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Assessment of inner reliability in the Gauss-Helmert model / Andreas Ettlinger in Journal of applied geodesy, vol 14 n° 1 (January 2020)  

Public [article]  inJournal of applied geodesy > vol 14 n° 1 (January 2020) . - pp 13 - 28 Titre : Assessment of inner reliability in the Gauss-Helmert model Type de document : Article/Communication Auteurs : Andreas Ettlinger, Auteur ; Hans Neuner, Auteur Année de publication : 2020 Article en page(s) : pp 13 - 28 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] coefficient de corrélation [Termes IGN] compensation par moindres carrés [Termes IGN] détection d'erreur [Termes IGN] erreur systématique [Termes IGN] fiabilité des données [Termes IGN] filtre de Kalman [Termes IGN] modèle d'erreur [Termes IGN] modèle de Gauss-Helmert [Termes IGN] valeur aberrante Résumé : (auteur) In this contribution, the minimum detectable bias (MDB) as well as the statistical tests to identify disturbed observations are introduced for the Gauss-Helmert model. Especially, if the observations are uncorrelated, these quantities will have the same structure as in the Gauss-Markov model, where the redundancy numbers play a key role. All the derivations are based on one-dimensional and additive observation errors respectively offsets which are modeled as additional parameters to be estimated. The formulas to compute these additional parameters with the corresponding variances are also derived in this contribution. The numerical examples of plane fitting and yaw computation show, that the MDB is also in the GHM an appropriate measure to analyze the ability of an implemented least-squares algorithm to detect if outliers are present. Two sources negatively influencing detectability are identified: columns close to the zero vector in the observation matrix B and sub-optimal configuration in the design matrix A. Even if these issues can be excluded, it can be difficult to identify the correct observation as being erroneous. Therefore, the correlation coefficients between two test values are derived and analyzed. Together with the MDB these correlation coefficients are an useful tool to assess the inner reliability – and therefore the detection and identification of outliers – in the Gauss-Helmert model. Numéro de notice : A2020-040 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jag-2019-0013 Date de publication en ligne : 19/10/2019 En ligne : https://doi.org/10.1515/jag-2019-0013 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=94511 [article]