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Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula / Vegard Ophaug in Journal of geodesy, vol 94 n° 12 (December 2020)  

Public [article]  inJournal of geodesy > vol 94 n° 12 (December 2020) . - n° 120 Titre : Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula Type de document : Article/Communication Auteurs : Vegard Ophaug, Auteur ; Christian Gerlach, Auteur Année de publication : 2020 Article en page(s) : n° 120 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude [Termes IGN] collocation par moindres carrés [Termes IGN] covariance [Termes IGN] erreur [Termes IGN] fonction spline [Termes IGN] formule de Stokes [Termes IGN] géoïde local [Termes IGN] propagation d'erreur Résumé : (auteur) Current International Association of Geodesy efforts within regional geoid determination include the comparison of different computation methods in the quest for the “1-cm geoid.” Internal (formal) and external (empirical) approaches to evaluate geoid errors exist, and ideally they should agree. Spherical radial base functions using the spline kernel (SK), least-squares collocation (LSC), and Stokes’s formula are three commonly used methods for regional geoid computation. The three methods have been shown to be theoretically equivalent, as well as to numerically agree on the millimeter level in a closed-loop environment using synthetic noise-free data (Ophaug and Gerlach in J Geod 91:1367–1382, 2017. https://doi.org/10.1007/s00190-017-1030-1PANIST). This companion paper extends the closed-loop method comparison using synthetic data, in that we investigate and compare the formal error propagation using the three methods. We use synthetic uncorrelated and correlated noise regimes, both on the 1-mGal (=10−5 ms−2) level, applied to the input data. The estimated formal errors are validated by comparison with empirical errors, as determined from differences of the noisy geoid solutions to the noise-free solutions. We find that the error propagations of the methods are realistic in both uncorrelated and correlated noise regimes, albeit only when subjected to careful tuning, such as spectral band limitation and signal covariance adaptation. For the SKs, different implementations of the L-curve and generalized cross-validation methods did not provide an optimal regularization parameter. Although the obtained values led to a stabilized numerical system, this was not necessarily equivalent to obtaining the best solution. Using a regularization parameter governed by the agreement between formal and empirical error fields provided a solution of similar quality to the other methods. The errors in the uncorrelated regime are on the level of ∼5 mm and the method agreement within 1 mm, while the errors in the correlated regime are on the level of ∼10 mm, and the method agreement within 5 mm. Stokes’s formula generally gives the smallest error, closely followed by LSC and the SKs. To this effect, we note that error estimates from integration and estimation techniques must be interpreted differently, because the latter also take the signal characteristics into account. The high level of agreement gives us confidence in the applicability and comparability of formal errors resulting from the three methods. Finally, we present the error characteristics of geoid height differences derived from the three methods and discuss them qualitatively in relation to GNSS leveling. If applied to real data, this would permit identification of spatial scales for which height information is preferably derived by spirit leveling or GNSS leveling. Numéro de notice : A2020-784 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-020-01443-y date de publication en ligne : 27/11/2020 En ligne : https://doi.org/10.1007/s00190-020-01443-y Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=96528 [article]

Compensation of geometric parameter errors for terrestrial laser scanner by integrating intensity correction / Wanli Liu in IEEE Transactions on geoscience and remote sensing, vol 58 n° 10 (October 2020)  

Public [article]  inIEEE Transactions on geoscience and remote sensing > vol 58 n° 10 (October 2020) . - pp 7483 - 7495 Titre : Compensation of geometric parameter errors for terrestrial laser scanner by integrating intensity correction Type de document : Article/Communication Auteurs : Wanli Liu, Auteur ; Shuaishuai Sun, Auteur ; Zhixiong Li, Auteur ; et al., Auteur Année de publication : 2020 Article en page(s) : pp 7483 - 7495 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Lasergrammétrie [Termes IGN] analyse harmonique [Termes IGN] angle d'incidence [Termes IGN] compensation [Termes IGN] erreur de mesure [Termes IGN] erreur géométrique [Termes IGN] erreur instrumentale [Termes IGN] fonction spline d'interpolation [Termes IGN] modèle mathématique [Termes IGN] réseau neuronal artificiel [Termes IGN] télémétrie laser terrestre Résumé : (auteur) The accuracy of geometric parameters (mainly referred to the incidence angle and measuring distance) in a terrestrial laser scanner (TLS) is not only influenced by the TLS intrinsic systematic instrumental error but also the extrinsic received intensity data. However, the current error compensation methods for geometric parameters mainly focus on the calibration of TLS intrinsic systematic instrumental error and rarely consider the extrinsic intensity data correction. For this reason, this article presents a new method integrating the TLS intrinsic systematic instrumental error calibration and extrinsic intensity data correction to compensate the TLS geometric parameter error. The error compensation procedure is implemented as follows. First, the error compensation mathematical model integrated with TLS intrinsic systematic instrumental error calibration parameters and extrinsic intensity data correction coefficient is established. Second, the hybrid harmonic analysis (HA) and the adaptive wavelet neural network (AWNN) algorithm are proposed to calculate the TLS incidence angle error compensation values. Subsequently, the cubic spline interpolation (CSI) is applied to compute the measuring distance error compensate values. Finally, the TLS (model FARO Focus S150) and the hemispherical angle calibration instrument were used to evaluate the proposed compensation method. The experimental results demonstrate that the geometric parameters are significantly influenced by the intensity data received from TLS, and the proposed method can effectively improve the overall accuracy of the TLS incidence angle and measuring distance. Numéro de notice : A2020-602 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1109/TGRS.2020.2984885 date de publication en ligne : 15/04/2020 En ligne : https://doi.org/10.1109/TGRS.2020.2984885 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95957 [article]

Spheroidal spline interpolation and its application in geodesy / Mostafa Kiani in Geodesy and cartography, vol 46 n° 3 (October 2020)  

Public [article]  inGeodesy and cartography > vol 46 n° 3 (October 2020) . - pp 123 - 135 Titre : Spheroidal spline interpolation and its application in geodesy Type de document : Article/Communication Auteurs : Mostafa Kiani, Auteur ; Nabi Chegini, Auteur ; Abdolreza Safari, Auteur Année de publication : 2020 Article en page(s) : pp 123 - 135 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse harmonique [Termes IGN] espace de Hilbert [Termes IGN] fonction de Green [Termes IGN] fonction spline d'interpolation [Termes IGN] force de gravitation [Termes IGN] optimisation (mathématiques) [Termes IGN] sphèroïde Résumé : (auteur) The aim of this paper is to study the spline interpolation problem in spheroidal geometry. We follow the minimization of the norm of the iterated Beltrami-Laplace and consecutive iterated Helmholtz operators for all functions belong-ing to an appropriate Hilbert space defined on the spheroid. By exploiting surface Green’s functions, reproducing kernels for discrete Dirichlet and Neumann conditions are constructed in the spheroidal geometry. According to a complete system of surface spheroidal harmonics, generalized Green’s functions are also defined. Based on the minimization problem and corresponding reproducing kernel, spline interpolant which minimizes the desired norm and satisfies the given discrete conditions is defined on the spheroidal surface. The application of the results in Geodesy is explained in the gravity data interpolation over the globe. Numéro de notice : A2020-783 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.3846/gac.2020.11316 En ligne : https://doi.org/10.3846/gac.2020.11316 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=96479 [article]

Precise local quasigeoid modelling using GNSS/levelling height anomalies and gravity data / Marek Trojanowicz in Survey review, Vol 52 n°370 (January 2020)  

Public [article]  inSurvey review > Vol 52 n°370 (January 2020) . - pp 76 - 83 Titre : Precise local quasigeoid modelling using GNSS/levelling height anomalies and gravity data Type de document : Article/Communication Auteurs : Marek Trojanowicz, Auteur ; Edward Osada, Auteur ; Krzysztof Karsznia, Auteur Année de publication : 2020 Article en page(s) : pp 76 - 83 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] collocation par moindres carrés [Termes IGN] données géophysiques [Termes IGN] données GNSS [Termes IGN] Earth Gravity Model 2008 [Termes IGN] erreur en altitude [Termes IGN] fonction spline d'interpolation [Termes IGN] formule de Molodensky [Termes IGN] modèle de géopotentiel local [Termes IGN] modèle numérique de surface [Termes IGN] nivellement [Termes IGN] Pologne [Termes IGN] quasi-géoïde Résumé : (auteur) This study compares four approaches of local quasigeoid modelling using GNSS/levelling height anomalies. The first two approaches utilise only a dense network of points with known GNSS/levelling height anomalies and the EGM2008 model. They are based on the interpolation of residual values of height anomalies by applying the least squares collocation (LSC) and the thin plate spline (TPS). The next two approaches use additional data in the form of surface gravity data and the digital elevation model. One of these approaches is based on the classical Molodensky method combined with LSC. The other approach utilises the method of geophysical gravity data inversion (GGI). During the research, the authors used a local network of points with precisely defined GNSS/levelling height anomalies located in South-Western Poland. They obtained comparable results for all tested approaches at the maximum analysed density of GNSS/levelling points (about 1point30km2). The differences between the modelling results became apparent only with an increase in the distance between the GNSS/levelling data points and the reduced accuracy of the used global geopotential model. Numéro de notice : A2020-027 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/00396265.2018.1525981 date de publication en ligne : 10/10/2018 En ligne : https://doi.org/10.1080/00396265.2018.1525981 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=94479 [article]

Robust interpolation of DEMs from lidar-derived elevation data / Chuanfa Chen in IEEE Transactions on geoscience and remote sensing, vol 56 n° 2 (February 2018)  

Public [article]  inIEEE Transactions on geoscience and remote sensing > vol 56 n° 2 (February 2018) . - pp 1059 - 1068 Titre : Robust interpolation of DEMs from lidar-derived elevation data Type de document : Article/Communication Auteurs : Chuanfa Chen, Auteur ; Yanyan Li, Auteur ; Na Zhao, Auteur ; Changqing Yan, Auteur Année de publication : 2018 Article en page(s) : pp 1059 - 1068 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Lasergrammétrie [Termes IGN] données lidar [Termes IGN] données localisées 3D [Termes IGN] fonction spline [Termes IGN] interpolation [Termes IGN] méthode robuste [Termes IGN] modèle numérique de surface Résumé : (Auteur) Light detection and ranging (lidar)-derived elevation data are commonly subjected to outliers due to the boundaries of occlusions, physical imperfections of sensors, and surface reflectance. Outliers have a serious negative effect on the accuracy of digital elevation models (DEMs). To decrease the impact of outliers on DEM construction, we propose a robust interpolation algorithm of multiquadric (MQ) based on a regularized least absolute deviation (LAD) technique. The objective function of the proposed method includes a regularization-based smoothing term and an LAD-based fitting term, respectively, used to smooth noisy samples and resist the influence of outliers. To solve the objective function of the proposed method, we develop a simple scheme based on the split-Bregman iteration algorithm. Results from simulated data sets indicate that when sample points are noisy or contaminated by outliers, the proposed method is more accurate than the classical MQ and two recently developed robust algorithms of MQ for surface modeling. Real-world examples of interpolating 1 private and 11 publicly available airborne lidar-derived data sets demonstrate that the proposed method averagely produces better results than two promising interpolation methods including regularized spline with tension (RST) and gridded data-based robust thin plate spline (RTPS). Specifically, the image of RTPS is too smooth to retain terrain details. Although RST can keep subtle terrain features, it is distorted by some misclassified object points (i.e., pseudooutliers). The proposed method obtains a good tradeoff between resisting the effect of outliers and preserving terrain features. Overall, the proposed method can be considered as an alternative for interpolating lidar-derived data sets potentially including outliers. Numéro de notice : A2018-193 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1109/TGRS.2017.2758795 date de publication en ligne : 17/10/2017 En ligne : https://doi.org/10.1109/TGRS.2017.2758795 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89858 [article]

On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation / Vegard Ophaug in Journal of geodesy, vol 91 n° 11 (November 2017)  

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The extension of the parametrization of the radio source coordinates in geodetic VLBI and its impact on the time series analysis / Maria Karbon in Journal of geodesy, vol 91 n° 7 (July 2017)  

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A penalized spline-based attitude model for high-resolution satellite imagery / Hongbo Pan in IEEE Transactions on geoscience and remote sensing, vol 54 n° 3 (March 2016)  

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Creation of parametric BIM objects from point clouds using nurbs / Luigi Barazzetti in Photogrammetric record, vol 30 n° 152 (December 2015 - February 2016)  

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Adaptive algorithm for large scale DTM interpolation from lidar data for forestry applications in steep forested terrain / Almasi S. Maguya in ISPRS Journal of photogrammetry and remote sensing, vol 85 (November 2013)

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Bayesian and frequentist regression methods / Jon Wakefield (2013)  

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Interpolation spatiale / Pierre Bosser (2012) 

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Camera calibration using composed cubic splines / A. Arfaoui in Geomatica, vol 65 n° 2 (June 2011)

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Effects of topographic variability and Lidar sampling density on several DEM interpolation methods / Q. Guo in Photogrammetric Engineering & Remote Sensing, PERS, vol 76 n° 6 (June 2010)  

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Superresolution enhancement of hyperspectral CHRIS/Proba images with a thin-plate spline nonrigid transform model / J. Chan in IEEE Transactions on geoscience and remote sensing, vol 48 n° 6 (June 2010)

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