Solving Algebraic Computational Problems in Geodesy and Geoinformatics: The Answer to Modern ChallengesSpringer Science & Business Media, 29 août 2005 - 334 pages While preparing and teaching ‘Introduction to Geodesy I and II’ to - dergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taughtrequiredsomeskillsinalgebra,andinparticular,computeral- bra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we haveattemptedtoputtogetherbasicconceptsofabstractalgebra which underpin the techniques for solving algebraic problems. Algebraic c- putational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds,theconceptsand techniquespresented hereinarenonetheless- plicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robotics apply resection and intersection techniques which require - gebraic solutions. Solution of nonlinear systems of equations is an indispensable task in almost all geosciences such as geodesy, geoinformatics, geophysics (just to mention but a few) as well as robotics. These equations which require exact solutions underpin the operations of ranging, resection, intersection and other techniques that are normally used. Examples of problems that require exact solutions include; • three-dimensional resection problem for determining positions and orientation of sensors, e. g. , camera, theodolites, robots, scanners etc. , VIII Preface • coordinate transformation to match shapes and sizes of points in di?erent systems, • mapping from topography to reference ellipsoid and, • analytical determination of refraction angles in GPS meteorology. |
Table des matières
1 | |
4 | 25 |
Groebner Basis | 45 |
Polynomial Resultants | 47 |
GaussJacobi Combinatorial Algorithm | 56 |
Local versus Global Positioning Systems | 77 |
Partial Procrustes and the Orientation Problem | 89 |
Positioning by Ranging | 105 |
Positioning by Intersection Methods | 199 |
29 | 215 |
GPS Meteorology in Environmental Monitoring | 217 |
Algebraic Diagnosis of Outliers | 245 |
Procrustes Algorithm II | 259 |
Computer Algebra Systems CAS | 293 |
Appendix | 303 |
Buchberger Algorithm | 310 |
From Geocentric Cartesian to Ellipsoidal Coordinates | 147 |
Positioning by Resection Methods | 165 |
3 | 184 |
327 | |
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Expressions et termes fréquents
7-parameter adjusted value algebraic approach atmospheric bending angles Cartesian coordinates Chap closed form coefficients combinations combinatorial solutions computer algebra computer algebra systems datum transformation determinant Deviation dispersion matrix distance equations Example expression frame F Gauss Gauss-Jacobi combinatorial algorithm geodesy geodesy and geoinformatics geodetic geoinformatics given Global Positioning System GPS meteorology GPS satellites impact parameters In-order intersection iterative least squares level reference frame lexicographic ordering linear Gauss-Markov model MATLAB measured monomials nonlinear systems obtained occultation orientation parameters outlier partial Procrustes points polynomial equations polynomial resultants polynomial rings positional norms presented procedures Procrustes algorithm pseudo-observations pseudo-range quadratic equation reduced Groebner basis reference ellipsoid reference frame respectively rotation matrix solved station K1 step Sylvester resultants systems of equations Table techniques three known stations three-dimensional orientation three-dimensional resection tions transformation problem univariate polynomial unknown station variables variance-covariance matrix vector W-LESS water vapour Y₁