Solving Algebraic Computational Problems in Geodesy and Geoinformatics

1. Front Matter

   Pages I-XVII

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2. Introduction

   Pages 1-6

3. Basics of Ring Theory

   Pages 7-16

4. Basics of Polynomial Theory

   Pages 17-28

5. Groebner Basis

   Pages 29-45

6. Polynomial Resultants

   Pages 47-55

7. Gauss-Jacobi Combinatorial Algorithm

   Pages 57-76

8. Local versus Global Positioning Systems

   Pages 77-88

9. Partial Procrustes and the Orientation Problem

   Pages 89-104

10. Positioning by Ranging

    Pages 105-146

11. From Geocentric Cartesian to Ellipsoidal Coordinates

    Pages 147-164

12. Positioning by Resection Methods

    Pages 165-198

13. Positioning by Intersection Methods

    Pages 199-216

14. GPS Meteorology in Environmental Monitoring

    Pages 217-244

15. Algebraic Diagnosis of Outliers

    Pages 245-258

16. Transformation Problem: Procrustes Algorithm II

    Pages 259-292

17. Computer Algebra Systems (CAS)

    Pages 293-301

18. Back Matter

    Pages 303-333

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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 toreference ellipsoid and, • analytical determination of refraction angles in GPS meteorology.

• Algebraic computations
• Engineering
• GPS meteorology
• geodesy
• geoinformatics
• networks

• Department of Geophysics, Kyoto University, Japan

  Joseph L. Awange

• Department of Geodesy, Stuttgart University, Stuttgart, Germany

  Erik W. Grafarend

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