Algorithms for Global Positioning

Gilbert Strang, Kai Borre

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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. Contents: Preface and Outline; Abbreviations; 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; Glossary; Bibliography; Index of M-Files; Index