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Bias in least-squares adjustment of implicit functional models / Michael Lösler in Survey review, Vol 53 n° 378 (May 2021)  

Public [article]  inSurvey review > Vol 53 n° 378 (May 2021) . - pp 223 - 234 Titre : Bias in least-squares adjustment of implicit functional models Type de document : Article/Communication Auteurs : Michael Lösler, Auteur ; Rüdiger Lehmann, Auteur ; Frank Neitzel, Auteur ; et al., Auteur Année de publication : 2021 Article en page(s) : pp 223 - 234 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] compensation par moindres carrés [Termes IGN] erreur systématique [Termes IGN] fonction de Bessel [Termes IGN] méthode de Monte-Carlo [Termes IGN] modèle non linéaire [Termes IGN] modèle stochastique [Termes IGN] série de Taylor [Termes IGN] substitution [Termes IGN] transformation de coordonnées Résumé : (auteur) To evaluate the benefit of a measurement procedure onto the estimated parameters, the dispersion of the parameters is usually used. To draw objective conclusions, unbiased or at least almost unbiased estimates are required. In geodesy, most of the functional relations are nonlinear but the statistical properties of the estimates are usually obtained by a linearised substitute-problem. Since the statistical properties of linear models cannot be passed to the nonlinear case, the estimates are biased. In this contribution, the bias of the parameters as well as the bias of the dispersion in nonlinear implicit models is investigated, using a second-order Taylor expansion. Nonlinear implicit models are general models and are used, for instance, in the framework of surface-fitting or coordinate transformation, which considers errors for the coordinates in source and target system. The bias is introduced as a further indicator to validate the benefit of an adapted measurement process using more precise measuring instruments. Since some parametrisations yield an ill-posed problem, also the case of a singular equation system is investigated. To demonstrate the second-order effect onto the estimates, a best-fitting plane is adjusted under varying configurations. Such a configuration is recommended in evaluating uncertainties of optical 3D measuring systems, e.g. in the framework of the VDI/VDE 2634 guideline. The estimated bias is used as an indicator whether a large number of poor observations provides better results than a small but precise sample. Numéro de notice : A2021-404 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/00396265.2020.1715680 date de publication en ligne : 29/01/2020 En ligne : https://doi.org/10.1080/00396265.2020.1715680 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=97717 [article]

Triangulation network of 1929–1944 of the first 1:500 urban map of València / Miriam Villar-Cano in Survey review, vol 52 n° 373 (July 2020)  

Public [article]  inSurvey review > vol 52 n° 373 (July 2020) . - pp 317 - 329 Titre : Triangulation network of 1929–1944 of the first 1:500 urban map of València Type de document : Article/Communication Auteurs : Miriam Villar-Cano, Auteur ; Ángel Marqués‐Mateu, Auteur ; María Jesús Jiménez-Martínez, Auteur Année de publication : 2020 Article en page(s) : pp 317 - 329 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Triangulation [Termes IGN] 1:500 [Termes IGN] arpentage [Termes IGN] carte ancienne [Termes IGN] cartographie urbaine [Termes IGN] données de terrain [Termes IGN] European Terrestrial Reference System 1989 [Termes IGN] réseau de triangulation [Termes IGN] transformation de coordonnées [Termes IGN] Valence (Espagne) Résumé : (auteur) Triangulation is a surveying method on which earlier maps made were based. Although the origins of the method can be traced back to the 16th century, it is still used today, with minor changes, to adjust networks observed with modern geodetic techniques. In this paper we present the geodetic survey work that was carried out for the primary triangulation network of the first 1:500 urban map of the city of València (Spain). It spanned from 1929 to 1944 and resulted in 421 maps covering about 174 square kilometres. We focus on four key elements to define the geometric framework of a map: (1) the geodetic network, (2) the cartographic projection, (3) the baseline measurements, and (4) the primary triangulation. The paper is based on the interpretation of original documents and field books recovered from the archives of the València City Council. In order to check the accuracy and consistency of the survey work, we recomputed all calculations directly from the field data, following the mathematical procedures of the time. We obtained a set of transformation parameters to convert the coordinates of 1929 to current coordinates based on the European Terrestrial Reference System of 1989 (ETRS89). Results showed that the 1929 primary triangulation angles and coordinates are accurate to 8 s of arc and 35 cm respectively, and that the coordinates transform well into the current reference system with average residuals of 26 cm across nine control points, demonstrating the high quality of the 1929 work. Numéro de notice : A2020-395 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/00396265.2018.1564599 date de publication en ligne : 03/01/2019 En ligne : https://doi.org/10.1080/00396265.2018.1564599 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95421 [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]

Error propagation for the Molodensky G1 term / Jack C. McCubbine in Journal of geodesy, vol 93 n°6 (June 2019)  

Public [article]  inJournal of geodesy > vol 93 n°6 (June 2019) . - pp 889 - 898 Titre : Error propagation for the Molodensky G1 term Type de document : Article/Communication Auteurs : Jack C. McCubbine, Auteur ; Will E. Featherstone, Auteur ; Nicholas J. Brown, Auteur Année de publication : 2019 Article en page(s) : pp 889 - 898 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] anomalie de pesanteur [Termes IGN] Australie [Termes IGN] géoïde gravimétrique [Termes IGN] géoïde local [Termes IGN] hauteur ellipsoïdale [Termes IGN] incertitude de position [Termes IGN] intégrale de Stokes [Termes IGN] modèle numérique de surface [Termes IGN] problème des valeurs limites [Termes IGN] propagation d'erreur [Termes IGN] quasi-géoïde [Termes IGN] transformation de coordonnées Résumé : (auteur) Molodensky G terms are used in the computation of the quasigeoid. We derive error propagation formulas that take into account uncertainties in both the free air gravity anomaly and a digital elevation model. These are applied to generate G1 terms and their errors on a 1″ × 1″ grid over Australia. We use these to produce Molodensky gravity anomaly and accompanying uncertainty grids. These uncertainties have average value of 2 mGal with maximum of 54 mGal. We further calculate a gravimetric quasigeoid model by the remove–compute–restore technique. These Molodensky gravity anomaly uncertainties lead to quasigeoid uncertainties with a mean of 4 mm and maximum of 80 mm when propagated through a deterministically modified Stokes’s integral over an integration cap radius of 0.5°. Numéro de notice : A2019-351 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-018-1211-6 date de publication en ligne : 09/11/2018 En ligne : https://doi.org/10.1007/s00190-018-1211-6 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93395 [article]

A bevy of area-preserving transforms for map projection designers / Daniel "daan" Strebe in Cartography and Geographic Information Science, vol 46 n° 3 (May 2019)  

Public [article]  inCartography and Geographic Information Science > vol 46 n° 3 (May 2019) . - pp 260 - 276 Titre : A bevy of area-preserving transforms for map projection designers Type de document : Article/Communication Auteurs : Daniel "daan" Strebe, Auteur Année de publication : 2019 Article en page(s) : pp 260 - 276 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Projections [Termes IGN] projection [Termes IGN] projection Aitoff [Termes IGN] projection de Bonne [Termes IGN] projection de Hammer-Aitoff [Termes IGN] projection équivalente [Termes IGN] transformation affine [Termes IGN] transformation de coordonnées [Termes IGN] web mapping Résumé : (Auteur) Sometimes map projection designers need to create equal-area projections to best fill the projections’ purposes. However, unlike for conformal projections, few transformations have been described that can be applied to equal-area projections to develop new equal-area projections. Here, I survey area-preserving transformations, giving examples of their applications and proposing an efficient way of deploying an equal-area system for raster-based Web mapping. Together, these transformations provide a toolbox for the map projection designer working in the area-preserving domain. Numéro de notice : A2019-094 Affiliation des auteurs : non IGN Thématique : GEOMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/15230406.2018.1452632 date de publication en ligne : 05/04/2018 En ligne : https://doi.org/10.1080/15230406.2018.1452632 Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92342 [article]

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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)  

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