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Dépouillements


Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix / Gaël Kermarrec in Journal of geodesy, vol 90 n° 9 (September 2016)
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[article]
Titre : Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix Type de document : Article/Communication Auteurs : Gaël Kermarrec, Auteur ; Steffen Schön, Auteur Année de publication : 2016 Article en page(s) : pp 793 – 805 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] compensation par moindres carrés
[Termes IGN] corrélation
[Termes IGN] données GPS
[Termes IGN] estimateur
[Termes IGN] matrice de covariance
[Termes IGN] matrice diagonale
[Termes IGN] pondération
[Termes IGN] positionnement différentiel
[Termes IGN] positionnement par GPS
[Termes IGN] régression
[Termes IGN] série temporelle
[Vedettes matières IGN] Traitement de données GNSSRésumé : (auteur) Based on the results of Luati and Proietti (Ann Inst Stat Math 63:673–686, 2011) on an equivalence for a certain class of polynomial regressions between the diagonally weighted least squares (DWLS) and the generalized least squares (GLS) estimator, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented. The equivalent covariance matrix is much easier to compute than a diagonalization of the covariance matrix via eigenvalue decomposition which also implies a change of the least squares equations. This condensed matrix, for use in the least squares adjustment, can be seen as a diagonal or reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix. The least squares results obtained with the equivalent diagonal matrices and those given by the fully populated covariance matrix are mathematically strictly equivalent for the mean estimator in terms of estimate and its a priori cofactor matrix. It is shown that this equivalence can be empirically extended to further classes of design matrices such as those used in GPS positioning (single point positioning, precise point positioning or relative positioning with double differences). Applying this new model to simulated time series of correlated observations, a significant reduction of the coordinate differences compared with the solutions computed with the commonly used diagonal elevation-dependent model was reached for the GPS relative positioning with double differences, single point positioning as well as precise point positioning cases. The estimate differences between the equivalent and classical model with fully populated covariance matrix were below the mm for all simulated GPS cases and below the sub-mm for the relative positioning with double differences. These results were confirmed by analyzing real data. Consequently, the equivalent diagonal covariance matrices, compared with the often used elevation-dependent diagonal covariance matrix is appropriate to take correlations in GPS least squares adjustment into account, yielding more accurate cofactor matrices of the unknown. Numéro de notice : A2016-654 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0911-z En ligne : http://dx.doi.org/10.1007/s00190-016-0911-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81856
in Journal of geodesy > vol 90 n° 9 (September 2016) . - pp 793 – 805[article]A conventional value for the geoid reference potential W0 / L. Sánchez in Journal of geodesy, vol 90 n° 9 (September 2016)
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[article]
Titre : A conventional value for the geoid reference potential W0 Type de document : Article/Communication Auteurs : L. Sánchez, Auteur ; Robert Cunderlik, Auteur ; N. Dayoub, Auteur ; et al., Auteur Année de publication : 2016 Article en page(s) : pp 815 - 835 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] données GOCE
[Termes IGN] données GRACE
[Termes IGN] force de gravitation
[Termes IGN] géoïde terrestre
[Termes IGN] potentiel de pesanteur terrestre
[Termes IGN] surface de la mer
[Termes IGN] télémétrie laser sur satelliteRésumé : (auteur) W0 is defined as the potential value of a particular level surface of the Earth’s gravity field called the geoid. Since the most accepted definition of the geoid is understood to be the equipotential surface that coincides with the worldwide mean ocean surface, a usual approximation of W0 is the averaged potential value WS at the mean sea surface. In this way, the value of W0 depends not only on the Earth’s gravity field modelling, but also on the conventions defining the mean sea surface. W0 computations performed since 2005 demonstrate that current published estimations differ by up to −2.6 m2 s−2 (corresponding to a level difference of about 27 cm), which could be caused by the differences in the treatment of the input data. The main objective of this study is to perform a new W0 estimation relying on the newest gravity field and sea surface models and applying standardised data and procedures. This also includes a detailed description of the processing procedure to ensure the reproducibility of the results. The following aspects are analysed in this paper: (1) sensitivity of the W0 estimation to the Earth’s gravity field model (especially omission and commission errors and time-dependent Earth’s gravity field changes); (2) sensitivity of the W0 estimation to the mean sea surface model (e.g., geographical coverage, time-dependent sea surface variations, accuracy of the mean sea surface heights); (3) dependence of the W0 empirical estimation on the tide system; and (4) weighted computation of the W0 value based on the input data quality. Main conclusions indicate that the satellite-only component (n=200) of a static (quasi-stationary) global gravity model is sufficient for the computation of W0. This model should, however, be based on a combination of, at least, satellite laser ranging (SLR), GRACE and GOCE data. The mean sea surface modelling should be based on mean sea surface heights referring to a certain epoch and derived from a standardised multi-mission cross-calibration of several satellite altimeters. We suggest that the uncertainties caused by geographically correlated errors, including shallow waters in coastal areas and sea water ice content at polar regions should be considered in the computation of W0 by means of a weighed adjustment using the inverse of the input data variances as a weighting factor. This weighting factor should also include the improvement provided by SLR, GRACE and GOCE to the gravity field modelling. As a reference parameter, W0 should be time-independent (i.e., quasi-stationary) and it should remain fixed for a long-term period (e.g., 20 years). However, it should have a clear relationship with the mean sea surface level (as this is the convention for the realisation of the geoid). According to this, a suitable recommendation is to adopt a potential value obtained for a certain epoch as the reference value W0 and to monitor the changes of the mean potential value at the sea surface WS. When large differences appear between W0 and WS (e.g., >±2 m2 s−2), the adopted W0 may be replaced by an updated (best estimate) value. In this paper, the potential value obtained for the epoch 2010.0 (62,636,853.4 m2 s−2) is recommended as the present best estimate for the W0 value. It differs −2.6 m2 s−2 from the so-called IERS W0 value (62,636,856.0 m2 s−2), which corresponds to the best estimate available in 1998. Numéro de notice : A2016-655 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0913-x En ligne : http://dx.doi.org/10.1007/s00190-016-0913-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81857
in Journal of geodesy > vol 90 n° 9 (September 2016) . - pp 815 - 835[article]PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK / Amir Khodabandeh in Journal of geodesy, vol 90 n° 9 (September 2016)
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[article]
Titre : PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK Type de document : Article/Communication Auteurs : Amir Khodabandeh, Auteur ; Peter J.G. Teunissen, Auteur Année de publication : 2016 Article en page(s) : pp 837 – 851 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Applications de géodésie spatiale
[Vedettes matières IGN] Navigation et positionnement
[Termes IGN] erreur systématique
[Termes IGN] positionnement cinématique en temps réel
[Termes IGN] positionnement ponctuel précis
[Termes IGN] récepteur GNSS
[Termes IGN] table géodésiqueRésumé : (auteur) PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be flexible enough to accommodate the occurrence of system-specific receiver biases. In this contribution we present such undifferenced, multi-system PPP-RTK full-rank models for both network and users. By an application of S-system theory, the multi-system estimable parameters are presented, thereby identifying how each of the three PPP-RTK components are affected by the presence of the system-specific biases. As a result different scenarios are described of how these biases can be taken into account. To have users benefit the most, we propose the construction of an ISB look-up table. It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model. By applying such corrections, the user model is strengthened and the number of integer-estimable user ambiguities is maximized. Numéro de notice : A2016-656 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0914-9 En ligne : http://dx.doi.org/10.1007/s00190-016-0914-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81858
in Journal of geodesy > vol 90 n° 9 (September 2016) . - pp 837 – 851[article]Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET) / Michael Kuhns in Journal of geodesy, vol 90 n° 9 (September 2016)
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[article]
Titre : Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET) Type de document : Article/Communication Auteurs : Michael Kuhns, Auteur ; Christian Hirt, Auteur Année de publication : 2016 Article en page(s) : pp 883 – 902 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] erreur d'approximation
[Termes IGN] glace
[Termes IGN] masse d'eau
[Termes IGN] masse de la Terre
[Termes IGN] modèle de densité
[Termes IGN] potentiel de pesanteur terrestre
[Termes IGN] rocheRésumé : (auteur) In gravity forward modelling, the concept of Rock-Equivalent Topography (RET) is often used to simplify the computation of gravity implied by rock, water, ice and other topographic masses. In the RET concept, topographic masses are compressed (approximated) into equivalent rock, allowing the use of a single constant mass–density value. Many studies acknowledge the approximate character of the RET, but few have attempted yet to quantify and analyse the approximation errors in detail for various gravity field functionals and heights of computation points. Here, we provide an in-depth examination of approximation errors associated with the RET compression for the topographic gravitational potential and its first- and second-order derivatives. Using the Earth2014 layered topography suite we apply Newtonian integration in the spatial domain in the variants (a) rigorous forward modelling of all mass bodies, (b) approximative modelling using RET. The differences among both variants, which reflect the RET approximation error, are formed and studied for an ensemble of 10 different gravity field functionals at three levels of altitude (on and 3 km above the Earth’s surface and at 250 km satellite height). The approximation errors are found to be largest at the Earth’s surface over RET compression areas (oceans, ice shields) and to increase for the first- and second-order derivatives. Relative errors, computed here as ratio between the range of differences between both variants relative to the range in signal, are at the level of 0.06–0.08 % for the potential, ∼3–7 % for the first-order derivatives at the Earth’s surface (∼0.1 % at satellite altitude). For the second-order derivatives, relative errors are below 1 % at satellite altitude, at the 10–20 % level at 3 km and reach maximum values as large as ∼20 to 110 % near the surface. As such, the RET approximation errors may be acceptable for functionals computed far away from the Earth’s surface or studies focussing on the topographic potential only. However, for derivatives of the functionals computed near the Earth’s surface, the use of RET introduces very spurious errors, in some cases as large as the signal, rendering it useless for smoothing or reducing of field observation, thus rigorous mass modelling should be used for both spatial and spectral domain methods. Numéro de notice : A2016-657 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0917-6 En ligne : http://dx.doi.org/10.1007/s00190-016-0917-6 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81859
in Journal of geodesy > vol 90 n° 9 (September 2016) . - pp 883 – 902[article]