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Optimisation of GNSS networks, considering baseline correlations / M. Amin Alizadeh-Khameneh in Survey review, vol 51 n° 364 (January 2019)  

Public [article]  inSurvey review > vol 51 n° 364 (January 2019) . - pp 35 - 42 Titre : Optimisation of GNSS networks, considering baseline correlations Type de document : Article/Communication Auteurs : M. Amin Alizadeh-Khameneh, Auteur ; Lars E. Sjöberg, Auteur ; Anna B. O. Jensen, Auteur Année de publication : 2019 Article en page(s) : pp 35 - 42 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] corrélation [Termes IGN] données GNSS [Termes IGN] double différence [Termes IGN] ligne de base [Termes IGN] optimisation (mathématiques) [Termes IGN] réseau géodésique local [Termes IGN] Suède Résumé : (Auteur) By considering global navigation satellite system (GNSS) observations, one can perform optimisation according to some pre-defined criteria and come up with the best location of receivers and optimum number of baselines. In practice, it is quite common to neglect the effect of correlations between baselines, and instead assume single-baseline-adjusted data in the optimisation procedure. However, in each session of observation, usually more than two receivers are simultaneously taking data from a number of common GNSS satellites, implying that the single- or double-difference observations are correlated. Our study designs an optimal observation plan for a GPS network in Skåne in southern Sweden, with the aim of determining possible displacements. Assuming three receivers in each session of observations leads to correlation between the GPS baselines, and consequently a fully populated weight matrix for each session of observation. A bi-objective optimisation model of precision and reliability is chosen to optimise the variance factor of each session, and eventually, design an observation plan. It is shown in this study that observing six out of ten possible sessions is sufficient to enable the network to detect a 5 mm displacement at each station. Assuming that the double-difference phase observations are uncorrelated changes the observation plan by retaining two more sessions. However, defining the weight matrix based on the double-difference observations requires the correlations to be taken into account, and neglecting them leads to incorrect results. Numéro de notice : A2019-187 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Numéro de périodique nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/00396265.2017.1342896 Date de publication en ligne : 26/06/2017 En ligne : https://doi.org/10.1080/00396265.2017.1342896 Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92618 [article]

A numerical test of the topographic bias / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)  

Public [article]  inJournal of geodetic science > vol 8 n° 1 (January 2018) . - pp 14 - 17 Titre : A numerical test of the topographic bias Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur ; Mehdi S. Shafiei Joud, Auteur Année de publication : 2018 Article en page(s) : pp 14 - 17 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse numérique [Termes IGN] anomalie de pesanteur [Termes IGN] erreur systématique Résumé : (Auteur) In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre). Numéro de notice : A2018-612 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0002 Date de publication en ligne : 07/02/2018 En ligne : https://doi.org/10.1515/jogs-2018-0002 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92645 [article]

On the geoid and orthometric height vs. quasigeoid and normal height / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)  

Public [article]  inJournal of geodetic science > vol 8 n° 1 (January 2018) . - pp 115 - 120 Titre : On the geoid and orthometric height vs. quasigeoid and normal height Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur Année de publication : 2018 Article en page(s) : pp 115 - 120 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude normale [Termes IGN] altitude orthométrique [Termes IGN] géoïde [Termes IGN] quasi-géoïde Résumé : (Auteur) The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling. Numéro de notice : A2018-115 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0011 Date de publication en ligne : 31/12/2018 En ligne : https://doi.org/10.1515/jogs-2018-0011 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92664 [article]

On the topographic bias and density distribution in modelling the geoid and orthometric heights / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)  

Public [article]  inJournal of geodetic science > vol 8 n° 1 (January 2018) . - pp 30 - 33 Titre : On the topographic bias and density distribution in modelling the geoid and orthometric heights Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur Année de publication : 2018 Article en page(s) : pp 30 - 33 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude orthométrique [Termes IGN] analyse numérique [Termes IGN] erreur systématique [Termes IGN] géoïde [Termes IGN] incertitude géométrique [Termes IGN] montagne Résumé : (Auteur) It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators. Numéro de notice : A2018-614 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0004 Date de publication en ligne : 02/03/2018 En ligne : https://doi.org/10.1515/jogs-2018-0004 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92662 [article]