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On weighted total least-squares with linear and quadratic constraints / Vahid Mahboub in Journal of geodesy, vol 87 n° 3 (March 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 3 (March 2013) . - pp 279 - 286 Titre : On weighted total least-squares with linear and quadratic constraints Type de document : Article/Communication Auteurs : Vahid Mahboub, Auteur ; Mohammad Ali Sharifi, Auteur Année de publication : 2013 Article en page(s) : pp 279 - 286 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] méthode des moindres carrés [Termes IGN] pondération [Termes IGN] programmation par contraintes Résumé : (Auteur) A weighted total least-squares (WTLS) approach with linear and quadratic constraints is developed. This method is according to the traditional Lagrange approach to optimize the target function of this problem. The WTLS and constrained total least-squares (CTLS) approach had been distinctively investigated, however, these two problems have not been simultaneously considered yet; furthermore, among the contributions on the CTLS problem, only Schaffrin and Felus considered linear and quadratic constraints together; nevertheless, in many practical examples, some elements of the design/coefficient matrix are fixed and should not be modified and this approach cannot deal with these cases. The main necessity of this research appears after the desirable property of the WTLS approach in preserving the structure of the design matrix was proven by Mahboub. In other words, currently, the WTLS approach is one of the most efficient methods for solving the so-called errors-in-variables model and an attempt for equipping it with constraints seems necessary. Also it is demonstrated that the additional constraints have a ’regularization role’ for ill-conditioned problems and the unconstrained solution suffers from ill-conditioning effects which give it an added advantage over the unconstrained WTLS algorithm. Four geodetic applications indicate the significant of this problem in the presence of colored and white noise in the data. Numéro de notice : A2013-119 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0598-8 Date de publication en ligne : 30/10/2012 En ligne : https://doi.org/10.1007/s00190-012-0598-8 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32257 [article]

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