Awange J.L., Grafarend E.W. Solving Algebraic Computational Problems in Geodesy and Geoinformatics. The Answer to Modern Challenge

Springer, 2005. – 344 p. – ISBN: 3-540-23425-XPreface

Basics of Ring Theory
Some Applications to Geodesy and Geoinformatics
Numbers from Operational Perspective
Number Rings
Concluding Remarks
Basics of Polynomial Theory
Polynomial Equations
Polynomial Rings
Factoring Polynomials
Polynomial Roots
Minimal Polynomials
Polynomials with Real Coefficients
Concluding Remarks
Groebner Basis
The Origin
Basics of Groebner Basis
Buchberger Algorithm
Concluding Remarks
Polynomial Resultants
Resultants: An Alternative to Groebner Basis
Sylvester Resultants
Multipolynomial Resultants
Concluding Remarks
Gauss-Jacobi Combinatorial Algorithm
Estimating Unknown Parameters
Combinatorial Approach: The Origin
Linear and Nonlinear Gauss-Markov Models
Gauss-Jacobi Combinatorial Formulation
Combinatorial Solution of Nonlinear Gauss-Markov Model
Concluding Remarks
Local versus Global Positioning Systems
Positioning Systems
Global Positioning System (GPS)
Local Positioning Systems (LPS)
Test Network Stuttgart Central
Concluding Remarks
Partial Procrustes and the Orientation Problem
Motivation
Procrustes: Origin and Applications
Partial Procrustes Solution
Practical Applications
Concluding Remarks
Positioning by Ranging
Applications of Distances
Ranging by Global Positioning System (GPS)
Ranging by Local Positioning Systems (LPS)
Concluding Remarks
From Geocentric Cartesian to Ellipsoidal Coordinates
Mapping Topographical Points onto Reference Ellipsoid
Mapping Geometry
Minimum Distance Mapping
Concluding Remarks
Positioning by Resection Methods
Resection Problem and its Importance
Geodetic Resection
Photogrammetric Resection
Concluding Remarks
Positioning by Intersection Methods
Intersection Problem and its Importance
Geodetic Intersection
Photogrammetric Intersection
Concluding Remarks
GPS Meteorology in Environmental Monitoring
Satellite Environmental Monitoring
GPS Remote Sensing
Refraction (Bending) Angles
Algebraic Analysis of some CHAMP Data
Concluding Remarks
Algebraic Diagnosis of Outliers
Outliers in Observation Samples
Algebraic Diagnosis of Outliers
Concluding Remarks
Transformation Problem: Procrustes Algorithm II
7-Parameter Datum Transformation and its Importance
Algebraic (Analytic) Determination of Transformation Parameters
Concluding Remark
Computer Algebra Systems (CAS)
General and Special Purpose CAS
Some CAS Software Useful in Geodesy and Geoinformatics
MatLAB
MAPLE
MATHEMATICA
REDUCE
Concluding Remarks
Appendix
A-1: Definitions
A-2: C.F. Gauss combinatorial approach
References
Index