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Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach / A. Lannes in Journal of geodesy, vol 87 n° 8 (August 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 8 (August 2013) . - pp 709 - 831 Titre : Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach Type de document : Article/Communication Auteurs : A. Lannes, Auteur ; J.L. Prieur, Auteur Année de publication : 2013 Article en page(s) : pp 709 - 831 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] ambiguïté entière [Termes IGN] erreur systématique [Termes IGN] étalonnage d'instrument [Termes IGN] horloge [Termes IGN] phase GNSS [Termes IGN] positionnement cinématique en temps réel [Termes IGN] positionnement par GNSS [Termes IGN] positionnement ponctuel précis [Termes IGN] réseau géodésique permanent Résumé : (Auteur) In global navigation satellite systems (GNSS), the problem of retrieving clock-phase biases from network data has a basic rank defect. We analyse the different ways of removing this rank defect, and define a particular strategy for obtaining these phase biases in a standard form. The minimum-constrained problem to be solved in the least-squares (LS) sense depends on some integer vector which can be fixed in an arbitrary manner. We propose to solve the problem via an undifferenced approach based on the notion of closure ambiguity. We present a theoretical justification of this closure-ambiguity approach (CAA), and the main elements for a practical implementation. The links with other methods are also established. We analyse all those methods in a unified interpretative framework, and derive functional relations between the corresponding solutions and our CAA solution. This could be interesting for many GNSS applications like real-time kinematic PPP for instance. To compare the methods providing LS estimates of clock-phase biases, we define a particular solution playing the role of reference solution. For this solution, when a phase bias is estimated for the first time, its fractional part is confined to the one-cycle width interval centred on zero; the integer-ambiguity set is modified accordingly. Our theoretical study is illustrated with some simple and generic examples; it could have applications in data processing of most GNSS networks, and particularly global networks using GPS, Glonass, Galileo, or BeiDou/Compass satellites. Numéro de notice : A2013-480 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0641-4 Date de publication en ligne : 18/06/2013 En ligne : https://doi.org/10.1007/s00190-013-0641-4 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32618 [article]

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GNSS algebraic structures / A. Lannes in Journal of geodesy, vol 85 n° 5 (May 2011)  

Public [article]  inJournal of geodesy > vol 85 n° 5 (May 2011) . - pp 273 - 290 Titre : GNSS algebraic structures Type de document : Article/Communication Auteurs : A. Lannes, Auteur ; Peter J.G. Teunissen, Auteur Année de publication : 2011 Article en page(s) : pp 273 - 290 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] double différence [Termes IGN] erreur systématique [Termes IGN] étalonnage d'instrument [Termes IGN] mesurage de phase [Termes IGN] phase GNSS [Termes IGN] positionnement cinématique en temps réel [Termes IGN] positionnement par GNSS [Termes IGN] positionnement ponctuel précis Résumé : (Auteur) The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be closure-phase ambiguities:' the so-called closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is not the case for the satellite-clock biases. The third objective of this paper is to make the link between the CD approach and the GNSS methods based on the notion of double difference. In particular, it is shown that the information provided by a maximum set of independent DDs may not reach that of a complete set of CDs. The corresponding defect is analyzed. One of the main results of the corresponding analysis concerns the DDCD relationship. In particular, it is shown that the DD ambiguities, once they have been fixed and validated, can be used as input data in the undifferenced CD equations.' The corresponding algebraic operations are described. The satellite pseudo-clock biases can therefore be also obtained via particular methods in which the notion of double differencing is involved. Numéro de notice : A2011-198 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-010-0435-x Date de publication en ligne : 05/01/2011 En ligne : https://doi.org/10.1007/s00190-010-0435-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30976 [article]

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