Journal of geodesy . vol 82 n° 3Paru le : 01/03/2008 ISBN/ISSN/EAN : 0949-7714 |
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Ajouter le résultat dans votre panierOn the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies / I. Prutkin in Journal of geodesy, vol 82 n° 3 (March 2008)
[article]
Titre : On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies Type de document : Article/Communication Auteurs : I. Prutkin, Auteur ; R. Klees, Auteur Année de publication : 2008 Article en page(s) : pp 147 - 156 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] anomalie de pesanteur
[Termes IGN] champ de pesanteur local
[Termes IGN] données GPS
[Termes IGN] géoïde local
[Termes IGN] nivellement par GPSRésumé : (Auteur) We consider the problem of local (quasi-)geoid modelling from terrestrial gravity anomalies. Whereas this problem is uniquely solvable (up to spherical harmonic degree one) if gravity anomalies are globally available, the problem is non-unique if gravity anomalies are only available within a local area, which is the typical situation in local/regional gravity field modelling. We derive a mathematical description of the kernel of the gravity anomaly operator. The non-uniqueness can be removed using external height anomaly information, e.g., provided by GPS-levelling. The corresponding problem is formulated as a Cauchy problem for the Laplace equation. The existence and uniqueness of the solution of the Cauchy problem is guaranteed by the Cauchy–Kowalevskaya theorem. We propose several numerical procedures to compute the solution of the Cauchy problem from given differences between gravimetric and geometric height anomalies. We apply the numerical techniques to real data over the Netherlands and Germany. We show that we can compute a unique quasi-geoid from observed gravimetric and geometric height anomalies, which agree with the data within the expected noise level. We conclude that observed differences between gravimetric height anomalies and geometric height anomalies derived from GPS and levelling cannot only be attributed to systematic errors in the data sets, but are also caused by the intrinsic non-uniqueness of the problem of local quasi-geoid modelling from gravity anomalies. Hence, GPS-levelling data are necessary to get a unique solution, which also implies that they should not be used to validate local quasi-geoid solutions computed on the basis of gravity anomalies. Copyright Springer Numéro de notice : A2008-166 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0161-1 En ligne : https://doi.org/10.1007/s00190-007-0161-1 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29161
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Code-barres Cote Support Localisation Section Disponibilité 266-08031 RAB Revue Centre de documentation En réserve L003 Disponible 266-08032 RAB Revue Centre de documentation En réserve L003 Disponible Fast error analysis of continuous GPS observations / M. Bos in Journal of geodesy, vol 82 n° 3 (March 2008)
[article]
Titre : Fast error analysis of continuous GPS observations Type de document : Article/Communication Auteurs : M. Bos, Auteur ; R. Fernandes, Auteur ; S. Williams, Auteur ; et al., Auteur Année de publication : 2008 Article en page(s) : pp 157 - 166 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] bruit blanc
[Termes IGN] classification par maximum de vraisemblance
[Termes IGN] données GPS
[Termes IGN] incertitude des données
[Termes IGN] série temporelleRésumé : (Auteur) It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD AthlonTM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE computations can be simplified to a O(N log N) process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for the uncertainty of the estimated trend if the data only contains power-law noise. Copyright Springer Numéro de notice : A2008-167 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0165-x En ligne : https://doi.org/10.1007/s00190-007-0165-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29162
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