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Solving Algebraic Computational Problems in Geodesy and Geoinformatics The Answer to Modern Challenges

:	Joseph Awange, Erik W. Grafarend
:	Solving Algebraic Computational Problems in Geodesy and Geoinformatics The Answer to Modern Challenges
:	Springer-Verlag
:	9783540268628
:	1
:	CHF 105.00
:

:	Geologie
:	English

:	334
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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 taughtrequiredsomeskillsinalg bra,andinparticular,computera - 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 haveattemptedtoputtogetherbas cconceptsofabstractalgebra 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.

	Preface	6
	Contents	11
	1 Introduction	16
	2 Basics of Ring Theory	22
	2.1 Some Applications to Geodesy and Geoinformatics	22
	2.2 Numbers from Operational Perspective	23
	2.3 Number Rings	27
	2.4 Concluding Remarks	31
	3 Basics of Polynomial Theory	32
	3.1 Polynomial Equations	32
	3.2 Polynomial Rings	34
	3.3 Factoring Polynomials	37
	3.4 Polynomial Roots	37
	3.5 Minimal Polynomials	39
	3.6 Polynomials with Real Coefficients	39
	3.7 Concluding Remarks	43
	4 Groebner Basis	44
	4.1 The Origin	44
	4.2 Basics of Groebner Basis	46
	4.3 Buchberger Algorithm	53
	4.4 Concluding Remarks	60
	5 Polynomial Resultants	61
	5.1 Resultants: An Alternative to Groebner Basis	61
	5.2 Sylvester Resultants	62
	5.3 Multipolynomial Resultants	64
	5.4 Concluding Remarks	68
	6 Gauss-Jacobi Combinatorial Algorithm	70
	6.1 Estimating Unknown Parameters	70
	6.2 Combinatorial Approach: The Origin	71
	6.3 Linear and Nonlinear Gauss-Markov Models	74
	6.4 Gauss-Jacobi Combinatorial Formulation	77
	6.5 Combinatorial Solution of Nonlinear Gauss-Markov Model	81
	6.6 Concluding Remarks	88
	7 Local versus Global Positioning Systems	90
	7.1 Positioning Systems	90
	7.2 Global Positioning System (GPS)	91
	7.3 Local Positioning Systems (LPS)	92
	7.4 Test Network Stuttgart Central	98
	7.5 Concluding Remarks	100
	8 Partial Procrustes and the Orientation Problem	102
	8.1 Motivation	102
	8.2 Procrustes: Origin and Applications	104
	8.3 Partial Procrustes Solution	108
	8.4 Practical Applications	112
	8.5 Concluding Remarks	117
	9 Positioning by Ranging	118
	9.1 Applications of Distances	118
	9.2 Ranging by Global Positioning System (GPS)	120
	9.3 Ranging by Local Positioning Systems (LPS)	135
	9.4 Concluding Remarks	159
	10 From Geocentric Cartesian to Ellipsoidal Coordinates	160
	10.1 Mapping Topographical Points onto Reference Ellipsoid	160
	10.2 Mapping Geometry	163
	10.3 Minimum Distance Mapping	166
	10.4 Concluding Remarks	177
	11 Positioning by Resection Methods	178
	11.1 Resection Problem and its Importance	178
	11.2 Geodetic Resection	181
	11.3 Photogrammetric Resection	206
	11.4 Concluding Remarks	210
	12 Positioning by Intersection Methods	212
	12.1 Intersection Problem and its Importance	212
	12.2 Geodetic Intersection	213
	12.3 Photogrammetric Intersection	227
	12.4 Concluding Remarks	229
	13 GPS Meteorology in Environmental Monitoring	230
	13.1 Satellite Environmental Monitoring	230
	13.2 GPS Remote Sensing	236
	13.3 Refraction (Bending) Angles	240
	13.4 Algebraic Analysis of some CHAMP Data	247
	13.5 Concluding Remarks	256
	14 Algebraic Diagnosis of Outliers	258
	14.1 Outliers in Observation Samples	258
	14.2 Algebraic Diagnosis of Outliers	260
	14.3 Concluding Remarks	271
	15 Transformation Problem: Procrustes Algorithm II	272
	15.1 7-Parameter Datum Transformation and its Importance	272
	15.2 Algebraic (Analytic) Determination of Transformation Parameters	275
	15.3 Concluding Remark	304
	16 Computer Algebra Systems (CAS)	306
	16.1 General and Special Purpose CAS	306
	16.2 Some CAS Software Useful in Geodesy and Geoinformatics	307
	16.3 Concluding Remarks	313
	Appendix	315
	Appendix A-1: Definitions	315
	Appendix A-2: C. F. Gauss Combinatorial Formulation	317
	References	320
	Index	338