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Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates / Georgios Panou in Journal of geodetic science, vol 11 n° 1 (January 2021)  

Public [article]  inJournal of geodetic science > vol 11 n° 1 (January 2021) . - pp 111 - 121 Titre : Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates Type de document : Article/Communication Auteurs : Georgios Panou, Auteur ; Romylos Korakitis, Auteur Année de publication : 2021 Article en page(s) : pp 111 - 121 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] coordonnées ellipsoïdales [Termes IGN] transformation de coordonnées Résumé : (auteur) In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates. Numéro de notice : A2021-983 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jogs-2020-0126 Date de publication en ligne : 04/12/2021 En ligne : https://doi.org/10.1515/jogs-2020-0126 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=100982 [article]

The direct geodesic problem and an approximate analytical solution in Cartesian coordinates on a triaxial ellipsoid / Georgios Panou in Journal of applied geodesy, vol 14 n° 2 (April 2020)  

Public [article]  inJournal of applied geodesy > vol 14 n° 2 (April 2020) . - pp 205 – 213 Titre : The direct geodesic problem and an approximate analytical solution in Cartesian coordinates on a triaxial ellipsoid Type de document : Article/Communication Auteurs : Georgios Panou, Auteur ; Romylos Korakitis, Auteur Année de publication : 2020 Article en page(s) : pp 205 – 213 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] coordonnées cartésiennes [Termes IGN] coordonnées ellipsoïdales [Termes IGN] données géodésiques [Termes IGN] ellipsoïde (géodésie) [Termes IGN] géométrie analytique [Termes IGN] série de Taylor [Termes IGN] sphèroïde [Termes IGN] transformation de coordonnées Résumé : (auteur) In this work, the direct geodesic problem in Cartesian coordinates on a triaxial ellipsoid is solved by an approximate analytical method. The parametric coordinates are used and the parametric to Cartesian coordinates conversion and vice versa are presented. The geodesic equations on a triaxial ellipsoid in Cartesian coordinates are solved using a Taylor series expansion. The solution provides the Cartesian coordinates and the angle between the line of constant v and the geodesic at the end point. An extensive data set of geodesics, previously studied with a numerical method, is used in order to validate the presented analytical method in terms of stability, accuracy and execution time. We conclude that the presented method is suitable for a triaxial ellipsoid with small eccentricities and an accurate solution is obtained. At a similar accuracy level, this method is about thirty times faster than the corresponding numerical method. Finally, the presented method can also be applied in the degenerate case of an oblate spheroid, which is extensively used in geodesy. Numéro de notice : A2020-218 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jag-2019-0066 Date de publication en ligne : 12/02/2020 En ligne : https://doi.org/10.1515/jag-2019-0066 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=94911 [article]

Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid / Georgios Panou in Journal of geodetic science, vol 9 n° 1 (January 2019)  

Public [article]  inJournal of geodetic science > vol 9 n° 1 (January 2019) . - pp 1 - 12 Titre : Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid Type de document : Article/Communication Auteurs : Georgios Panou, Auteur ; Romylos Korakitis, Auteur Année de publication : 2019 Article en page(s) : pp 1 - 12 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] constante [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] coordonnées ellipsoïdales [Termes IGN] problème des valeurs limites [Termes IGN] transformation de coordonnées Résumé : (auteur) In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new numerical method of converting Cartesian to ellipsoidal coordinates of a point on a triaxial ellipsoid are presented. An extensive test set for the coordinate conversion is used, in order to evaluate the performance of the two methods. The direct geodesic problem on a triaxial ellipsoid is described as an initial value problem and is solved numerically in Cartesian coordinates. The solution provides the Cartesian coordinates and the angle between the line of constant λ and the geodesic, at any point along the geodesic. Also, the Liouville constant is computed at any point along the geodesic, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to demonstrate the validity of the numerical method for the geodesic problem. We conclude that a complete, stable and precise solution of the problem is accomplished. Numéro de notice : A2019-407 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1515/jogs-2019-0001 En ligne : https://doi.org/10.1515/jogs-2019-0001 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93524 [article]

4D GPS water vapor tomography: new parameterized approaches / Donat Perler in Journal of geodesy, vol 85 n° 8 (August 2011)  

Public [article]  inJournal of geodesy > vol 85 n° 8 (August 2011) . - pp 539 - 550 Titre : 4D GPS water vapor tomography: new parameterized approaches Type de document : Article/Communication Auteurs : Donat Perler, Auteur ; Alain Geiger, Auteur ; Fabian Peter Hurter, Auteur Année de publication : 2011 Article en page(s) : pp 539 - 550 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Applications de géodésie spatiale [Termes IGN] Alpes [Termes IGN] coordonnées ellipsoïdales [Termes IGN] distribution spatiale [Termes IGN] données GPS [Termes IGN] données météorologiques [Termes IGN] filtre de Kalman [Termes IGN] prédiction [Termes IGN] réfraction atmosphérique [Termes IGN] réfringence [Termes IGN] signal GPS [Termes IGN] Suisse [Termes IGN] tomographie [Termes IGN] troposphère [Termes IGN] vapeur d'eau [Termes IGN] voxel Résumé : (Auteur) Water vapor is a key variable in numerical weather prediction, as it plays an important role in atmospheric processes. Nonetheless, the distribution of water vapor in the atmosphere is observed with a coarse resolution in time and space compared to the resolution of numerical weather models. GPS water vapor tomography is one of the promising methods to improve the resolution of water vapor measurements. This paper presents new parameterized approaches for the determination of water vapor distribution in the troposphere by GPS. We present the methods and give first results validating the approaches. The parameterization of voxels (volumetric pixels) by trilinear and spline functions in ellipsoidal coordinates are introduced in this study. The evolution in time of the refractivity field is modeled by a Kalman filter with a temporal resolution of 30s, which corresponds to the available GPS-data rate. The algorithms are tested with simulated and with real data from more than 40 permanent GPS receiver stations in Switzerland and adjoining regions covering alpine areas. The investigations show the potential of the new parameterized approaches to yield superior results compared to the non parametric classical one. The accuracy of the tomographic result is quantified by the inter-quartile range (IQR), which is decreased by 10–20% with the new approaches. Further, parameterized voxel solutions have a substantially smaller maximal error than the non parameterized ones. Simulations show a limited ability to resolve vertical structures above the top station of the network with GPS tomography. Numéro de notice : A2011-359 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-011-0454-2 Date de publication en ligne : 08/03/2011 En ligne : https://doi.org/10.1007/s00190-011-0454-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31138 [article]

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Hyperboloïdal coordinates : transformations and applications in special constructions / J. Feltens in Journal of geodesy, vol 85 n° 4 (April 2011)  

Public [article]  inJournal of geodesy > vol 85 n° 4 (April 2011) . - pp 239 - 254 Titre : Hyperboloïdal coordinates : transformations and applications in special constructions Type de document : Article/Communication Auteurs : J. Feltens, Auteur Année de publication : 2011 Article en page(s) : pp 239 - 254 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] coordonnées ellipsoïdales [Termes IGN] ellipsoïde de référence [Termes IGN] ouvrage d'art [Termes IGN] surveillance d'ouvrage [Termes IGN] transformation de coordonnées Résumé : (Auteur) The vector-based algorithms for biaxial and triaxial ellipsoidal coordinates presented by Feltens (J Geod 82: 493-504, 2008; 83: 129-137, 2009) have been extended to hyperboloids of one sheet. For the backward transformation from Cartesian to hyperboloidal coordinates, of two iterative process candidates one was identified to be well suited. It turned out that a careful selection of the center of curvature is essential for the establishment of a stable and reliable iteration process. In addition, for zero hyperboloidal heights a closed solution is presented. The hyperboloid algorithms are again based on simple formulae and have been successfully tested for various theoretical hyperboloids. The paper concludes with a practical application on a cooling construction. Numéro de notice : A2011-181 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-010-0432-0 Date de publication en ligne : 10/12/2010 En ligne : https://doi.org/10.1007/s00190-010-0432-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30959 [article]

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Solving algebraic computational problems in geodesy and geoinformatics / Joseph L. Awange (2005)

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Géodésie géomatique ou géodésie physique / Claude Million in XYZ, n° 95 (juin - août 2003)

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Differentielle Verschiebungen und Drehstreckungen in dreidimensionalen Koordinatensystemen / D. Ehlert (1991)

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Long range geoid control through the european GPS traverse / Wolfgang Torge (1989)

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Dreidimensionale Ausgleichung des Testnetzes Westharz / Wolfgang Torge (1978)

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Verfahren zur Lösung des Oberflächenintegrales für das Modell der einfachen Schicht in der Satellitengeodäsie / H. Fröhlich (1975)

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Mouvement approché d'un satellite artificiel (méthode de Vinti) / O. Godart (1973)

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Transformationen zwischen ellipsoidischen Koordinatensystemen / S. Heitz (1969)

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