Solving algebraic computational problems in geodesy and geoinformatics : the answer to modern challenges /

Solving algebraic computational problems in geodesy and geoinformatics : the answer to modern challenges /

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Bibliographic Details
Author / Creator:Awange, Joseph L., 1969-
Imprint:Berlin ; New York : Springer, c2005.
Description:1 online resource (xvii, 333 p.) : ill.
Language:English
Subject:
Geodesy -- Mathematics.
Geomatics.
Geodesy -- Mathematics.
Geomatics.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8874455
Hidden Bibliographic Details
Other authors / contributors:Grafarend, Erik W.
ISBN:354023425X (acid-free paper)
9783540234258 (acid-free paper)
3540268626 (electronic bk.)
9783540268628 (electronic bk.)
9786610234868
6610234868
Notes:Includes bibliographical references (p. [309]-326) and index.
Description based on print version record.
Summary:"The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems using computer algebra techniques of Ring, polynomials, Groebner basis, resultants, Gauss Jacobi combinatorial and Procrustes algorithms. Although 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 GPS-meteorology and many other problems. For mathematicians the book provides some practical examples of abstract algebra application and multidimensional scaling."--Jacket.
Other form:Print version: Awange, Joseph L., 1969- Solving algebraic computational problems in geodesy and geoinformatics. Berlin ; New York : Springer, c2005 354023425X
Table of Contents:
  • Preface
  • 1. Introduction
  • 2. Basics of Ring Theory
  • 2.1. Some Applications to Geodesy and Geoinformatics
  • 2.2. Numbers from Operational Perspective
  • 2.3. Number Rings
  • 2.4. Concluding Remarks
  • 3. Basics of Polynomial Theory
  • 3.1. Polynomial Equations
  • 3.2. Polynomial Rings
  • 3.2.1. Polynomial Objects as Rings
  • 3.2.2. Operations """"Addition"""" and """"Multiplication""""
  • 3.3. Factoring Polynomials
  • 3.4. Polynomial Roots
  • 3.5. Minimal Polynomials
  • 3.6. Polynomials with Real Coefficients
  • 3.6.1. Quadratic Polynomials
  • 3.6.2. Cubic Polynomials
  • 3.6.3. Quartic Polynomials
  • 3.7. Concluding Remarks
  • 4. Groebner Basis
  • 4.1. The Origin
  • 4.2. Basics of Groebner Basis
  • 4.3. Buchberger Algorithm
  • 4.3.1. Mathematica Computation of Groebner Basis
  • 4.3.2. Maple Computation of Groebner Basis
  • 4.4. Concluding Remarks
  • 5. Polynomial Resultants
  • 5.1. Resultants: An Alternative to Groebner Basis
  • 5.2. Sylvester Resultants
  • 5.3. Multipolynomial Resultants
  • 5.3.1. F. Macaulay Formulation:
  • 5.3.2. B. Sturmfels' Formulation
  • 5.4. Concluding Remarks
  • 6. Gauss-Jacobi Combinatorial Algorithm
  • 6.1. Estimating Unknown Parameters
  • 6.2. Combinatorial Approach: The Origin
  • 6.3. Linear and Nonlinear Gauss-Markov Models
  • 6.4. Gauss-Jacobi Combinatorial Formulation
  • 6.5. Combinatorial Solution of Nonlinear Gauss-Markov Model
  • 6.6. Concluding Remarks
  • 7. Local versus Global Positioning Systems
  • 7.1. Positioning Systems
  • 7.2. Global Positioning System (GPS)
  • 7.3. Local Positioning Systems (LPS)
  • 7.3.1. Local Datum Choice in an LPS 3-D Network
  • 7.3.2. Relationship between Global and Local Level Reference Frames
  • 7.3.3. Observation Equations
  • 7.4. Test Network Stuttgart Central
  • 7.5. Concluding Remarks
  • 8. Partial Procrustes and the Orientation Problem
  • 8.1. Motivation
  • 8.2. Procrustes: Origin and Applications
  • 8.2.1. Procrustes and the Magic Bed
  • 8.2.2. Multidimensional Scaling
  • 8.2.3. Applications of Procrustes in Medicine
  • 8.3. Partial Procrustes Solution
  • 8.3.1. Conventional Formulation
  • 8.3.2. Partial Derivative Formulation
  • 8.4. Practical Applications
  • 8.4.1. Three-dimensional Orientation Problem
  • 8.4.2. Determination of Vertical Deflection
  • 8.5. Concluding Remarks
  • 9. Positioning by Ranging
  • 9.1. Applications of Distances
  • 9.2. Ranging by Global Positioning System (GPS)
  • 9.2.1. The Pseudo-ranging Four-Points Problem
  • 9.2.2. Ranging to more than Four GPS Satellites
  • 9.2.3. Least Squares versus Gauss-Jacobi Combinatorial
  • 9.3. Ranging by Local Positioning Systems (LPS)
  • 9.3.1. Planar Ranging
  • 9.3.2. Three-dimensional Ranging
  • 9.4. Concluding Remarks
  • 10. From Geocentric Cartesian to Ellipsoidal Coordinates
  • 10.1. Mapping Topographical Points onto Reference Ellipsoid
  • 10.2. Mapping Geometry
  • 10.3. Minimum Distance Mapping
  • 10.3.1. Grafarend-Lohse's Mapping of {{\op T}}^2 \rightarrow {{\op E}}_{{a,a,b}}^2
  • 10.3.2. Groebner Basis' Mapping of {{\op T}}^2 \rightarrow {{\op E}}_{{a,a,b}}^2
  • 10.4. Concluding Remarks
  • 11. Positioning by Resection Methods
  • 11.1. Resection Problem and its Importance
  • 11.2. Geodetic Resection
  • 11.2.1. Planar Resection
  • 11.2.2. Three-dimensional Resection
  • 11.3. Photogrammetric Resection
  • 11.3.1. Grafarend-Shan Mobius Photogrammetric Resection
  • 11.3.2. Algebraic Photogrammetric Resection
  • 11.4. Concluding Remarks
  • 12. Positioning by Intersection Methods
  • 12.1. Intersection Problem and its Importance
  • 12.2. Geodetic Intersection
  • 12.2.1. Planar Intersection
  • 12.2.2. Three-dimensional Intersection
  • 12.3. Photogrammetric Intersection
  • 12.4. Concluding Remarks
  • 13. GPS Meteorology in Environmental Monitoring
  • 13.1. Satellite Environmental Monitoring
  • 13.2. GPS Remote Sensing
  • 13.2.1. Space Borne GPS Meteorology
  • 13.2.2. Ground based GPS meteorology
  • 13.3. Refraction (Bending) Angles
  • 13.3.1. Transformation of Trigonometric Equations to Algebraic
  • 13.3.2. Algebraic Determination of Bending Angles
  • 13.4. Algebraic Analysis of some CHAMP Data
  • 13.5. Concluding Remarks
  • 14. Algebraic Diagnosis of Outliers
  • 14.1. Outliers in Observation Samples
  • 14.2. Algebraic Diagnosis of Outliers
  • 14.2.1. Outlier Diagnosis in Planar Ranging
  • 14.2.2. Diagnosis of Multipath Error in GPS Positioning
  • 14.3. Concluding Remarks
  • 15. Transformation Problem: Procrustes Algorithm II
  • 15.1. 7-Parameter Datum Transformation and its Importance
  • 15.2. Algebraic (Analytic) Determination of Transformation Parameters
  • 15.2.1. Groebner Basis Transformation
  • 15.2.2. Gauss-Jacobi Combinatorial Transformation
  • 15.2.3. Procrustes Algorithm II
  • 15.2.4. Weighted Procrustes Transformation
  • 15.3. Concluding Remark
  • 16. Computer Algebra Systems (CAS)
  • 16.1. General and Special Purpose CAS
  • 16.2. Some CAS Software Useful in Geodesy and Geoinformatics
  • 16.2.1. MATLAB
  • 16.2.2. MAPLE
  • 16.2.3. MATHEMATICA
  • 16.2.4. REDUCE
  • 16.3. Concluding Remarks
  • Appendix
  • Appendix A-1. Definitions
  • Appendix A-2. C. F. Gauss combinatorial approach
  • References
  • Index

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