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GNSS integer ambiguity posterior probability calculation with controllable accuracy / Zemin Wu in Journal of geodesy, vol 96 n° 8 (August 2022)  

Public [article]  inJournal of geodesy > vol 96 n° 8 (August 2022) . - n° 53 Titre : GNSS integer ambiguity posterior probability calculation with controllable accuracy Type de document : Article/Communication Auteurs : Zemin Wu, Auteur Année de publication : 2022 Article en page(s) : n° 53 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] ambiguïté entière [Termes IGN] erreur moyenne quadratique [Termes IGN] estimation de précision [Termes IGN] incertitude de position [Termes IGN] positionnement par GNSS [Termes IGN] résolution d'ambiguïté Résumé : (auteur) Integer ambiguity resolution (IAR) is one of the key techniques in GNSS high precise positioning. However, an overlooked incorrect integer ambiguity solution may cause severe biases in the positioning results. The optimal integer aperture estimator (IAE) has the largest possible success rate given a certain fail rate. An alternative approach that take advantage of ambiguity integer nature to minimize the solution’s mean squared error (MSE) is known as the best integer equivariant (BIE) estimator. Both of which are associated with the posterior probability of the GNSS integer ambiguity. It is therefore of great significance to calculate posterior probability precisely and efficiently. Due to the occurrence of infinite sums, practical calculation approaches approximate the exact value by neglecting sufficiently small terms in the sum. As a result, they can only produce posterior probability calculation result, information about the result’s accuracy cannot be produced. In this contribution, the value of the posterior probability is bounded from below and from above by dividing the infinite sum into two parts: the major finite part and the minor infinite part. They are calculated partly by enumeration and partly by algebraical bounding. The obtained upper and lower bounds are rigorous and in closed form, so that can be conveniently used. Based on both of the bounds, a method of posterior probability calculation with controllable accuracy is proposed. It not only produces posterior probability calculation result, but also calculation error, which is always smaller than the user-defined acceptable error. Numerical experiments have verified that the proposed approach has advantages on both controllable calculation accuracy and adjustable computational workload. Numéro de notice : A2022-607 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-022-01633-w Date de publication en ligne : 10/08/2022 En ligne : https://doi.org/10.1007/s00190-022-01633-w Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=101386 [article]

Regularized integer least-squares estimation: Tikhonov’s regularization in a weak GNSS model / Zemin Wu in Journal of geodesy, vol 96 n° 4 (April 2022)  

Public [article]  inJournal of geodesy > vol 96 n° 4 (April 2022) . - n° 22 Titre : Regularized integer least-squares estimation: Tikhonov’s regularization in a weak GNSS model Type de document : Article/Communication Auteurs : Zemin Wu, Auteur ; Shaofeng Bian, Auteur Année de publication : 2022 Article en page(s) : n° 22 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] affaiblissement géométrique de la précision [Termes IGN] méthode des moindres carrés [Termes IGN] phase GNSS [Termes IGN] positionnement par GNSS [Termes IGN] régularisation de Tychonoff [Termes IGN] résolution d'ambiguïté Résumé : (auteur) The strength of the GNSS precise positioning model degrades in cases of a lack of visible satellites, poor satellite geometry or uneliminated atmospheric delays. The least-squares solution to a weak GNSS model may be unreliable due to a large mean squared error (MSE). Recent studies have reported that Tikhonov’s regularization can decrease the solution’s MSE and improve the success rate of integer ambiguity resolution (IAR), as long as the regularization matrix (or parameter) is properly selected. However, there are two aspects that remain unclear: (i) the optimal regularization matrix to minimize the MSE and (ii) the IAR performance of the regularization method. This contribution focuses on these two issues. First, the “optimal” Tikhonov’s regularization matrix is derived conditioned on an assumption of prior information of the ambiguity. Second, the regularized integer least-squares (regularized ILS) method is compared with the integer least-squares (ILS) method in view of lattice theory. Theoretical analysis shows that regularized ILS can increase the upper and lower bounds of the success rate and reduce the upper bound of the LLL reduction complexity and the upper bound of the search complexity. Experimental assessment based on real observed GPS data further demonstrates that regularized ILS (i) alleviates the LLL reduction complexity, (ii) reduces the computational complexity of determinate-region ambiguity search, and (iii) improves the ambiguity fixing success rate. Numéro de notice : A2022-262 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-021-01585-7 Date de publication en ligne : 28/03/2022 En ligne : https://doi.org/10.1007/s00190-021-01585-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=100251 [article]