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Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis / P. Xu in Journal of geodesy, vol 86 n° 8 (August 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 8 (August 2012) . - pp 661 - 675 Titre : Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis Type de document : Article/Communication Auteurs : P. Xu, Auteur ; J. Liu, Auteur ; C. Shi, Auteur Année de publication : 2012 Article en page(s) : pp 661 - 675 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] analyse de variance [Termes IGN] compensation non linéaire [Termes IGN] compensation par moindres carrés [Termes IGN] modèle d'erreur [Termes IGN] résidu [Termes IGN] traitement de données GNSS Résumé : (Auteur) The weighted total least squares (TLS) method has been developed to deal with observation equations, which are functions of both unknown parameters of interest and other measured data contaminated with random errors. Such an observation model is well known as an errors-in-variables (EIV) model and almost always solved as a nonlinear equality-constrained adjustment problem. We reformulate it as a nonlinear adjustment model without constraints and further extend it to a partial EIV model, in which not all the elements of the design matrix are random. As a result, the total number of unknowns in the normal equations has been significantly reduced. We derive a set of formulae for algorithmic implementation to numerically estimate the unknown model parameters. Since little statistical results about the TLS estimator in the case of finite samples are available, we investigate the statistical consequences of nonlinearity on the nonlinear TLS estimate, including the first order approximation of accuracy, nonlinear confidence region and bias of the nonlinear TLS estimate, and use the bias-corrected residuals to estimate the variance of unit weight. Numéro de notice : A2012-378 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0552-9 Date de publication en ligne : 23/03/2012 En ligne : https://doi.org/10.1007/s00190-012-0552-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31824 [article]

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