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Auteur Rüdiger Lehmann |
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Bias in least-squares adjustment of implicit functional models / Michael Lösler in Survey review, Vol 53 n° 378 (May 2021)
[article]
Titre : Bias in least-squares adjustment of implicit functional models Type de document : Article/Communication Auteurs : Michael Lösler, Auteur ; Rüdiger Lehmann, Auteur ; Frank Neitzel, Auteur ; et al., Auteur Année de publication : 2021 Article en page(s) : pp 223 - 234 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] compensation par moindres carrés
[Termes IGN] erreur systématique
[Termes IGN] fonction de Bessel
[Termes IGN] méthode de Monte-Carlo
[Termes IGN] modèle non linéaire
[Termes IGN] modèle stochastique
[Termes IGN] série de Taylor
[Termes IGN] substitution
[Termes IGN] transformation de coordonnéesRésumé : (auteur) To evaluate the benefit of a measurement procedure onto the estimated parameters, the dispersion of the parameters is usually used. To draw objective conclusions, unbiased or at least almost unbiased estimates are required. In geodesy, most of the functional relations are nonlinear but the statistical properties of the estimates are usually obtained by a linearised substitute-problem. Since the statistical properties of linear models cannot be passed to the nonlinear case, the estimates are biased. In this contribution, the bias of the parameters as well as the bias of the dispersion in nonlinear implicit models is investigated, using a second-order Taylor expansion. Nonlinear implicit models are general models and are used, for instance, in the framework of surface-fitting or coordinate transformation, which considers errors for the coordinates in source and target system. The bias is introduced as a further indicator to validate the benefit of an adapted measurement process using more precise measuring instruments. Since some parametrisations yield an ill-posed problem, also the case of a singular equation system is investigated. To demonstrate the second-order effect onto the estimates, a best-fitting plane is adjusted under varying configurations. Such a configuration is recommended in evaluating uncertainties of optical 3D measuring systems, e.g. in the framework of the VDI/VDE 2634 guideline. The estimated bias is used as an indicator whether a large number of poor observations provides better results than a small but precise sample. Numéro de notice : A2021-404 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/00396265.2020.1715680 Date de publication en ligne : 29/01/2020 En ligne : https://doi.org/10.1080/00396265.2020.1715680 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=97717
in Survey review > Vol 53 n° 378 (May 2021) . - pp 223 - 234[article]Congruence analysis of geodetic networks, hypothesis tests versus model selection by information criteria / Rüdiger Lehmann in Journal of applied geodesy, vol 11 n° 4 (December 2017)
[article]
Titre : Congruence analysis of geodetic networks, hypothesis tests versus model selection by information criteria Type de document : Article/Communication Auteurs : Rüdiger Lehmann, Auteur ; Michael Lösler, Auteur Année de publication : 2017 Article en page(s) : pp 271 - 283 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux
[Termes IGN] analyse de données
[Termes IGN] congruence
[Termes IGN] déformation géométrique
[Termes IGN] réseau géodésiqueRésumé : (Auteur) Geodetic deformation analysis can be interpreted as a model selection problem. The null model indicates that no deformation has occurred. It is opposed to a number of alternative models, which stipulate different deformation patterns. A common way to select the right model is the usage of a statistical hypothesis test. However, since we have to test a series of deformation patterns, this must be a multiple test. As an alternative solution for the test problem, we propose the p-value approach. Another approach arises from information theory. Here, the Akaike information criterion (AIC) or some alternative is used to select an appropriate model for a given set of observations. Both approaches are discussed and applied to two test scenarios: A synthetic levelling network and the Delft test data set. It is demonstrated that they work but behave differently, sometimes even producing different results. Hypothesis tests are well-established in geodesy, but may suffer from an unfavourable choice of the decision error rates. The multiple test also suffers from statistical dependencies between the test statistics, which are neglected. Both problems are overcome by applying information criterions like AIC. Numéro de notice : A2017-792 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jag-2016-0049 En ligne : https://doi.org/10.1515/jag-2016-0049 Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89064
in Journal of applied geodesy > vol 11 n° 4 (December 2017) . - pp 271 - 283[article]Transformation model selection by multiple hypotheses testing / Rüdiger Lehmann in Journal of geodesy, vol 88 n° 12 (December 2014)
[article]
Titre : Transformation model selection by multiple hypotheses testing Type de document : Article/Communication Auteurs : Rüdiger Lehmann, Auteur Année de publication : 2014 Article en page(s) : pp 1117 - 1130 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux
[Termes IGN] analyse comparative
[Termes IGN] modèle de Gauss-Markov
[Termes IGN] transformation de coordonnéesRésumé : (Auteur) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp , which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. Numéro de notice : A2014-567 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-014-0747-3 Date de publication en ligne : 24/07/2014 En ligne : https://doi.org/10.1007/s00190-014-0747-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=74753
in Journal of geodesy > vol 88 n° 12 (December 2014) . - pp 1117 - 1130[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-2014121 SL Revue Centre de documentation Revues en salle Disponible On the formulation of the alternative hypothesis for geodetic outlier detection / Rüdiger Lehmann in Journal of geodesy, vol 87 n° 4 (April 2013)
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Titre : On the formulation of the alternative hypothesis for geodetic outlier detection Type de document : Article/Communication Auteurs : Rüdiger Lehmann, Auteur Année de publication : 2013 Article en page(s) : pp 373 - 386 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques
[Termes IGN] algorithme de décalage moyen
[Termes IGN] compensation de coordonnées
[Termes IGN] erreur géométrique
[Termes IGN] méthode de Monte-Carlo
[Termes IGN] valeur aberrante
[Termes IGN] variable aléatoire
[Termes IGN] varianceRésumé : (Auteur) The concept of outlier detection by statistical hypothesis testing in geodesy is briefly reviewed. The performance of such tests can only be measured or optimized with respect to a proper alternative hypothesis. Firstly, we discuss the important question whether gross errors should be treated as non-random quantities or as random variables. In the first case, the alternative hypothesis must be based on the common mean shift model, while in the second case, the variance inflation model is appropriate. Secondly, we review possible formulations of alternative hypotheses (inherent, deterministic, slippage, mixture) and discuss their implications. As measures of optimality of an outlier detection, we propose the premium and protection, which are briefly reviewed. Finally, we work out a practical example: the fit of a straight line. It demonstrates the impact of the choice of an alternative hypothesis for outlier detection. Numéro de notice : A2013-220 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0607-y Date de publication en ligne : 21/12/2012 En ligne : https://doi.org/10.1007/s00190-012-0607-y Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32358
in Journal of geodesy > vol 87 n° 4 (April 2013) . - pp 373 - 386[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-2013041 SL Revue Centre de documentation Revues en salle Disponible Studies on the use of the boundary element method in physical geodesy / Rüdiger Lehmann (1997)
Titre : Studies on the use of the boundary element method in physical geodesy Type de document : Monographie Auteurs : Rüdiger Lehmann, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1997 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 113 Importance : 103 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8194-9 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] discrétisation
[Termes IGN] équation intégrale
[Termes IGN] problème des valeurs limites
[Termes IGN] surface de référence
[Termes IGN] Terre (planète)Index. décimale : 30.40 Géodésie physique Résumé : (Auteur) This report investigates various aspects of the application of the boundary element method in physical geodesy. Mainly the increasing accuracy requirements for the high resolution gravity field and geoid deter-mination have induced the further development of classical methods for the solution of geodetic boundary value problems, but also new techniques were established. The boundary element method permits the nu-merical solution of linearized geodetic boundary value problems, formulated as geodetic boundary integral equations. Previous geodetic investigations have focused on the strongly singular boundary integral equations in a local scale, which were solved successfully by means of Galerkin discretization methods with piecewise constant trial functions.
We extend these results in various directions : We consider the closed surface of the Earth as the bound-ary surface. Additionally, we solve a hypersingular boundary integral equation, and also piecewise linear trial/test functions are applied. Modern numerical cubature methods for the different types of integrals are tested and implemented. For the solution of the resulting linear system of equations, we apply highly efficient generalized CG methods.
A very important aspect of this report is the application of modern parallel computers. Problems of imple-mentation of the boundary element method on such types of computers are in the focus of current research in engineering sciences. Some new problems arise, concerning the parallelization of data structures and algo-rithms, and their solutions are discussed comprehensively. The performance of the parallelization is tested on a MIMD computer with distributed memory of type IBM SP.
Final numerical investigations make the pros and cons of the applied solution methods clearer.Numéro de notice : 28249 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63595 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 28249-01 30.40 Livre Centre de documentation Géodésie Disponible 28249-02 30.40 Livre Centre de documentation Géodésie Disponible Zur Bestimmung des Erdschwerefeldes unter Verwendung des Maximum-Entropie-Prinzips / Rüdiger Lehmann (1994)Permalink