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Algorithmes de calcul de positions GNSS basés sur les méthodes des moindres carrés avancées

George Georges 1
1 OPERA - OPERA (OPtimisation Et RéseAux)
UTBM - Université de Technologie de Belfort-Montbeliard
Abstract : In this thesis, the neural approach TLS EXIN was proposed in a new way in order to estimate the position of a GPSreceiver. The general idea of this approach is to develop a more robust method for calculating the position.The ¿pseudorange alone¿ method is one of the simplest techniques and most widely used for estimating the GPSpositioning and it results in solving an overdetermined system of linear equations Ax¿b. In general, the ordinaryleast squares (OLS) and weighted least squares (WLS) are the commonly used methods to estimate the position ofa receiver for their quickness and robustness, but the particular structure of the data matrix A and the noise affectingits entries are not considered. This thesis, instead, aims to address these problems and study the behavior of leastsquares (LS) methods in the presence of a noisy data matrix A.The approach of total least squares (TLS) takes into account the noise in A and b. It is a less robust technique thanOLS and more sensitive to data changes. It is general solved as a direct method. Instead, the neural network TLSEXIN, which is an iterative algorithm (gradient flow) for solving TLS, works better both because it may exploit theinitial condition information derived from the previous epochs, and, in case of null initial conditions, yields anaccurate estimate even in case of close-to-degenerate data matrix.To perform tests between different methods of least squares, two sets of data were collected. The first one comesfrom the TERIA network and includes data collected from different reference stations located throughout France.While the second one is the result of a measurement campaign using GPS (Ublox NL-6002U).Using the real data, a low condition number has been estimated: in this case all LS methods yield equivalentestimates: as a consequence, OLS and WLS are to be preferred for their low computational cost. However, theworst scenario has been investigated which may occur in case of a distant satellite, resulting in the ill-conditioning ofthe GPS problem. This extreme situation justifies the use of the TLS EXIN neural network. The results obtainedconfirm of this approach even for very large condition numbers.
Keywords : GNSS OLS WLS TLS TLS-EXIN
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George Georges. Algorithmes de calcul de positions GNSS basés sur les méthodes des moindres carrés avancées. Automatique / Robotique. Université de Technologie de Belfort-Montbeliard, 2016. Français. ⟨NNT : 2016BELF0298⟩. ⟨tel-01871943⟩

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