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Zur analytischen Optimierung geodätischer Netze / R. Kelm (1976)

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Titre :	Zur analytischen Optimierung geodätischer Netze : Allgemeine Analyse bis zur Entwicklung der Minoren- und Graphenmethode
Titre original :	[Pour l'optimisation analytique des réseaux géodésiques : Analyse générale jusqu'au développement des méthodes de graphes et ...]
Type de document :	Thèse/HDR
Auteurs :	R. Kelm, Auteur
Editeur :	Munich : Bayerische Akademie der Wissenschaften
Année de publication :	1976
Collection :	DGK - C
Sous-collection :	Dissertationen num. 220
Importance :	146 p.
Format :	21 x 30 cm
ISBN/ISSN/EAN :	978-3-7696-9276-1
Note générale :	Bibliographie
Langues :	Allemand (ger)
Descripteur :	[Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] graphe [Termes IGN] programmation non linéaire [Termes IGN] réseau géodésique
Index. décimale :	30.10 Systèmes de référence et réseaux géodésiques
Résumé :	(Auteur) Analytical optimisation of geodetic nets is defined as the process of determining the optimal free parameters of the net design (net configuration and observation plan parameters) according to an analytical criterion using mathematical solution methods. The optimisation criterion consists of the demands on the net accuracy (accuracy criterion) and the demands on the net expense (expense criterion). The accuracy criterion depends mainly on the application purpose of the net to be optimised, whereas the expense criterion has to conform to its special proposition. However, in order to achieve universal results, the analysis is based on a general optimisation case : the planned net being a universal application net should be optimised in such a way that the net accuracy is reached with minimal expenses. As to the accuracy of the planned net - in the case of the net joining together with the given net - it is to be regarded free. For theoretical, practical, and economic reasons optimisation of this universal case represents an approximation problem. The solution of this should lead to geodetically plausible optimisation results within the demanded accuracy limits using the simplest possible solution methods (basic demand on the analytical optimisation). The approximations are concerned with components of the optimisation model which is free of any hypothesis : model parameters (covering the parameters to be optimised, the net expense and their fields of value), accuracy functions (covering the accuracy criterion), risk functions (covering the optimisation criterion), and the model operator (covering the solution procedure). The accuracy foundation is based on the stochastic model of modern estimation theory : The weight coefficient matrix derived from it is suitable to estimate the influence of exact and approximating reference systems and coordinate systems; it is proved that known and newly developed accuracy measures, as functions of the weight coefficient matrix elements are independent of arbitrary coordinate transformations and in that are qualified for optimisation purposes. The application purpose of the common use net calls for optimisation demands from the point accuracy of the direction, the value, and the net configuration. These demands are met by the accuracy function of the point error ellipse; its approximative optimisation is carried out by the stage model. The demand of the error circle structure fixes the optimal configuration, and the adjustment to the absolute accuracies required leads to the optimal weights (parameters of the observation plan). In order to continue the analysis an analytic decomposition of the potential accuracy and risk function into their net specific components is necessary. For this the determinant -and graph- method is developed. The determinant method decomposes the global accuracy functions of the weight coefficient matrix of arbitrary rank and the elements of the regular coefficient matrix into functions where the parameters are determinants of the coefficient matrix. Finally, the graph method decomposes the determinants into net specific elements : into the weights and into the point invariant and coordinate dependent configuration parameters. The following examples of graph methodical analysis prove : symmetric structures of the stochastic processes in the weight coefficient matrix are only achievable under strict configuration conditions; in uniquely determined nets the graph methodical decomposition of the trace or determinant of the weight coefficient matrix - widely used as a risk function - leads to direct solutions, thus avoiding complicated algorithms of the nonlinear programming. In the uniquely determined net of the external reference system however, only the trace proving its suitable approximative risk function is the one which meets the basic demand when minimised point by point in the stage model. A qualitative graph analysis in arbitrary nets leads to the expectation that the proposed direction of a point-by-point optimisation in the stage model promotes the development of concrete optimisation strategies.
Numéro de notice :	28188
Affiliation des auteurs :	non IGN
Thématique :	POSITIONNEMENT
Nature :	Thèse étrangère
Permalink :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=63535

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
28188-01	30.10	Livre	Centre de documentation	Géodésie	Disponible

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2014 -2024 IGN

Centre de documentation
scientifique