The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems. Numerous examples are illustrated with Mathematica using the computer algebra techniques of Ring, Polynomials, Groebner basis, Resultants (including Dixon resultants), Gauss-Jacobi combinatorial and Procrustes algorithms, as well as homotopy methods. While these problems are traditionally solved by approximate methods, this book presents alternative algebraic techniques based on computer algebra tools. ¬ This new approach meets such modern challenges as resection by laser techniques, solution of orientation in Robotics, transformation and bundle block adjustment in Geoinformatics, densification of Engineering networks, analytical solution for GNSS-meteorology and many other problems. For Mathematicians, the book provides some practical examples of the application of abstract algebra and multidimensional scaling.
Author(s): Joseph L. Awange, Erik W. Grafarend, Béla Paláncz, Piroska Zaletnyik (auth.)
Edition: 2
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 377
Tags: Computer Applications in Earth Sciences; Geographical Information Systems/Cartography; Computational Mathematics and Numerical Analysis; Remote Sensing/Photogrammetry; Mathematical Applications in Earth Sciences
Front Matter....Pages i-xviii
Introduction....Pages 1-5
Front Matter....Pages 7-7
Basics of ring theory....Pages 9-16
Basics of polynomial theory....Pages 17-32
Groebner basis....Pages 33-47
Polynomial resultants....Pages 49-62
Linear homotpy....Pages 63-77
Solutions of Overdetermined Systems....Pages 79-99
Extended Newton-Raphson method....Pages 101-110
Procrustes solution....Pages 111-135
Front Matter....Pages 137-137
LPS-GNSS orientations and vertical deflections....Pages 139-153
Cartesian to ellipsoidal mapping....Pages 155-171
Positioning by ranging....Pages 173-216
Positioning by resection methods....Pages 217-248
Positioning by intersection methods....Pages 249-263
GNSS environmental monitoring....Pages 265-287
Algebraic diagnosis of outliers....Pages 289-301
Datum transformation problems....Pages 303-338
Back Matter....Pages 339-377