Relativity of GPS measurement

Thomas B. Bahder
Phys. Rev. D 68, 063005 – Published 29 September 2003
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Abstract

The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities introduced in the electromagnetic field amplitude by the P-code broadcast by the GPS satellites. We compute the world function of space-time near Earth, and we use it to define a scalar phase function that describes the space-time grid. We use this scalar phase function to define the measured pseudorange, which turns out to be a two-point space-time scalar under generalized coordinate transformations. Though the measured pseudorange is an invariant, it depends on the world lines of the receiver and satellite. While two colocated receivers measure two different pseudoranges to the same satellite, they obtain the correct position and time, independent of their velocity. We relate the measured pseudorange to the geometry of space-time and find corrections to the conventional model of the pseudorange that are on the order of the gravitational radius of the Earth.

  • Received 16 June 2003

DOI:https://doi.org/10.1103/PhysRevD.68.063005

©2003 American Physical Society

Authors & Affiliations

Thomas B. Bahder*

  • U. S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783-1197, USA

  • *Email address: bahder@arl.army.mil

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Vol. 68, Iss. 6 — 15 September 2003

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