Location estimation from the ground up / Sivan Toledo.

Format:

Book

Author/Creator:

Toledo, Sivan, author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Fundamentals of algorithms ; FA17.

Fundamentals of algorithms ; FA17

Language:

English

Subjects (All):

Distances--Measurement.

Distances.

Distances--Mathematical models.

Distance measuring instruments, Electronic.

Physical Description:

1 PDF (xvi, 200 pages).

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2020]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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.

Contents:

Fundamentals

Location-estimation systems

From leveling to linear least-squares problems

Solving linear least-squares problems with the QR factorization

Projections and reductions to linear equations

Estimation through optimization : probabilistic justifications

Rank deficient problems and the SVD

Solving nonlinear least-squares problems

Evaluating derivatives

Time-of-arrival localization and separability

A posteriori error analysis

A priori analysis : the Cramer-Rao bound

Arrival-time estimation

Cross correlation using the fast Fourier transform

Kalman variations : least squares for dynamical systems

Carrier-phase observations and integer least squares.

Notes:

Description based on title page of print version.

Includes bibliographical references (pages 195-198) and index.

ISBN:

1-61197-629-4

OCLC:

1156413349

Publisher Number:

FA17 SIAM