Algorithms for Global Positioning

The emergence of satellite technology has changed the lives of millions of people. In particular, GPS has brought an unprecedented level of accuracy to the field of geodesy. This text is a guide to the algorithms and mathematical principles that account for the success of GPS technology and replaces the authors' previous work, Linear Algebra, Geodesy, and GPS (1997). An initial discussion of the basic concepts, characteristics and technical aspects of different satellite systems is followed by the necessary mathematical content which is presented in a detailed and self-contained fashion. At the heart of the matter are the positioning algorithms on which GPS technology relies, the discussion of which will affirm the mathematical contents of the previous chapters. Numerous ready-to-use MATLAB codes are included for the reader. This comprehensive guide will be invaluable for engineers and academic researchers who wish to master the theory and practical application of GPS technology.

Preface and outline; Abbreviations; The mathematics of GPS; 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 of one-way observations; Part IV. Geodesy and Earth Coordinates: 11. Geometry of the ellipsoid; 12. Conformal mappings of the ellipsoid; Glossary; Bibliography; Index of M-files; Index.

A detailed and self-contained guide to the mathematical and algorithmic aspects of GPS, complete with numerous ready-made MATLAB codes for the reader. Ideal for engineers and researchers who wish to master both the theory and practical application of GPS technology.

Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. In addition, he is the author of many textbooks and his service to the mathematics community is extensive, having spent time as President of SIAM, Chair of the Joint Policy Board for Mathematics as well as membership of various other committees and boards. The awards that Professor Strang has received for his research and teaching include the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (MIT, 2003) and the Von Neumann Prize Medal of the U.S. Association for Computational Mechanics (2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences and an Honorary Fellow of Balliol College, Oxford.
Kai Borre is a professor of geodesy at Aalborg University where he teaches and performs research in the field 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. He is the coauthor of several popular textbooks in the areas of geodesy and GPS.