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Auteur W. Baarda |
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Titre : Linking up spatial models in geodesy extended S-transformations Type de document : Rapport Auteurs : W. Baarda, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1995 Collection : Netherlands Geodetic Commission Publications on Geodesy, ISSN 0165-1706 num. 41 Importance : 144 p. Format : 21 x 27 cm ISBN/ISSN/EAN : 978-90-6132-253-5 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] modélisation spatialeIndex. décimale : 30.04 Mathématiques appliquées à la géodésie Note de contenu : 1. Introduction.
2. A preliminary consideration of the three-dimensional S-coordinate frame preferred by the author.
3.1 An estimation of the position of the centre of mass of the earth in an S-coordinate frame according to Section 2, with possible consequences for the linking up of mathematical models in geodesy.
3.2 An intermezzo treating by means of quaternions the mathematical formulation of the S-coordinate frame chosen, and some consequences.
3.2.0 Introduction.
3.2.1 The similarity transformation including the gravity potential. A form element for this potential.
3.2.2.1 The formula for the three-dimensional S-coordinate. The S-transformation as a connection onto assumed fixed coordinates.
3.2.2.2 The relation between two- and three-dimensional S-coordinates. An elegant formula for the three-dimensional S-coordinate as a function of three intrinsic quantities.
3.2.3 Application of the law of propagation of variances by means of isomorphic matrices.
3.2.4 The construction of Criterion Matrices. The important theorem stating that sphericity of three-dimensional point- and relative standard ellipsoids is not conserved in an S-transformation, contrary to the corresponding property of circularity in the two-dimensional situation.
4.1 Again the connection between gravimetric and geometric theory, treated sketchily but with concentration on the fundamentals. The linking up of a mathematical model by dimensionless quantities. An objectionable interpretation of compound quantities as "free-air reduction to the geoid". A more appropriate definition of "relative sea-topography".
4.2 An analysis of the modified integral formulas of Stokes and Hotine, based on ideas of Rummel and Teunissen. A choice for the present satellite era. The lasting influence of the transition from sea to land.
4.3 The influence of PMPC ≠ 0, PC being the centre of mass of the earth and PM the origin of a quasi-centric S-coordinate frame for terrestrial data.
4.4 Once more the integral formula of Hotine. Effects of first degree spherical harmonics. A suggestion for application. An afterthought.
5. Supplementary remarks on the linking up of the gravimetric-geometric model. Correction terms in the modified integral formulas of Stokes, Hotine and Vening Meinesz, deviating from the terms found in the literature.
6. Possible consequences of the gravimetric-geometric S-system for (terrestrial) mechanics. The corresponding dimensionless time quantity.
7.1 A sketch of problems in point positioning on the earth by means of satellite observations.
7.2 The effect of PMPC ≠ 0 on launch data of a satellite.
7.3 Correction of DΠ-quantities (orbit data) for earth rotation.
8.1 An alternative way of writing the formulas of the Kepler ellipse for the computation of a satellite orbit. Difference formulas for dimensionless quantities, such as the dimensionless time interval.
8.2.1 The linking up of the mathematical model from section 8.1. The influence of PMPC ≠ 0.
8.2.2 Comparison of the S-system in satellite orbit computation with the S-system in physical geodesy; possible small differences in scale in mass, potential and time.
8.2.3 Questions arising when rewriting the higher-order terms of orbit computations by means of the dimensionless quantities introduced.
9.1 Establishment of control by satellite measurements. The bird's-tail construction. Difference formulas with an appraisal of the influence of PMPC ≠ 0.
9.2 An investigation into possibilities for the estimation of PMPC ≠ 0.
9.3.1 A more realistic process of measurement by means of series of pseudo-distances (distance measurements from one station with the same but unknown length scale).
9.3.2 Synchronous measurements in several stations, with an estimation of the maximum distance between stations if a (practically acceptable) elimination of the influence of orbit errors is to be attained. Measurement of the distance differences.
10. A short after-consideration. The application of dimensionless quantities in satellite gradiometry.
11. Concluding word with remarks concerning relativity theory, a possible influence of the choice of terrestrial datum points on the precision of the determination of points of satellite orbits, doubts about the alleged precision of computed quantities in physical geodesy obtained by satellite gradiometry.Numéro de notice : 61671 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/41Baarda.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60964 Exemplaires(2)
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Titre : Geodetic work in the Netherlands 1987-1990 : Report prepared for the general assembly of the International Association of Geodesy, XXth [20th] general assembly of the International Union of Geodesy and Geophysics, Vienna, 1991 Type de document : Rapport Auteurs : W. Baarda, Éditeur scientifique Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1991 Collection : Netherlands Geodetic Commission Publications on Geodesy, ISSN 0165-1706 Conférence : IAG 1991, 20th general assembly and symposium, From Mars to Greenland : charting gravity with space and airborne instruments, fields tide methods results 11/08/1991 24/08/1991 Vienne Autriche Importance : 22 p. Format : 21 x 27 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] géoïde local
[Termes IGN] Global Positioning System
[Termes IGN] gravimétrie
[Termes IGN] Pays-Bas
[Termes IGN] problème des valeurs limites
[Termes IGN] technologies spatialesIndex. décimale : 30.00 Géodésie - généralités Numéro de notice : 63945 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=44372 Exemplaires(1)
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Titre : A connection between geometric and gravimetric geodesy : a first sketch Type de document : Rapport Auteurs : W. Baarda, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1979 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 25 Importance : 110 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-90-6132-225-2 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] équation intégrale
[Termes IGN] géodésie mathématique
[Termes IGN] harmonique sphérique
[Termes IGN] intégraleIndex. décimale : 30.04 Mathématiques appliquées à la géodésie Résumé : (auteur) [introduction] The sketch given here evolved as a spare time activity from the presentation and discussion of the paper IBjerhammer, 1962]. The struggle with the subject concerned the main lines: not all mathematical details have been satisfactorily solved and the theory is not complete, hence the sketchy character of the treatment. The incentive to this investigation came from two sides:
a. In setting up a spatial theory of geometric geodesy the need was felt for a connection with gravimetric {or physical} geodesy that was independent of the classical ellipsoidal approach.
b. Since the lectures by F.A. Vening Meinesz in 1938 and 1939, the field of physical geodesy has always fascinated me and held my interest. However, as the number of publications on this field grew, the theoretical structure became less and less clear to me. Spherical and nonspherical approximations followed each other in arbitrary order, just as the use of Poisson and Green integrals. The use of approximate values was somewhat curious, leading, on the one hand, to a kind of physical interpretation such as the 'telluroid', and on the other hand to a 'fundamental equation of geodesy' which sometimes was a hindrance. Further, the whole theory seems to be due to an 'ill-posed problem', although the application of the collocation technique removes this difficulty or leaves it aside. And, finally, why is the purpose of geodesy the determination of a vague concept like the 'geoid', and not the determination of the topographical land and sea surface of the earth?
In the course of years I have in developing the present approach become more and more convinced that its main lines have a real significance. Many classical results can be recognized in the new theory; its basic thought is connected with the model theory on which I based the adjustment theory of geometric geodesy. Yet many questions and problems are left open: newly developed measuring processes have not found their place yet, methods of dynamical satellite geodesy have not been sufficiently analysed, the elaboration and interpretation of the relationships found are still somewhat problematic. It is hoped that criticism will provide a check on the results obtained.
Let the following summary precede the theory. The core of the theory is the connection of
results of geometric networks
spirit levelling
gravity {and vertical gravity gradient} observations
to the third integral identity of Green. The way in which this connection is established is determined by the analysis of measuring processes, leading to a connection via dimensionless compound difference quantities. Linearization of the integral equations necessitates a closer study of Poisson's integral; it appears that effects of Gauss's integral and Poisson's integral cancel each other in the linearized equations. The closed model of approximate values turns out to be of dominating importance; spherical approximation {Poisson's integral} requires an order of magnitude of difference-quantities that is smaller than is now in use for anomalies. This leads to a stronger interaction with geophysical model hypothesis.
The solution of linearized integral equations leads to Stokes-like integral formulae, the so-called Green integrals, with possibilities for regional applications on land and sea, including some aspects of satellite geodesy.
A guess is made with respect to the background of the inverses of these Stokes-like integral formulae, deduced by Molodenskii.
Concepts like the 'fundamental equation of physical geodesy', 'free air reduction', 'geoid' and 'height' are critically examined. The sketch concludes with some remarks on collocation theory, leading to a consideration of the choice between the use of collocation or of integral formulae in the present theory.Note de contenu : 1- Introductory remarks
2- Estimable quantities and S-transformations in physical geodesy
3- Series of spherical harmonics. Poisson integrals
4- Green integrals
5- Tentative considerations concerning Green integrals
6- Additional considerations
7- Remarks on collocationNuméro de notice : 52488 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/25Baarda.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=59364 Exemplaires(2)
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Titre : S-transformations and criterion matrices Type de document : Rapport Auteurs : W. Baarda, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1973 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 18 Importance : 168 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-90-6132-218-4 Note générale : Bibliographie
Lien vers la seconde édition révisée de 1981Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux
[Termes IGN] matrice
[Termes IGN] transformation de coordonnéesIndex. décimale : 30.11 Transformation de coordonnées Résumé : (auteur) In the publication "A Testing Procedure for Use in Geodetic Networks" [9] a sketch was given for a possible programme of subjects to be studied in Special Study Group No. 1.14 * of the International Geodetic Association. This was an extension of first ideas expressed in 1962 [4a], with a supplement in [4]. Three main problems were formulated:
(1.1) the construction of an artifical covariance matrix, to serve as a mathematical translation of the lower limit of precision required by the purposes of geodetic networks;
(1.2) the use of statistical tests in connection with the adjustment of networks in order to assure the reliability of geodetic networks in relation to their purpose in society; (1.3) the consequences for geodetic networks of a relativation of the concepts north and time.
In [9] {see also [10] for basic theory}, a first solution for (1.2) was given, which since then has been applied to the computation of many densification networks in The Netherlands. The results were very satisfactory, but the method has so far not led to reactions from the members of S.S.G. No. 1.14, and has received little attention from geodesists outside The Netherlands.
The present paper presents a solution for (1.1), a consistent theory which replaces the first draft discussed in November 1964 at Stockholm with the then President of S.S.G. No. 1.14, Professor L. Asplund. The theory has been developed since 1962 by the author and J. E. Alberda, along seemingly very different lines. Many discussions have first led to an improvement of individual ideas, and then, when in 1969 the present paper was drafted, to the insight that the two theories must be identical in essence. A separate publication by Alberda is to be expected; perhaps the differences in argumentation will lead to a clarification of the rather difficult line of thought.
In both investigations, use is made of the theory of the so-called S-transformations, {Dutch: Schrankingstransformaties; English: transformations related to Similarity transformations}, formulated by Baarda around 1944, and applied in the HTW-1956, published in [7], [3] and [5] in the form of 'Similarity covariance transformations'. The present theory was, however, only made possible by a more consistent approach of the S-transformations based on the theory of difference equations for the linearization of functional relationships in adjustment theory. This theory was developed in [1]; a first treatment can be found in [4] section 3.4.
Both researchers also used the criteria for the form and the size of standard ellipses of coordinates of points in a network, which were more or less sketchily formulated by Baarda in the HTW-1956. Alberda chose the way of a further consistent elaboration of this formulation, whereas Baarda in the first instance rejected the approach of the HTW-1956, because it was in conflict with studies on model theory, such as given in [4], section 4, and in the 'Polygon Theory in the Complex Plane' [2].Numéro de notice : 48625 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport de recherche DOI : sans En ligne : https://www.ncgeo.nl/downloads/18Baarda.pdf Format de la ressource électronique : URL second édition Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=58860 Exemplaires(2)
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Titre : A testing procedure for use in geodetic networks Type de document : Rapport Auteurs : W. Baarda, Auteur Editeur : Delft : Netherlands Geodetic Commission NGC Année de publication : 1968 Collection : Netherlands Geodetic Commission Publications on Geodesy Sous-collection : New series num. 9 Importance : 98 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux
[Termes IGN] contrôle
[Termes IGN] réseau géodésiqueIndex. décimale : 30.10 Systèmes de référence et réseaux géodésiques Résumé : (auteur) In this paper an outline for the continuation of the work in I.A.G. Special Study Group No. 1.14 is given, based on the paper "Statistical Concepts in Geodesy". As a first step, a testing procedure for geodetic networks is discussed, using one-sided F-tests; a definition of the concept "reliability of geodetic networks" is proposed.
1. The testing procedure is a part of the so-called unlinking of the computing model and consequently a part of the prediction. This new theory was developed to obtain a clearer line of thought in testing and to overcome existing confusion by pointing out the interconnection of consequences. The theory is as much as possible connected to current methods; the purpose was to find a theory applicable in practice.
2. For geodetic networks it is important to have the possibility to make checks soon after completion of the measurements in order to make partial remeasurements possible while towers and signals are still standing. Remeasurement shortly afterwards, even remeasuring slightly too much, will in the long run prove to be cheaper than hidden {gross} errors. The latter will often lead to strong local distortion of the network and render difficult the effective control of densification measurements or possibly even prevent that the objectives of such measurements are attained.
3. Because of the random character of observations it is impossible to signalize {gross} errors with certainty. At the best only statements having a certain probability of success, can be made. The order of magnitude of this probability βo, has to be agreed upon; it is one of the parameters in the theory. βo leads to a lower bound for the order of magnitude of a function λo of gross errors which can just be signalized by a test; λo is determined by one specified alternative hypothesis, provided that a second parameter is fixed. Multidimensional tests are reduced to a one-dimensional test via this particular alternative hypothesis. The second parameter then is the significance level αo of this one-dimensional test. The significance level α of a b-dimensional test is then dependent on b, if in combination with the same βo the same bound for the signalization of errors λo is required. This leads, on the one hand, to the designed testing procedure, and on the other hand to the definition of the "reliability of geodetic networks".
4. Planning the precision as well as the reliability of geodetic networks requires a quantification of the demands following from the purpose of the network. This quantification is the most difficult problem and it is certainly not solved yet. In view of the difficulty of foreseeing future applications of the network, it is questionable whether more than the formulation of partial or relative purposes and their quantifications can ever be attained. It will be necessary to come to a conclusion in order to make a justified choice of values {αo, βo}, possibly by applying the decision theory approach.
5. Methods for "data-snooping" follow from the reasoning developed. Connections with publications by Bjerhammer are given, whereas a comparison is made with related problems from mathematical statistics.
6. The reasoning is generally applicable and need not be restricted to geodetic networks.
It can also be applied when arbitrary distribution functions are used, possibly along with F-statistics, provided the power function of the tests can be computed. In this paper only the method using F-distributions has been worked out.Numéro de notice : 44943 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Rapport d'étude technique DOI : sans En ligne : https://www.ncgeo.nl/downloads/09Baarda.pdf Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=58259 Exemplaires(1)
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