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Algorithms for Global PositioningAlgorithms for Global Positioning

Kai Borre and Gilbert Strang

Wellesley-Cambridge Press 12

Good mathematics and great technology now produce highly accurate positions (latitude, longitude, and height). This book describes the ideas, the hardware, and the algorithms that make this accuracy possible.

Here is how the process happens: satellites broadcast their positions (and those signals contain their departure times); receivers decode the signals (and establish their arrival times); an algorithm using the speed of light multiplied by the travel times gives the distances from the satellites to the receiver (the pseudoranges); four or more pseudoranges determine the X, Y, and Z position of the receiver; and new satellites and new receivers, together with least squares and Kalman filters, reduce the errors in position, signal speed, and signal path.

The authors present the essential ideas in two ways: words and equations to explain the algorithms; and MATLAB codes to implement the algorithms. The reader will want to learn (in both ways) how this astonishing system works. This book aims to help.

About the Authors
Kai Borre is a professor in geodesy at Aalborg University, Denmark. For more than 30 years
Borre has conducted research and performed education in the area of satellite based positioning. In 1996 he established the Danish GPS Center and since 2000 has been head of a two-year international M.Sc. program in GPS technology. Borre is a coauthor of the widely used textbooks, Linear Algebra,
Geodesy, and GPS and A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach.

Gilbert Strang is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College, Oxford University. He is also a prolific author, with a dozen highly regarded textbooks and monographs to his credit. Strang served as SIAM's president from 1999-2000 and chaired the U.S. National Committee on Mathematics from 2003-4. He won the Henrici and Su Buchin prizes at ICIAM 2007 and the Von Neumann Medal of the U.S. Association of Computational Mechanics. He is a SIAM Fellow and a member of the National Academy of Sciences.


Preface and Outline;
The Fundamental Theorem of Linear Algebra;
A GPS Software Receiver;

Part I: Satellite Signals and Coordinate Systems;
1: Essential Ideas and Applications of GNSS;
2: GNSS Signals and Modulations;
3: Change of Coordinate Systems;

Part II: Optimal Estimates;
4: Random Variables and Covariance Matrices;
5: Random Processes;
6: Linear Algebra for Weighted Least Squares;
7: Singular Normal Equations and Networks;
8: Kalman Filters;

Part III: Positioning Algorithms;
9: Receiver Position from One-Way Pseudoranges;
10: Differences on One-Way Observations;

Part IV: Geodesy and Earth Coordinates;
11: Geometry of the Ellipsoid;
12: Conformal Mappings of the Ellipsoid;

Index of M-Files;

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April 2012 / xl + 433 / Hardcover / ISBN 978-0-980232-73-8
List Price $90.00 / SIAM Member Price $63.00 / Order Code WC12
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)