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Location estimation from the ground up. (English) Zbl 1448.86002
Fundamentals of Algorithms 17. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-628-1/pbk; 978-1-61197-629-8/ebook). xv, 200 p. (2020).
Publisher’s description: The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models. It also presents algorithms that are used to resolve these models to obtain location estimates, including the simplest linear models, nonlinear models (location estimation using satellite navigation systems and estimation of the signal arrival time from those satellites), dynamical systems (estimation of an entire path taken by a vehicle), and models with integer ambiguities (GPS location estimation that is centimeter-level accurate).
Location Estimation from the Ground Up:
clearly presents analytic and algorithmic topics not covered in other books, including simple algorithms for Kalman filtering and smoothing, the solution of separable nonlinear optimization problems, estimation with integer ambiguities, and the implicit-function approach to estimating covariance matrices when the estimator is a minimizer or maximizer;
takes a unified approach to estimation while highlighting the differences between classes of estimation problems; and
is the only book on estimation written for math and computer science students and graduates.
Problems at the end of each chapter, many with solutions, help readers deepen their understanding of the material and guide them through small programming projects that apply theory and algorithms to the solution of real-world location-estimation problems.
The book’s core audience consists of engineers, including software engineers and algorithm developers, and graduate students who work on location-estimation projects and who need help translating the theory into algorithms, code, and deep understanding of the problem in front of them. Instructors in mathematics, computer science, and engineering may also find the book of interest as a primary or supplementary text for courses in location estimation and navigation.
MSC:
86-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics
86A32 Geostatistics
86A30 Geodesy, mapping problems
62P25 Applications of statistics to social sciences
93E11 Filtering in stochastic control theory
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
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