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Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances / Karl Rudolf Koch in Journal of geodesy, vol 84 n° 6 (June 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 6 (June 2010) . - pp 383 - 397 Titre : Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur ; H. Kukhlmann, Auteur ; W. Schuh, Auteur Année de publication : 2010 Article en page(s) : pp 383 - 397 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Lasergrammétrie [Termes IGN] covariance [Termes IGN] données lidar [Termes IGN] données localisées 3D [Termes IGN] matrice de covariance [Termes IGN] méthode de Monte-Carlo [Termes IGN] modèle linéaire Résumé : (Auteur) Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities. The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered. Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating them for each application. Numéro de notice : A2010-282 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-010-0375-5 Date de publication en ligne : 19/03/2010 En ligne : https://doi.org/10.1007/s00190-010-0375-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30476 [article]

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