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Location Estimation from the Ground Up

Sivan Toledo
Publication Date: 
Number of Pages: 
Fundamentals of Algorithms
[Reviewed by
Brian Borchers
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Location Estimation from the Ground Up is a textbook in SIAM's Fundamentals of Algorithms series.  Its focus is on the mathematics, statistics, and algorithms used in determining locations by GPS and other Global Navigation Satellite Systems (GNSS).  This technology is widely used in cell phones, sports watches, and automotive navigation systems.  Geophysicists also make use of GNSS to track motions along geological faults at rates measured in millimeters per year.  This may seem like a very specialized topic, but the author uses the application of location estimation to bring together a number of broadly applicable topics in computational mathematics in a textbook that should be accessible to graduate students in geophysics and engineering.
Mathematical topics discussed include linear least squares problems, the QR and SVD factorizations, nonlinear least-squares problems, maximum likelihood estimation, cross-correlation of signals, Kalman filtering, and integer least squares.  The mathematics is presented in a way that should be accessible to engineering and science students with some background in calculus, linear algebra, probability, and statistics.  The numerous examples and exercises are mostly based on applications of these topics to location estimation.
Compare this book with Gilbert Strang and Kai Borre's book, Linear Algebra, Geodesy, and GPS.  Both books cover very similar mathematical ground.  Strang and Borre begin with seven chapters on linear algebra that are somewhat more basic than the linear algebra chapters in Location Estimation from the Ground Up.  The second part of Linear Algebra, Geodesy, and GPS discusses the location estimation problem in general, while the third part dives into the details of the GPS system and GPS signal processing.  In comparison, the chapters of Location Estimation from the Ground Up are organized by mathematical topics, and the applications to GNSS are spread throughout the book.  That might make it somewhat more difficult to use this textbook for students who are already familiar with the required linear algebra.
This book would be suitable for use in a specialized course on the mathematics of GNSS aimed at students in geophysics or engineering.  It might also be useful as a source of examples for instructors of courses in computational mathematics and statistics that touch on the mathematical topics mentioned above.

Brian Borchers is a professor of mathematics at New Mexico Tech and the editor of MAA Reviews.