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Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates / Christian Marx in Journal of geodetic science, vol 11 n° 1 (January 2021)  

Public [article]  inJournal of geodetic science > vol 11 n° 1 (January 2021) . - pp 122 - 130 Titre : Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates Type de document : Article/Communication Auteurs : Christian Marx, Auteur Année de publication : 2021 Article en page(s) : pp 122 - 130 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] axe de rotation de la Terre [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] ellipsoïde de révolution [Termes IGN] série de Taylor Résumé : (auteur) The direct geodetic problem is regarded on the biaxial and triaxial ellipsoid. A known solution method suitable for low eccentricities, which uses differential equations in Cartesian coordinates and Taylor series expansions of these coordinates, is advanced in view of its practical application. According to previous works, this approach has the advantages that no singularities occur in the determination of the coordinates, its mathematical formulation is simple and it is not computationally intensive. The formulas of the solution method are simplified in the present contribution. A test of this method using an extensive test data set on a biaxial Earth ellipsoid shows its accuracy and practicability for distances of any length. Based on the convergence behavior of the series of the test data set, a truncation criterion for the series expansions is compiled taking into account accuracy requirements of the coordinates. Furthermore, a procedure is shown which controls the truncation of the series expansions by accuracy requirements of the direction to be determined in the direct problem. The conducted tests demonstrate the correct functioning of the methods for the series truncation. However, the considered solution method turns out to be significantly slower than another current method for biaxial ellipsoids, which makes it more relevant for triaxial ellipsoids. Numéro de notice : A2021-984 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jogs-2020-0127 Date de publication en ligne : 13/12/2021 En ligne : https://doi.org/10.1515/jogs-2020-0127 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=100983 [article]

Outlier Detection by means of Monte Carlo Estimation including resistant Scale Estimation / Christian Marx in Journal of applied geodesy, vol 9 n° 2 (June 2015)  

Public [article]  inJournal of applied geodesy > vol 9 n° 2 (June 2015) . - pp 123 - 142 Titre : Outlier Detection by means of Monte Carlo Estimation including resistant Scale Estimation Type de document : Article/Communication Auteurs : Christian Marx, Auteur Année de publication : 2015 Article en page(s) : pp 123 - 142 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] compensation par moindres carrés [Termes IGN] détection d'anomalie [Termes IGN] estimation statistique [Termes IGN] méthode de Monte-Carlo [Termes IGN] méthode robuste [Termes IGN] valeur aberrante Résumé : (auteur) The identification of outliers in measurement data is hindered if they are present in leverage points as well as in rest of the data. A promising method for their identification is the Monte Carlo estimation (MCE), which is subject of the present investigation. In MCE the data are searched for data subsamples without leverage outliers and with few (or no) non-leverage outliers by a random generation of subsamples. The required number of subsamples by which several of such subsamples are generated with a given probability is derived. Each generated subsample is rated based on the residuals resulting from an adjustment. By means of a simulation it is shown that a least squares adjustment is suitable. For the rating of the subsamples, the sum of squared residuals is used as a measure of the fit. It is argued that this (unweighted) sum is also appropriate if data have unequal weights. An investigation of the robustness of a final Bayes estimation with the result of the Monte Carlo search as prior information reveals its inappropriateness. Furthermore, the case of an unknown variance factor is considered. A simulation for different scale estimators for the variance factor shows their impracticalness. A new resistant scale estimator is introduced which is based on a generalisation of the median absolut deviation. Taking into account the results of the investigations, a new procedure for MCE considering a scale estimation is proposed. Finally, this method is tested by simulation. MCE turns out to be more reliable in the identification of outliers than a conventional resistant estimation method. Numéro de notice : A2015-392 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jag-2014-0029 En ligne : http://www.degruyter.com/view/j/jag.2014.9.issue-2/jag-2014-0029/jag-2014-0029.x [...] Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=76863 [article]