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Weighted total least squares for solving non-linear problem: GNSS point positioning / S. Jazaeri in Survey review, vol 47 n° 343 (July 2015)  

Public [article]  inSurvey review > vol 47 n° 343 (July 2015) . - pp 265 - 271 Titre : Weighted total least squares for solving non-linear problem: GNSS point positioning Type de document : Article/Communication Auteurs : S. Jazaeri, Auteur ; Ali Reza Amiri-Simkooei, Auteur Année de publication : 2015 Article en page(s) : pp 265 - 271 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Navigation et positionnement [Termes IGN] erreur de mesure [Termes IGN] estimation des paramètres [Termes IGN] matrice de covariance [Termes IGN] méthode des moindres carrés [Termes IGN] modèle non linéaire [Termes IGN] pondération [Termes IGN] positionnement par GNSS [Termes IGN] positionnement ponctuel précis Résumé : (auteur) In this contribution, two algorithms are developed for parameter estimation in a non-linear measurement error model with errors in both the coefficient matrix and the vector of measurement. They are based on the complete description of the variance–covariance matrices of the observation errors and of the coefficient matrix errors without any restriction. The paper reinvestigates the nonlinear measurement model associated with GNSS point positioning. Various simulation experiments indicate that GNSS point positioning is much better formulated as a non-linear WTLS problem with errors in both the coefficient matrix and measurement variables. The efficacy of the proposed algorithms is verified through the numerical results. Numéro de notice : A2015-920 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1179/1752270614Y.0000000132 En ligne : https://doi.org/10.1179/1752270614Y.0000000132 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=79730 [article]

Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory / S. Jazaeri in Journal of geodesy, vol 86 n° 2 (February 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 2 (February 2012) . - pp 123 - 137 Titre : Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory Type de document : Article/Communication Auteurs : S. Jazaeri, Auteur ; Ali Reza Amiri-Simkooei, Auteur ; M. Sharifi, Auteur Année de publication : 2012 Article en page(s) : pp 123 - 137 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] analyse comparative [Termes IGN] données GNSS [Termes IGN] méthode des moindres carrés [Termes IGN] résolution d'ambiguïté Résumé : (Auteur) GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications. It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares (ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr–Euchner enumeration (M-SE) and modification of Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension 45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application of the proposed algorithms to the real GPS data. Numéro de notice : A2012-142 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-011-0501-z Date de publication en ligne : 30/07/2011 En ligne : https://doi.org/10.1007/s00190-011-0501-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31589 [article]

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