Centre de documentation
scientifique

The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise / R. Klees in Journal of geodesy, vol 84 n° 12 (December 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 12 (December 2010) . - pp 731 - 749 Titre : The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise Type de document : Article/Communication Auteurs : R. Klees, Auteur ; I. Prutkin, Auteur Année de publication : 2010 Article en page(s) : pp 731 - 749 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude normale [Termes IGN] altitude orthométrique [Termes IGN] bruit (théorie du signal) [Termes IGN] champ de pesanteur local [Termes IGN] collocation par moindres carrés [Termes IGN] données GNSS [Termes IGN] géoïde gravimétrique [Termes IGN] hauteur ellipsoïdale [Termes IGN] matrice de covariance [Termes IGN] nivellement par GPS [Termes IGN] problème des valeurs limites [Termes IGN] Suisse [Termes IGN] variance Résumé : (Auteur) We propose a methodology for the combination of a gravimetric (quasi-) geoid with GNSS-levelling data in the presence of noise with correlations and/or spatially varying noise variances. It comprises two steps: first, a gravimetric (quasi-) geoid is computed using the available gravity data, which, in a second step, is improved using ellipsoidal heights at benchmarks provided by GNSS once they have become available. The methodology is an alternative to the integrated processing of all available data using least-squares techniques or least-squares collocation. Unlike the corrector-surface approach, the pursued approach guarantees that the corrections applied to the gravimetric (quasi-) geoid are consistent with the gravity anomaly data set. The methodology is applied to a data set comprising 109 gravimetric quasi-geoid heights, ellipsoidal heights and normal heights at benchmarks in Switzerland. Each data set is complemented by a full noise covariance matrix. We show that when neglecting noise correlations and/or spatially varying noise variances, errors up to 10% of the differences between geometric and gravimetric quasi-geoid heights are introduced. This suggests that if high-quality ellipsoidal heights at benchmarks are available and are used to compute an improved (quasi-) geoid, noise covariance matrices referring to the same datum should be used in the data processing whenever they are available. We compare the methodology with the corrector-surface approach using various corrector surface models. We show that the commonly used corrector surfaces fail to model the more complicated spatial patterns of differences between geometric and gravimetric quasi-geoid heights present in the data set. More flexible parametric models such as radial basis function approximations or minimum-curvature harmonic splines perform better. We also compare the proposed method with generalized least-squares collocation, which comprises a deterministic trend model, a random signal component and a random correlated noise component. Trend model parameters and signal covariance function parameters are estimated iteratively from the data using non-linear least-squares techniques. We show that the performance of generalized least-squares collocation is better than the performance of corrector surfaces, but the differences with respect to the proposed method are still significant. Numéro de notice : A2010-559 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-010-0406-2 Date de publication en ligne : 29/08/2010 En ligne : https://doi.org/10.1007/s00190-010-0406-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30751 [article]

Exemplaires(2)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-02010121	SL	Revue	Centre de documentation	Revues en salle	Disponible
266-2010121	SL	Revue	Centre de documentation	Revues en salle	Disponible

A data-driven approach to local gravity field modelling using spherical radial basis functions / R. Klees in Journal of geodesy, vol 82 n° 8 (August 2008)  

Public [article]  inJournal of geodesy > vol 82 n° 8 (August 2008) . - pp 457 - 471 Titre : A data-driven approach to local gravity field modelling using spherical radial basis functions Type de document : Article/Communication Auteurs : R. Klees, Auteur ; Robert Tenzer, Auteur ; I. Prutkin, Auteur ; Tobias Wittwer, Auteur Année de publication : 2008 Article en page(s) : pp 457 - 471 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] fonction de base radiale [Termes IGN] hauteur ellipsoïdale [Termes IGN] nivellement par GPS [Termes IGN] Pays-Bas [Termes IGN] problème des valeurs limites Résumé : (Auteur) We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004. Copyright Springer Numéro de notice : A2008-319 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0196-3 En ligne : https://doi.org/10.1007/s00190-007-0196-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29312 [article]

Exemplaires(2)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-08071	RAB	Revue	Centre de documentation	En réserve L003	Disponible
266-08072	RAB	Revue	Centre de documentation	En réserve L003	Disponible

On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies / I. Prutkin in Journal of geodesy, vol 82 n° 3 (March 2008)  

Public [article]  inJournal of geodesy > vol 82 n° 3 (March 2008) . - pp 147 - 156 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 GPS Résumé : (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 [article]

Exemplaires(2)

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