely to have corrections also available for a 30 s smoothing time constant due to limited capacity of the VDB datalink. This can be written as The ratios between the blue and red curve in Figure 3 represent the expected increase in noise from GAST D to an Ifree service. For low elevations the observed ratio is about 1.8 while it decreases to a value of about 1.3 for high elevations. In summary these evaluations have shown that the best nominal performance can be expected from single frequency L5/E5a measurements. Slightly worse are the currently used L1 measurements. Through the combination of two noisy code measurements the Ifree dual frequency solution has by far the largest residual uncertainty and thus the worst nominal performance of the schemes discussed. An exact quantification of the noise increase remains to be done for a quantitative performance assessment of all the schemes.

L L L L Ifree LL ff ff        (3)

FEASIBILITIES AND CHALLENGES OF THE DIFFERENT PROCESSING SCHEMES

Multi-Constellation / Multi-Frequency GBAS services will require additional messages to be broadcast using the VHF Data Broadcast (VDB). These messages have to meet two important constraints in order to allow seamless operations.

On the one hand backwards compatibility has to be ensured. On the other hand, the VDB capacity is quite limited. This is especially true for future GBAS ground facilities at complex airports where multiple VDB transmit antennas will be necessary in order to provide sufficient VDB coverage for all runways. Such an example is depicted in Figure 4. Here, a possible distribution of VDB messages for a dualantenna GAST-C / GAST-D setup supporting two constellations is shown. Seven (out of eight) slots per frame are already almost completely allotted to legacy VDB messages and are not available for future multi constellation and multi frequency VDB messages. Thus, only one complete slot (slot H in Figure 4) will be available for additional messages.

In order to meet all CAT-III requirements in such a constrained environment, special care has to be taken with respect to the VDB format definition for MC/MF GBAS services. Within SESAR 15.3.7, first proposals for implementing such services are available. No final decision has been taken yet.

The current VDB proposals thus introduce new concepts like splitting messages including the corrections from a second frequency over multiple consecutive frames by reducing the minimum update rates of the corrections. According to these schemes which are described in detail in [START_REF] Stanisak | Possible VDB Formatting for Multi-Constellation / Multi-Frequency GBAS[END_REF] it would be possible to transmit legacy corrections for GAST C/D, additionally 30s and 100s smoothed corrections and integrity parameters from a second constellation for L1/E1. The available VDB capacity for corrections for a second frequency, however, is limited. Depending on the exact scheme chosen it might not always be possible to send the additional corrections at the same update rate of 2 Hz but maybe at just 1 Hz or even 0.5 Hz. Such a decrease in update rate has several implications. It obviously becomes very difficult reaching the required 2 seconds time to alarm requirement for automatic landings in case of update rates as low as 0.5 Hz. For that case an additional high-rate message which contains integrity flags to invalidate corrections if necessary has to be sent at every message transmission (i.e. at a rate of 2 Hz). Furthermore, the range rate corrections gain much more importance as the extrapolation time based on the RRCs increases significantly. This situation is depicted in Figure 5 and could lead to larger errors which have to be bounded accordingly.

Figure 5 PRC and RRC over time

A study including theoretical calculations and actual measurements on this effect showed, however, that with a rather small inflation of the expected standard deviations such a scheme could be feasible [START_REF] Milner | Evolution of Corrections Processing for the MC/MF Ground Based Augmentation System (GBAS)[END_REF]. An increase in the parameters would lead to increased protection levels which is of course not desirable. Again, a quantitative assessment of the increase in the uncertainty versus the decrease in the expected nominal noise and multipath performance has to be performed in order to determine a quantitative result on the expectable total performance. As it might be possible to live with an only slightly decreased update rate it is likely that the performance of L5/E5a is still going to yield some benefit of the L1/E1 performance.

In summary, it is possible with the corrections mentioned above to support the following service types:

-Legacy GAST C/D service -Extended GAST C/D service, including corrections and integrity parameters for a second constellation -GAST E service, i.e. an L5/E5a CAT I mode based on GAST C positioning and integrity concepts -GAST F SF service, i.e. an L5/E5a only positioning service with lower measurement noise but possibly with slightly increased integrity parameters due to the potentially lower update rate of the corrections. Ionospheric threat mitigation, however, requires a second frequency -GAST F DF service, i.e. a dual-frequency service type (single or dual constellation) by combining the single frequency corrections and measurements to an ionospheric free solution

The GAST F DF service type in this scenario has one implication about the smoothing time for the correction for the second frequency: If these corrections should be used to form ionospheric free combinations, the same smoothing time constant as for the corresponding corrections on L1/E1 has to be applied. That means that either 100 s or 30 s are the only candidates for an L5/E5a smoothing time constant. Due to the larger impact of noise and multipath due to the use of two noisy code measurements the longer smoothing time of 100 s is the much more likely candidate to be chosen.

PROPOSAL OF A DFDC GBAS ARCHITECTURE

Considering the expectable performance of the discussed processing techniques, along with the constraints on backwards compatibility and VDB capacity one proposal for a dual frequency dual constellation GBAS architecture is drawn in Figure 6 and can be described by the following processing modes:

-Use GAST F SF (i.e. single frequency L5/E5a, dual constellation) whenever possible as primary navigation mode -In case of an ionospheric event switch to GAST F DF for an ionospheric free solution (single or dual constellation, dual frequency)

DISCUSSION AND CONCLUSIONS

In this paper we investigated the expectable performance of different single and dual frequency and dual constellation GBAS processing modes. Based on the observations and taking into account several constraints mainly coming from VDB capacity we suggested an architecture of a DFDC GBAS which is supported by a proposal of how to transmit the necessary corrections and integrity parameters. As previously mentioned, this draft scheme is not to be seen as an agreed draft solution within SESAR as there are many tradeoffs between this and other different architecture candidates still to be made.

Some of the downsides of this proposal include:

Iono detection: There has so far been no method agreed on which would ensure timely and reliable detection of ionospheric disturbances in case of a single frequency L5/E5a processing. As every future L5/E5a capable receiver is assumed to have L1/E1 included an onboard ionospheric estimate and a comparison to the received corrections is one strategy currently under investigation. This would mean, however, that GAST E is not a true single frequency mode if the monitoring for ionospheric disturbances is based on a dual frequency method. Thus, there is no stand-alone L5/E5a CAT II/III mode as backup, e.g. in case of L1 RFI. A downgrade to CAT I would in such a case be the consequence. New extensive validation: Each new mode requires extensive validation activity and appropriate performance and error models. Using existing positioning with new integrity monitoring and an ionospheric free mode would only have one additional mode to be validated while this proposal requires the effort for two new modes. Furthermore, any switching between modes requires extensive validation and might lead to go-arounds. Thus the number of modes should be kept as low as possible. Iono-free performance: As shown above, the performance decreases significantly with respect to all singlefrequency modes if a dual frequency combination is formed. It still remains to be seen if the GAST F performance will be sufficient to support CAT II/III approaches while maintaining a sufficiently high availability.

These and several more implications are all taken into account and investigated further within SESAR in order to define an optimized architecture which is feasible under all given constraints and at the same time provides most benefits to its users.

DISCLAIMER

The contents presented in this document are for informative purposes only. The authors' institutions grant permission to ION for the purposes of the conference only. The opinions expressed herein reflect the authors' view only. This document is provided "as is", without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose and non-infringement. The SJU does not, in particular, make any warranties or representations as to the accuracy or completeness of this document. Under no circumstances shall the SESAR Joint Undertaking be liable for any loss, damage, liability or expense incurred or suffered that is claimed to have resulted from the use of any of the information included herein including, without limitation, any fault, error, omission, interruption or delay with respect thereto. The use of this document is at the [recipients of the document] sole risk. Any reproduction or use of this document other than the ones defined above requires the prior written approval of the SJU.

  where ffmd K is the fault-free missed detection multiplier, according to the desired level of integrity, N is the number of satellites used for positioning, the s -values are the projection factors for each satellite from the pseudorange into the position domain, the i  are the standard deviations of overbounding distributions of the expected residual pseudorange error for each satellite i and v D is the vertical difference in a position solution based on 100s and another position solution based on 30s smoothed pseudoranges in case of GAST D and 0 in case of GAST C. From Equation (1) it is becomes obvious that the protection level is mainly influenced by the satellite geometry (defining the s -values) and the expected residual errors on the corrected pseudorange measurements (represented by i  ).

Figure 2 

 2 Figure 2 Sigma pr_ground from GBAS test bed in Braunschweig for GPS L5 and Galileo E5a with a 100s smoothing time constant.As in the L1/E1 case the Galileo signals mostly have slightly lower values than GPS. Overall the L5/E5a signals perform somewhat better than the L1/E1 signals after 100 s smoothing but the difference in these measurements is moderate. Looking at data from flight trials, however, the difference between the signals on the two frequencies is much more pronounced as shown in[START_REF] Circiu | Evaluation of GPS L5, Galileo E1 and Galileo E5a Performance in Flight Trials for Multi Frequency Multi Constellation GBAS[END_REF][START_REF]DLR presentation at the 16 th International GBAS Working Group[END_REF]. Especially when it comes to bounding the errors on the airborne side by models this advantage can bring a substantial benefit with , pr airhaving the largest contribution to the protection levels near the airport. The previous figures were showing the curves for single frequency processing. As previously described, it is also possible to form an Ifree combination Ifree

where 1 L f and 5 Lf

 15 denote the carrier frequencies of the navigation signals. In the same way it is possible to combine the pseudorange corrections for L1 and L5 with the same smoothing time constant in order to obtain an Ifree correction. This property makes all the ionospheric monitoring in the ground and airborne systems unnecessary, however at the cost of significantly increased uncertainty in the position solution. The noise increase results from the combination of the noise and residual errors on the L1/E1 and on the L5/E5a measurements. A plot for GPS only measurements showing this property is depicted in Figure3. It shows a comparison of the Ifree performance based on 100 s smoothing in comparison to the 30 s smoothed L1 curve. The comparison of the two different smoothing times is useful in this case since CAT II/III capability in GAST D is provided based on 30 s smoothed measurements.

Figure 3

 3 Figure 3 Sigma pr_ground from GBAS test bed in Braunschweig for an Ifree combination (red) in comparison with the L1 signals from GPS only.

Figure 4 VDB

 4 Figure 4 VDB message scheme for a dual-antenna setup. Only the white spaces are available for additional information for a second frequency and constellation.

Figure 6

 6 Figure 6 Processing scheme for a dual frequency dual constellation GBAS

ACKNOWLEDGMENTS

A large portion of this work was conducted in the frame of SESAR. The authors would like to thank the whole project team of SESAR project 15.3.7 for their inputs, comments and fruitful discussions on this topic.