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The geodetic boundary value problem in two dimensions and its iterative solution / Martin Van Gelderen (1991)
Titre : The geodetic boundary value problem in two dimensions and its iterative solution Type de document : Thèse/HDR Auteurs : Martin Van Gelderen, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1991 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 35 Importance : 143 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-241-2 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Résumé : (auteur) In this thesis, the geodetic boundary value problem (GBVP) for a completely hypothetical earth is developed. As already shown in (Gerontopoulos, 1978) the complete GBVP for a 2D earth can be set up. It can serve as an example for the real 3D one, with the advantage of less complex mathematics and better performable numerical simulations.
In chapter one, the points of departure of this thesis are discussed. It is underlined that we do not seek for a strict mathematical solution of the GBVP, as done by Gerontopoulos, but investigate aspects of the 2D GBVP that have correspondence with the 3D case. This introductory chapter is concluded by an overview of the history of the problem of the determination of the figure of the earth.
Chapter two serves as preparation for the formulation and solution of the GBVP. Some points of the potential theory in the plane are treated and special attention is paid to the series solution of the potential for a circular boundary, which is an ordinary Fourier series. Finally expressions are derived for the integral kernels appearing in the solution of the GBVP.
In chapter three, the linear observation equations are derived for the classical observations potential, gravity and astronomical latitude, and for the components of the gravity gradient tensor. From several combinations of these observables, the potential, and the position are solved with the observation equations in circular, and constant radius approximation. For their solution, closed integral expressions are given. The systems of equations can be either uniquely determined or overdetermined. This yields solutions for the disturbing potential which are almost identical to the 3D problem. It is also possible to solve, in this approximation, the GBVP analytically from discrete measurements. The analytical expression derived for the inverse normal matrix can be used for error propagation. It is shown that the integral of astronomical leveling can be derived from the solution of the GBVP with observations of astronomical latitude. Furthermore, attention is paid to the zeroth and first degree coefficients, and to the application of the theory of reliability to the GBVP.
In chapter four, first the effect of the neglect of the topography and the ellipticity is analysed. It follows an iteration method can be applied in order to obtain solutions of the GBVP without, or with only little, approximation. Then, five levels of approximation are defined: three linear approximations (with or without the topography and/or the ellipticity taken into account), a quadratic model and the exact, non-linear equations. In the iteration the analytical solutions of the GBVP'S in circular, constant radius approximation are used for the solution step. For the backward substitution the model is applied for which the solution is sought for. The problems are solved numerically by iteration in chapter five. The iterative solution of the problem in circular approximation, occasionally referred to as the simple problem of Molodensky, is also given as a series of integrals. For the convergence of
the iteration criteria are derived.
In chapter five, the generation of a synthetical world is presented. The features of the real world, with respect to the topography and the gravity field, are used to determine its appearance. The observations are computed, from which the potential and the position are solved by the iteration, for all five levels of approximation defined. The fixed, scalar and vectorial problem are considered. It turns out that, in case band limited observations without noise are used, the ellipticity of the earth,
not taken into account in the solution step of the iteration, is the main obstacle for convergence. This can be overcome by the use of a potential series with elliptical coordinates, instead of the polar coordinates usually applied. The theoretical condition for convergence of the iteration is tested, and for several circumstances the accuracy of the solution of the potential and position unknowns is computed. We mention: uniquely determined and overdetermined problems, band limited observations, block averages and point values, number of points etc. Finally, the error spectra of the solved coefficients are compared to the error estimates obtained by error propagation with the analytical expression for the inverse normal matrix of the GBVP in circular, constant radius approximation, and a simple noise model for the observations. If the data noise is the dominant error source, this error estimation turns out to work very well.Numéro de notice : 60364 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère DOI : sans En ligne : https://www.ncgeo.nl/downloads/35VanGelderen.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60738 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 60364-01 30.40 Livre Centre de documentation Géodésie Disponible 60364-02 30.40 Livre Centre de documentation Géodésie Disponible
Titre : The role of orbit errors in processing of satellite altimeter data Type de document : Rapport Auteurs : E.J.O. Schrama, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1989 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 33 Importance : 170 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-239-9 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Technologies spatiales
[Termes IGN] altimétrie satellitaire par radar
[Termes IGN] données altimétriques
[Termes IGN] invariance
[Termes IGN] mécanique orbitale
[Termes IGN] orbitographie
[Termes IGN] pesanteur terrestre
[Termes IGN] Seasat
[Termes IGN] vitesse radialeRésumé : (auteur) The problem of radial orbit errors in processing of satellite altimeter data is largely due to the inaccuracy of the gravity model which is required for the computation of the trajectory of the spacecraft. A commonly used technique for removing these errors consists of minimizing the crossover differences of profiles measured by the altimeter radar.
Several versions of the technique of least squares crossover minimization have been investigated using either SEASAT observations or simulated data. In these adjustments coefficients of error functions are estimated which are either locally defined over short arc segments, globally over long arc segments, or continuously over an entire arc having a length of several days. The solution of the corresponding normal equations consists of a homogeneous and a particular part.
For each crossover minimization problem (CMP) the homogeneous solution is always given as an analytical expression describing the invariances of the altimetric sea surface with respect to the crossover differences. These invariances are described by a surface deformation function which is characteristic for the problem in question. The number of coefficients in this function equals to the rank defect of the normal matrix in the CMP.
For the particular solution of a local CMP (using "tilt and bias" functions) it was found that 2 non-intersecting and non-overlapping master arc segments have to be fixed. However for global chronological segmented CMP's (using 3 parameter sine-cosine functions) only 1 master arc segment needs to be fixed for a particular solution. For continuous CMP's a particular solution is found by including 9 constraint equations in the form of pseudo observation equations. In this case the error function consists of a Fourier series truncated at a cutoff frequency of 2.3 cycles per revolution including a 2 parameter function modeling a long periodic effect in the orbit.
The underlying problem of gravitational radial orbit errors is described by means of the linear perturbations theory, which is based on the Lagrange planetary equations. Additionally the problem is formulated by means of the Hill equations describing perturbed satellite motions in an idealized circular orbit. It is shown that the non-resonant particular radial solution of the Hill equations coincides with the first-order radial solution derived from the linear perturbations theory assuming a
near circular orbit.
The first-order radial solution has been compared with a simulated signal derived by numerical integration of the equations of motion. The simulated signal consists of the radial differences between two trajectories (resembling the SEASAT 3 day repeat configuration) integrated with different gravity models. It was found that the analytical orbit error model resembles closely the simulated signal after removal of a long periodic effect.
The validity of the general solutions of two global CMP's has been investigated by means of a simulation experiment. In this experiment crossover differences are simulated by means of the radial orbit error signal described above. In a second step it is attempted to reconstruct this signal by minimizing the simulated differences.
This experiment revealed that the general solution of the segmented CMP appears to be hampered by unrealistic velocity discontinuity effects of successive arc segment error functions. In addition, it fails to describe the C11 and S11 and higher degree and order components of a geographically correlated radial orbit error. This is not surprising since one can prove that the homogeneous solution of the segmented CMP (without velocity discontinuities) corresponds to the C00 and C10 component of the geographically correlated radial orbit error. For this reason the global segmented CMP is reformulated in a continuous approach where it is shown that the homogeneous solution coincides with the geographically correlated radial orbit error. Computations showed that the simulated signal deviates to approximately 15 cm r.m.s. with respect to the general solution of the continuous CMP.
Employing the latter technique 5 independent particular solutions of a radial orbit error signal have been computed from SEASAT crossover data. These solutions appear to be highly correlated and suggest the presence of a disturbing effect likely to be caused by gravity modeling errors. Additionally it was found that the individual solutions resemble a concentration of signal near the once per revolution frequency in the radial orbit error spectrum. This solution could in principle be used to improve a part of the gravity model that is used in the trajectory computation of the satellite.
In the last part an integrated approach is described where the problem of modeling errors in the orbit, the geoid and the permanent part of the sea surface topography (PST) caused by ocean circulation are considered simultaneously. It is argued that an application of the integrated approach is justified if simultaneously gravity model improvement is performed employing tracking data of other satellites at different inclinations and eccentricities. Other aspects of the integrated approach concern the modeling problems of the PST field, an omission effect of the gravity field and the relation with the global continuous CMP.Numéro de notice : 57963 Affiliation des auteurs : non IGN Thématique : IMAGERIE/POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/33Schrama.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60322 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 57963-01 21.10 Livre Centre de documentation Technologies spatiales Disponible 57963-02 21.10 Livre Centre de documentation Technologies spatiales Disponible
Titre : NavGrav, navigation and gravimetric experiment, at the North Sea Type de document : Rapport Auteurs : R.H.N. Haagmans, Auteur ; G.J. Husti, Auteur ; P. Plugers, Auteur ; J.H.M. Smit, Auteur ; G.L. Strang Van Hees, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1988 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 32 Importance : 135 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-237-5 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] altimétrie
[Termes IGN] centre de gravité
[Termes IGN] gravimétrie
[Termes IGN] Nord, mer du
[Termes IGN] positionnement par GPS
[Termes IGN] radionavigationIndex. décimale : 30.00 Géodésie - généralités Numéro de notice : 57769 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport d'étude technique DOI : sans En ligne : https://www.ncgeo.nl/downloads/32Haagmans.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60265 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 57769-01 30.00 Livre Centre de documentation Géodésie Disponible 57769-02 30.00 Livre Centre de documentation Géodésie Disponible On the great circle reduction in the data analysis for the astrometric satellite Hipparcos / Hans van der Marel (1988)
Titre : On the great circle reduction in the data analysis for the astrometric satellite Hipparcos Type de document : Thèse/HDR Auteurs : Hans van der Marel, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1988 Collection : Netherlands Geodetic Commission Publications on Geodesy, ISSN 0165-1706 num. 8 Importance : 228 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-235-1 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Astronomie
[Termes IGN] analyse de données
[Termes IGN] astrométrie
[Termes IGN] catalogue d'étoiles
[Termes IGN] Hipparcos
[Termes IGN] lissage de données
[Termes IGN] orientation
[Termes IGN] parallaxe annuelle
[Termes IGN] réductionIndex. décimale : 31.00 Astronomie - généralités Numéro de notice : 57230 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère DOI : sans En ligne : https://www.ncgeo.nl/downloads/31VanDerMarel.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60176 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 57230-01 31.00 Livre Centre de documentation En réserve M-103 Disponible On the principles, assumptions and methods of geodetic very long baseline interferometry / Frits J.J. Brouwer (1985)
Titre : On the principles, assumptions and methods of geodetic very long baseline interferometry Type de document : Rapport Auteurs : Frits J.J. Brouwer, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1985 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 7-4 Importance : 180 p. Format : 20 x 28 cm ISBN/ISSN/EAN : 978-90-6132-232-0 Note générale : Bibliographie Langues : Français (fre) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] données ITGB
[Termes IGN] fiabilité des données
[Termes IGN] interférométrie à très grande base
[Termes IGN] modèle physique
[Termes IGN] positionnement par arcs courts
[Termes IGN] précision du positionnementIndex. décimale : 30.63 Télémétrie laser sur satellite, Télémétrie laser sur lune, VLBI Numéro de notice : 55532 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/29Brouwer.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=59861 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 55532-01 30.63 Livre Centre de documentation Géodésie Disponible The geometry of geodetic inverse linear mapping and non-linear adjustment / Peter J.G. Teunissen (1985)PermalinkPermalinkPermalinkA further inquiry into the theory of S-transformations and criterion matrices / Martien Molenaar (1981)PermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalink