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Optimales Design geodätischer Netze 1 / Erik W. Grafarend (1973)

Public Titre : Optimales Design geodätischer Netze 1 Titre original : [Conception optimale des réseaux géodésiques 1] Type de document : Monographie Auteurs : Erik W. Grafarend, Auteur ; P. Harland, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1973 Collection : DGK - A Sous-collection : Höhere Geodäsie num. 074 Importance : 38 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Triangulation [Termes IGN] optimisation (mathématiques) [Termes IGN] réseau géodésique Index. décimale : 30.30 Triangulation - géodésie terrestre Résumé : (Auteur) Part 1 of a series of articles for the optimal design of geodetic nets is devoted to the question what kind of configuration of the net points is best in some sense. We assume the weight matrix of the observations (second order design matrix) to be known and ask for an optimal configuration matrix of the net points (first order design matrix). The Gauss-Markov model is used to find best linear unbiased estimators. + Best + is interpreted with a catalogue of more than hundred different risk functions, classified to D, A, I and E. A D-optimal design minimizes the determinant of the variance-covariance matrix of the net points, called the generalized variance, A-optimal design minimizes the trace of this dispersion matrix, called the average variance. An I-optimal design is a balance of the error ellipses in the net to be circular and identical. In an E-optimal design all eigenva-lues of the variance-covariance matrix of the net coordinates are identical. Of special importance are the Hilbert basis theorems, syzygies, Taylor-Karman structures , an equivalence and a simultaness lemma for optimal design. To get some experience with the universe of risk functions and to be able to find the appropiate ones, five million risk functions were calculated and analyzed for intersection, resection and fixed geodetic net problems. In general, the D-design is more sensitive than the A-design. For a fixed configuration of net points the D-design gives very often saddle points instead of minima. In a free configuration of net points the globel optima for D and A are identical because of syzygies. Compared to the other gain functions the I-optimal design has some favorable features. Its homogenous and isotropic geodetic net is distinguished by error ellipses which are circular and identical at different points. Numéro de notice : 28876 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63641

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