Centre de documentation
scientifique

Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks / Marek Banas in Reports on geodesy and geoinformatics, vol 111 n° 1 (June 2021)  

Public [article]  inReports on geodesy and geoinformatics > vol 111 n° 1 (June 2021) Titre : Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks Type de document : Article/Communication Auteurs : Marek Banas, Auteur ; Jozef Czaja, Auteur ; Janusz Dabrowski, Auteur Année de publication : 2021 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] matrice de covariance [Termes IGN] modèle de Gauss-Markov [Termes IGN] point de nivellement [Termes IGN] réseau de contrôle Résumé : (auteur) Alignment of an engineering object project in the field is always conducted at the points of the geodetic control network, the coordinates of which are determined on the basis of the results of its elements survey and with connection to the national spatial reference system. The points of the national spatial reference system determined on the basis of previous surveys have specified coordinates with adequate accuracy, which is included in their covariance matrix. The coordinates of the geodetic control network points are determined more accurately than the points of the national spatial reference system and this means that the results of surveys of the geodetic control network have to be adequately incorporated into the coordinates of the reference points. In order to perform this incorporation, it may be assumed that the coordinates of the reference points are random, that is, they have a covariance matrix, which should be used in the process of adjusting the results of the geodetic control network observation. This research paper presents the principles for the estimation of the Gauss-Markov model parameters applied in case of those geodetic control networks in which the coordinates of the reference points have random character. On the basis of the observation equations δ + AX = L for the geodetic control network and using the weighting matrix P and the matrix of conditional covariances (P−1 + ACXAT) for the observation vector L, the parameter vector X is estimated in the form of the derived formula X^=(CX−1+ATPA)−1ATP⋅L . The verification of these estimation principles has been illustrated by the example of a fragment of a levelling geodetic control network consisting of three geodetic control points and two reference points of the national spatial reference system. The novel feature of the proposed solution is the application of covariance matrices of the reference point coordinates to adjust the results of the survey of geodetic control networks and to determine limit standard deviations for the estimated coordinates of geodetic control network points. Numéro de notice : A2021-780 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.2478/rgg-2021-0001 En ligne : https://doi.org/10.2478/rgg-2021-0001 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=98797 [article]