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Adjustment of geodetic measurements with mixed multiplicative and additive random errors / Peilang Xu in Journal of geodesy, vol 87 n° 7 (July 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 7 (July 2013) . - pp 629 - 643 Titre : Adjustment of geodetic measurements with mixed multiplicative and additive random errors Type de document : Article/Communication Auteurs : Peilang Xu, Auteur ; Yun Shi, Auteur ; Junhuan Peng, Auteur ; et al., Auteur Année de publication : 2013 Article en page(s) : pp 629 - 643 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] analyse comparative [Termes IGN] compensation [Termes IGN] données géodésiques [Termes IGN] erreur aléatoire Résumé : (Auteur) Adjustment has been based on the assumption that random errors of measurements are added to functional models. In geodetic practice, we know that accuracy formulae of modern geodetic measurements often consist of two parts: one proportional to the measured quantity and the other constant. From the statistical point of view, such measurements are of mixed multiplicative and additive random errors. However, almost no adjustment has been developed to strictly address geodetic data contaminated by mixed multiplicative and additive random errors from the statistical point of view. We systematically develop adjustment methods for geodetic data contaminated with multiplicative and additive errors. More precisely, we discuss the ordinary least squares (LS) and weighted LS methods and extend the bias-corrected weighted LS method of Xu and Shimada (Commun Stat B29:83–96, 2000) to the case of mixed multiplicative and additive random errors. The first order approximation of accuracy for all these three methods is derived. We derive the biases of weighted LS estimates. The three methods are then demonstrated and compared with a synthetic example of surface interpolation. The bias-corrected weighted LS estimate is unbiased up to the second order approximation and is of the best accuracy. Although the LS method can warrant an unbiased estimate for a linear model with multiplicative and additive errors, it is less accurate and always produces a very poor estimate of the variance of unit weight. Numéro de notice : A2013-398 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0635-2 Date de publication en ligne : 03/03/2013 En ligne : https://doi.org/10.1007/s00190-013-0635-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32536 [article]

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