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Adjustment of geodetic measurements with mixed multiplicative and additive random errors / Peilang Xu in Journal of geodesy, vol 87 n° 7 (July 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 7 (July 2013) . - pp 629 - 643 Titre : Adjustment of geodetic measurements with mixed multiplicative and additive random errors Type de document : Article/Communication Auteurs : Peilang Xu, Auteur ; Yun Shi, Auteur ; Junhuan Peng, Auteur ; et al., Auteur Année de publication : 2013 Article en page(s) : pp 629 - 643 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] analyse comparative [Termes IGN] compensation [Termes IGN] données géodésiques [Termes IGN] erreur aléatoire Résumé : (Auteur) Adjustment has been based on the assumption that random errors of measurements are added to functional models. In geodetic practice, we know that accuracy formulae of modern geodetic measurements often consist of two parts: one proportional to the measured quantity and the other constant. From the statistical point of view, such measurements are of mixed multiplicative and additive random errors. However, almost no adjustment has been developed to strictly address geodetic data contaminated by mixed multiplicative and additive random errors from the statistical point of view. We systematically develop adjustment methods for geodetic data contaminated with multiplicative and additive errors. More precisely, we discuss the ordinary least squares (LS) and weighted LS methods and extend the bias-corrected weighted LS method of Xu and Shimada (Commun Stat B29:83–96, 2000) to the case of mixed multiplicative and additive random errors. The first order approximation of accuracy for all these three methods is derived. We derive the biases of weighted LS estimates. The three methods are then demonstrated and compared with a synthetic example of surface interpolation. The bias-corrected weighted LS estimate is unbiased up to the second order approximation and is of the best accuracy. Although the LS method can warrant an unbiased estimate for a linear model with multiplicative and additive errors, it is less accurate and always produces a very poor estimate of the variance of unit weight. Numéro de notice : A2013-398 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0635-2 Date de publication en ligne : 03/03/2013 En ligne : https://doi.org/10.1007/s00190-013-0635-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32536 [article]

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Optimized formulas for the gravitational field of a tesseroid / Thomas Grombein in Journal of geodesy, vol 87 n° 7 (July 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 7 (July 2013) . - pp 645 - 660 Titre : Optimized formulas for the gravitational field of a tesseroid Type de document : Article/Communication Auteurs : Thomas Grombein, Auteur ; Kurt Seitz, Auteur ; Bernard Heck, Auteur Année de publication : 2013 Article en page(s) : pp 645 - 660 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] coordonnées sphériques [Termes IGN] intégrale de Newton [Termes IGN] tesseroid Résumé : (Auteur) Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid’s potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach. Numéro de notice : A2013-399 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0636-1 Date de publication en ligne : 18/05/2013 En ligne : https://doi.org/10.1007/s00190-013-0636-1 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32537 [article]

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Generalized inner constraints for geodetic network densification problems / Christopher Kotsakis in Journal of geodesy, vol 87 n° 7 (July 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 7 (July 2013) . - pp 661 - 673 Titre : Generalized inner constraints for geodetic network densification problems Type de document : Article/Communication Auteurs : Christopher Kotsakis, Auteur Année de publication : 2013 Article en page(s) : pp 661 - 673 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] contrainte d'intégrité [Termes IGN] densification géodésique [Termes IGN] réseau géodésique Résumé : (Auteur) The estimated coordinates from a minimum-constrained (MC) network adjustment are generally influenced by two different error sources, that is the data noise from the available measurements and the so-called datum noise due to random errors in the fiducial coordinates that are used for the datum definition with regard to an external reference frame. Although the latter source does not affect the estimable characteristics of a MC solution, it still contributes a datum-related noise to the estimated positions which reflects the uncertainty of the coordinate system itself for the adjusted network. The aim of this paper is to develop a new type of MCs which minimizes both of the aforementioned effects in the final coordinates of an adjusted network. This particular problem has not been treated in the geodetic literature and the solution which is presented herein offers an elegant unification of the classic inner constraints into a more general framework for the datum choice problem of network optimization theory. Furthermore, the findings of our study provide a useful and rigorous tool for frame densification problems by means of an optimal MC adjustment in geodetic networks. Numéro de notice : A2013-400 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0637-0 Date de publication en ligne : 23/05/2013 En ligne : https://doi.org/10.1007/s00190-013-0637-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32538 [article]

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Mapping GPS positional errors using spatial linear mixed models / A.F. Militino in Journal of geodesy, vol 87 n° 7 (July 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 7 (July 2013) . - pp 675 - 685 Titre : Mapping GPS positional errors using spatial linear mixed models Type de document : Article/Communication Auteurs : A.F. Militino, Auteur ; M.D. Ugarte, Auteur ; et al., Auteur Année de publication : 2013 Article en page(s) : pp 675 - 685 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] carte thématique [Termes IGN] données GPS [Termes IGN] erreur de positionnement [Termes IGN] estimation statistique [Termes IGN] modèle linéaire [Termes IGN] Navarre (Espagne) [Termes IGN] précision des mesures [Termes IGN] réseau géodésique Résumé : (Auteur) Nowadays, GPS receivers are very reliable because of their good accuracy and precision; however, uncertainty is also inherent in geospatial data. Quality of GPS measurements can be influenced by atmospheric disturbances, multipathing, synchronization of clocks, satellite geometry, geographical features of the observed region, low broadcasting coverage, inadequate transmitting formats, or human or instrumental unknown errors. Assuming that the scenario and technical conditions that can influence the quality of GPS measurements are optimal, that functional and stochastic models that process the signals to a geodetic measurement are correct, and that all the GPS observables are taken in the same conditions, it is still possible to estimate the positional errors as the difference between the real coordinates and those measured by the GPS. In this paper, three spatial linear mixed models, one for each axis, are used for modelling real-time kinematic GPS accuracy and precision, of a multiple-reference-station network in dual-frequency with carrier phase measurements. Along the paper, the proposed models provide an estimate of the “accuracy” in terms of bias defined as the difference between real coordinates and measured coordinates after being processed and “precision” through the standard errors of the estimated differences. This is done using ten different transmitting formats. Mapping and quantifying these differences can be interesting for users and GPS professionals. The performance of these models is illustrated by mapping positional error estimates within the whole region of Navarre, Spain. Sampled data have been taken in 54 out of the 211 geodetic vertex points of this region. Maps show interesting error patterns depending on transmitting formats, the different axes, and the geographical characteristics of the region. Higher differences are found in regions with bad broadcasting coverage, due to the presence of mountains and high degree of humidity. Numéro de notice : A2013-401 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0638-z Date de publication en ligne : 03/09/2013 En ligne : https://doi.org/10.1007/s00190-013-0638-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32539 [article]

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