Algorithms for global positioning
type: Item
instance of: scholarly article
zbMATH Open document ID: 1244.86001
author: Kai Borre
author: Gilbert Strang
publication date: 2012-06-15T00:00:00Z
Mathematics Subject Classification ID: 86-01
Mathematics Subject Classification ID: 86-04
Mathematics Subject Classification ID: 86A04
Mathematics Subject Classification ID: 86A30
Mathematics Subject Classification ID: 90C15
zbMATH DE Number: 6046670
zbMATH Keywords: linear algebra
zbMATH Keywords: global navigation satellite system
zbMATH Keywords: GPS
zbMATH Keywords: spread spectrum technique
zbMATH Keywords: binary phase shift keying
zbMATH Keywords: MATLAB codes
zbMATH Keywords: pseudoranges
zbMATH Keywords: space-based augmentation systems
zbMATH Keywords: differential GPS
zbMATH Keywords: GPS software receiver
zbMATH Keywords: Galileo
zbMATH Keywords: GLONASS
zbMATH Keywords: Compass
zbMATH Keywords: QZSS
zbMATH Keywords: Kalman filter
zbMATH Keywords: geometry of ellipsoid
zbMATH Keywords: conformal mappings
zbMATH Keywords: geodesy
zbMATH Keywords: least squares algorithm
describes a project that uses: Matlab
MaRDI profile type: Publication
title: Algorithms for global positioning
review text: Accurate time keeping was a problem for centuries. Now, this picture has totally changed because of new technological developments, electronics and artificial satellites. Today, atomic clocks tell the time with an accuracy better than \(10^{-11}\) seconds. Satellite positioning, a combination of engineering tools, mathematics of coordinate mapping and numerical calculations, influences the life of many people. NEWLINENEWLINENEWLINE NEWLINEThe present book is an extension of the authors' text from 1997 ``Linear Algebra, Geodesy, and GPS'' [Wellesley, MA: Wellesley-Cambridge Press. xvi, 624 p. (1997; Zbl 1007.86001)]. It describes the linear algebra and the specialised algorithms for receivers to compute their positions. Thus it starts with a section on the fundamental theorem of linear algebra. As the Global Positioning System (GPS) is used as an example of the central ideas of global satellite navigation technology, a detailed discussion of a GPS software receiver follows. From coordinates of at least four satellites and their four pseudoranges (distances between satellite and receiver, calculated as traveltime of the signal times speed of light), the receiver can compute its own position as well as the offset between GPS time and the local time in the receiver. The accuracy of the computed position is recently usually a few meters. The examples and data sets presented in the book come from the GPS Center in Aalborg. The book provides, besides GPS data, also information on other used and planned global positioning systems like Galileo, GLONASS, Compass, and QZSS. Chapter 1 contains a survey of important civilian GPS applications. It considers essential ideas and applications of ``Global Navigation Satellite Systems'' (GNSS) including satellite based augmentation to compensate ionospheric time delay (WAAS in USA, EGNOS in Europe, GAGAN in India, and QZSS in Japan). When the algorithm level is presented, using pseudoranges and carrier ranges and corrections, one sees …
reviewed by: Claudia-Veronika Meister
description: scientific article; zbMATH DE number 6046670