Linear Algebra, Geodesy, and GPS book

Discussion in 'Global Navigation Satellite Systems' started by Tim Stark, Sep 4, 2007.

  1. Tim Stark

    Tim Stark Guest

    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
     
    Tim Stark, Sep 4, 2007
    #1
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  2. Tim Stark

    Sam Wormley Guest

    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
    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.........................................527
    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........................................569
    17.7 An Example from Practice.........................574

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

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

    http://www-math.mit.edu/~gs
     
    Sam Wormley, Sep 4, 2007
    #2
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  3. Tim Stark

    John Guest

    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
     
    John, Sep 6, 2007
    #3
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