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Linear Algebra, Geodesy, and GPS book

 
 
Tim Stark
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      09-04-2007, 02:42 AM
Hello folks,

Well, I found a geodesy book called "Linear Algebra, Geodesy, and GPS". Is
that for terra mapping and nagivation programming? Does anyone have good
reviews with that book?

Thanks,
Tim

 
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Sam Wormley
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      09-04-2007, 02:52 AM
Tim Stark wrote:
> Hello folks,
>
> Well, I found a geodesy book called "Linear Algebra, Geodesy, and
> GPS". Is that for terra mapping and nagivation programming? Does
> anyone have good reviews with that book?
>
> Thanks,
> Tim


"Linear Algebra, Geodesy, and GPS" by Gilbert Strang and Kai Borre
is an excellent book.

Linear Algebra, Geodesy, and GPS by Gilbert Strang and Kai Borre

Wellesley-Cambridge Press Box 812060 Wellesley MA 02181
fax 617 253-4358 phone 781 431-8488 email http://www.gps-forums.net/(E-Mail Removed)
640 pages (1997) hardcover ISBN 0-9614088-6-3
http://www-math.mit.edu/~gs


The book has three closely connected parts. The first is Linear Algebra,
which is the fundamental tool in positioning calculations. The second is
Geodesy, which includes the correct weightings for observation errors and
the development of least squares. The third is GPS, which we describe in
detail at several levels : first the basic structure of the GPS system, then
the algorithms that yield accurate positions from inaccurate pseudoranges,
and finally the Kalman filtering (and "Bayes" filtering) that give superior
accuracy in postprocessing a long series of observations.

If you wanted to order this book, I only need to ask for email with the best
mailing address. The book will come with an invoice ; a check to the Press
(not credit card) is perfect. The cost including domestic postage is $60.
Orders can equally well go to Wellesley-Cambridge Press (fax 617 253 4358).

For international orders the cost with surface postage is $62. I now
recommend the new Global Priority Airmail (if available to your country)
which only adds $5 to that cost. Personal checks in US dollars or
Eurocheques in English pounds are fine. Often the easiest is cash to
the Press and it is amazingly safe ; we take all risk.
**Please let me know what you prefer and the Press will follow through.**

A large library of MATLAB files is associated with the book. They were
created by Kai Borre and are freely available on the web. We hope that these
M-files will help readers to use the more individual and experimental
processing that MATLAB offers, compared with large-scale software packages.

I will enclose the Table of Contents below. I would be very grateful
if you could make this book known to friends. You could send them this
message and/or just show them the book ! Most of all I hope you will enjoy
this presentation of a technology that is developing so fast.

With thanks and very best regards, Gilbert Strang



TABLE OF CONTENTS

Preface........................................... ........ix
The Mathematics of GPS..................................xiii

Part I Linear Algebra

1 Vectors and Matrices....................................3
1.1 Vectors........................................... ..3
1.2 Lengths and Dot Products...........................11
1.3 Planes............................................ .20
1.4 Matrices and Linear Equations......................28
2 Solving Linear Equations...............................37
2.1 The Idea of Elimination............................37
2.2 Elimination Using Matrices.........................46
2.3 Rules for Matrix Operations........................54
2.4 Inverse Matrices...................................65
2.5 Elimination = Factorization: A = LU................75
2.6 Transposes and Permutations........................87
3 Vector Spaces and Subspaces...........................101
3.1 Spaces of Vectors.................................101
3.2 The Nullspace of A: Solving Ax = 0................109
3.3 The Rank of A: Solving Ax = b.....................122
3.4 Independence, Basis, and Dimension................134
3.5 Dimensions of the Four Subspaces..................146
4 Orthogonality..................................... ....157
4.1 Orthogonality of the Four Subspaces...............157
4.2 Projections....................................... 165
4.3 Least-Squares Approximations......................174
4.4 Orthogonal Bases and Gram-Schmidt.................184
5 Determinants...................................... ....197
5.1 The Properties of Determinants....................197
5.2 Cramer's Rule, Inverses, and Volumes..............206
6 Eigenvalues and Eigenvectors..........................211
6.1 Introduction to Eigenvalues.......................211
6.2 Diagonalizing a Matrix............................221
6.3 Symmetric Matrices................................233
6.4 Positive Definite Matrices........................237
6.5 Stability and Preconditioning.....................248
7 Linear Transformations................................251
7.1 The Idea of a Linear Transformation...............251
7.2 Choice of Basis: Similarity and SVD...............258

Part II Geodesy

8 Leveling Networks.....................................275
8.1 Heights by Least Squares..........................275
8.2 Weighted Least Squares............................280
8.3 Leveling Networks and Graphs......................282
8.4 Graphs and Incidence Matrices.....................288
8.5 One-Dimensional Distance Networks.................305
9 Random Variables and Covariance Matrices..............309
9.1 The Normal Distribution and X2...................309
9.2 Mean, Variance, and Standard Deviation............319
9.3 Covariance........................................ 320
9.4 Inverse Covariances as Weights....................322
9.5 Estimation of Mean and Variance...................326
9.6 Propagation of Means and Covariances..............328
9.7 Estimating the Variance of Unit Weight............333
9.8 Confidence Ellipses...............................337
10 Nonlinear Problems....................................343
10.1 Getting Around Nonlinearity......................343
10.2 Geodetic Observation Equations...................349
10.3 Three-Dimensional Model..........................362
11 Linear Algebra for Weighted Least Squares.............369
11.1 Gram-Schmidt on A and Cholesky on A T A..........369
11.2 Cholesky's Method in the Least-Squares Setting...372
11.3 SVD: The Canonical Form for Geodesy..............375
11.4 The Condition Number.............................377
11.5 Regularly Spaced Networks........................379
11.6 Dependency on the Weights........................391
11.7 Elimination of Unknowns..........................394
11.8 Decorrelation and Weight Normalization...........400
12 Constraints for Singular Normal Equations.............405
12.1 Rank Deficient Normal Equations..................405
12.2 Representations of the Nullspace.................406
12.3 Constraining a Rank Deficient Problem............408
12.4 Linear Transformation of Random Variables........413
12.5 Similarity Transformations.......................414
12.6 Covariance Transformations.......................421
12.7 Variances at Control Points......................423
13 Problems With Explicit Solutions......................431
13.1 Free Stationing as a Similarity Transformation...431
13.2 Optimum Choice of Observation Site...............434
13.3 Station Adjustment...............................438
13.4 Fitting a Straight Line..........................441

Part III Global Positioning System (GPS)

14 Global Positioning System.............................447
14.1 Positioning by GPS...............................447
14.2 Errors in the GPS Observables....................453
14.3 Description of the System........................458
14.4 Receiver Position From Code Observations.........460
14.5 Combined Code and Phase Observations.............463
14.6 Weight Matrix for Differenced Observations.......465
14.7 Geometry of the Ellipsoid........................467
14.8 The Direct and Reverse Problems..................470
14.9 Geodetic Reference System 1980...................471
14.10 Geoid, Ellipsoid, and Datum.....................472
14.11 World Geodetic System 1984......................476
14.12 Coordinate Changes From Datum Changes...........477
15 Processing of GPS Data................................481
15.1 Baseline Computation and M-Files.................481
15.2 Coordinate Changes and Satellite Position........482
15.3 Receiver Position from Pseudoranges..............487
15.4 Separate Ambiguity and Baseline Estimation.......488
15.5 Joint Ambiguity and Baseline Estimation..........494
15.6 The LAMBDA Method for Ambiguities................495
15.7 Sequential Filter for Absolute Position..........499
15.8 Additional Useful Filters........................505
16 Random Processes......................................515
16.1 Random Processes in Continuous Time..............515
16.2 Random Processes in Discrete Time................523
16.3 Modeling.........................................5 27
17 Kalman Filters........................................543
17.1 Updating Least Squares...........................543
17.2 Static and Dynamic Updates.......................548
17.3 The Steady Model.................................552
17.4 Derivation of the Kalman Filter..................558
17.5 Bayes Filter for Batch Processing................566
17.6 Smoothing........................................5 69
17.7 An Example from Practice.........................574

The Receiver Independent Exchange Format.................585
Glossary.......................................... .......601
References........................................ .......609

Index of M-files.........................................615
Index............................................. .......617

(E-Mail Removed) http://www-math.mit.edu/~gs
 
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John
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      09-06-2007, 06:38 AM
I agree - this is an excellent book. It isn't for the faint hearted.
You will get a "round the world" tour of mathematics and GPS
engineering. The book would make a great text for a 3 semester class.
I worked my way through most of the linear algebra, got bogged down in
the geodesy, and jumped ahead to GPS. Plan on investing time, and
you'll get a lot out of it. You also might want to check out Strang's
MIT lectures on "An Introduction to Linear Algebra. They are available
for free download from the MIT website. http://web.mit.edu/18.06/www/Video/video-fall-99.html

 
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