# Solving Algebraic Computational Problems in Geodesy and Geoinformatics

## The Answer to Modern Challenges

• Joseph L. Awange
• Erik W. Grafarend
Book

1. Front Matter
Pages I-XVII
2. Pages 1-6
3. Pages 7-16
4. Pages 17-28
5. Pages 29-45
6. Pages 47-55
7. Pages 57-76
8. Pages 77-88
9. Pages 89-104
10. Pages 105-146
11. Pages 147-164
12. Pages 165-198
13. Pages 199-216
14. Pages 217-244
15. Pages 245-258
16. Pages 259-292
17. Pages 293-301
18. Back Matter
Pages 303-333

### Introduction

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.

### Keywords

Algebraic computations Engineering GPS meteorology geodesy geoinformatics networks

#### Authors and affiliations

• Joseph L. Awange
• 1
• Erik W. Grafarend
• 2
1. 1.Department of GeophysicsKyoto UniversityJapan
2. 2.Department of GeodesyStuttgart UniversityStuttgartGermany

### Bibliographic information

• DOI https://doi.org/10.1007/b138214
• Copyright Information Springer-Verlag Berlin Heidelberg 2005
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Earth and Environmental Science
• Print ISBN 978-3-540-23425-8
• Online ISBN 978-3-540-26862-8