Application of linear algebra in global positioning system (GPS)

Document Type : Research Paper

Authors

Fasa University

Abstract

The Global Positioning System (GPS) is a navigation system consisting of a constellation of satellites orbiting the Earth. By receiving signals from at least three satellites, the system can calculate position, speed, and time information and display them in practical formats. Interestingly, relatively simple mathematical calculations are employed in this system. This article aims to familiarize young enthusiasms with the functioning of GPS and the equations used. Also, it specifically delves into algebraic issues in GPS. Firstly, the calculation of positions using the triangulation principle, the impact of time error and correction for the GPS receiver are discussed. Then, the concept of pseudo-range, solving pseudo-range equations, and extracting the estimation error of position and time are explained. Different types of errors in GPS are also examined. Finally, an interesting problem in GPS is presented and solved.

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References

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[8] J. L. Awange and E. W. Graferend, Algebraic solution of GPS pseuds-Ranging Equations, GPS solution, 5 (2002) 20–32.
[9] R. B. Thomsob, Global Positioning System: The mathematics of GPS Recievers, Math. Magszine, 71 (1998) 260–269.

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History

  • Receive Date: 22 December 2016
  • Revise Date: 10 December 2017
  • Accept Date: 16 December 2017
  • Publish Date: 22 May 2018

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