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Algorithms for Global Positioning, by 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
- Sales Rank: #1352992 in Books
- Published on: 2012-04-01
- Original language: English
- Number of items: 1
- Dimensions: 9.96" h x .98" w x 6.97" l, 2.17 pounds
- Binding: Hardcover
- 473 pages
About the Author
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.
Most helpful customer reviews
4 of 5 people found the following review helpful.
These authors have something to say!
By Jay Goldfarb
I own a copy of the previous work by these two authors - Linear Algebra, Geodesy, and GPS. Although I already had a reasonably strong background in both GPS and linear algebra, this earlier book was a fresh view of both these subjects and it became one of my favorite reference and review books. It's value could be verified by looking at the prices people were getting for used copies.
I just had a look at a colleague's copy of Algorithms for Global Positioning. This colleague had been looking for a used copy of the earlier book but had been dissuaded by the several-hundred-dollar prices. Today he asked me whether I thought the new book is a significant update, and I have to say that it has been rewritten in a way that really improves on the already very good previous volume. The only quibble I had with that earlier volume is that it was really two separate books - one on linear algebra and the second on GPS and geodesy. This new book fully integrates these topics in a very satisfying way.
0 of 1 people found the following review helpful.
Very informative. I bought both old and new versions.
By jnc
I've found for me I must buy several books on GPS topics in order to construct a useful software defined radio to implement the concepts. The newer version is definitely more helpful, but both are useful.
For those new to the topic, the coordinate system discussions and issues related to timing are particularly useful.
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