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Self-tuning robust adjustment within multivariate regression time series models with vector-autoregressive random errors / Boris Kargoll in Journal of geodesy, vol 94 n° 5 (May 2020)  

Public [article]  inJournal of geodesy > vol 94 n° 5 (May 2020) Titre : Self-tuning robust adjustment within multivariate regression time series models with vector-autoregressive random errors Type de document : Article/Communication Auteurs : Boris Kargoll, Auteur ; Gaël Kermarrec, Auteur ; Hamza Alkhatib, Auteur ; Johannes Korte, Auteur Année de publication : 2020 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques [Termes IGN] algorithme espérance-maximisation [Termes IGN] analyse vectorielle [Termes IGN] auto-régression [Termes IGN] bruit blanc [Termes IGN] corrélation croisée normalisée [Termes IGN] erreur aléatoire [Termes IGN] méthode de Monte-Carlo [Termes IGN] modèle stochastique [Termes IGN] régression linéaire [Termes IGN] série temporelle [Termes IGN] station GPS [Termes IGN] valeur aberrante Résumé : (auteur) The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN). Numéro de notice : A2020-291 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-020-01376-6 Date de publication en ligne : 10/05/2020 En ligne : https://doi.org/10.1007/s00190-020-01376-6 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95120 [article]

The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations: A proposal to account for correlations in least squares adjustment / Gaël Kermarrec in Journal of applied geodesy, vol 13 n° 2 (April 2019)  

Public [article]  inJournal of applied geodesy > vol 13 n° 2 (April 2019) . - pp 93 - 104 Titre : The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations: A proposal to account for correlations in least squares adjustment Type de document : Article/Communication Auteurs : Gaël Kermarrec, Auteur ; Ingo Neumann, Auteur ; Hamza Alkhatib, Auteur ; Steffen Schön, Auteur Année de publication : 2019 Article en page(s) : pp 93 - 104 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Acquisition d'image(s) et de donnée(s) [Termes IGN] analyse de variance [Termes IGN] compensation par faisceaux [Termes IGN] compensation par moindres carrés [Termes IGN] données lidar [Termes IGN] données localisées 3D [Termes IGN] matrice [Termes IGN] modèle stochastique Résumé : (Auteur) The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance–covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment. Numéro de notice : A2019-144 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jag-2018-0019 Date de publication en ligne : 24/01/2019 En ligne : https://doi.org/10.1515/jag-2018-0019 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92471 [article]

Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix / Gaël Kermarrec in Journal of geodesy, vol 90 n° 9 (September 2016)  

Public [article]  inJournal of geodesy > vol 90 n° 9 (September 2016) . - pp 793 – 805 Titre : Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix Type de document : Article/Communication Auteurs : Gaël Kermarrec, Auteur ; Steffen Schön, Auteur Année de publication : 2016 Article en page(s) : pp 793 – 805 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] compensation par moindres carrés [Termes IGN] corrélation [Termes IGN] données GPS [Termes IGN] estimateur [Termes IGN] matrice de covariance [Termes IGN] matrice diagonale [Termes IGN] pondération [Termes IGN] positionnement différentiel [Termes IGN] positionnement par GPS [Termes IGN] régression [Termes IGN] série temporelle [Vedettes matières IGN] Traitement de données GNSS Résumé : (auteur) Based on the results of Luati and Proietti (Ann Inst Stat Math 63:673–686, 2011) on an equivalence for a certain class of polynomial regressions between the diagonally weighted least squares (DWLS) and the generalized least squares (GLS) estimator, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented. The equivalent covariance matrix is much easier to compute than a diagonalization of the covariance matrix via eigenvalue decomposition which also implies a change of the least squares equations. This condensed matrix, for use in the least squares adjustment, can be seen as a diagonal or reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix. The least squares results obtained with the equivalent diagonal matrices and those given by the fully populated covariance matrix are mathematically strictly equivalent for the mean estimator in terms of estimate and its a priori cofactor matrix. It is shown that this equivalence can be empirically extended to further classes of design matrices such as those used in GPS positioning (single point positioning, precise point positioning or relative positioning with double differences). Applying this new model to simulated time series of correlated observations, a significant reduction of the coordinate differences compared with the solutions computed with the commonly used diagonal elevation-dependent model was reached for the GPS relative positioning with double differences, single point positioning as well as precise point positioning cases. The estimate differences between the equivalent and classical model with fully populated covariance matrix were below the mm for all simulated GPS cases and below the sub-mm for the relative positioning with double differences. These results were confirmed by analyzing real data. Consequently, the equivalent diagonal covariance matrices, compared with the often used elevation-dependent diagonal covariance matrix is appropriate to take correlations in GPS least squares adjustment into account, yielding more accurate cofactor matrices of the unknown. Numéro de notice : A2016-654 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0911-z En ligne : http://dx.doi.org/10.1007/s00190-016-0911-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81856 [article]