Relativity of GPS Measurement

TL;DR

This paper investigates how GPS pseudorange measurements are affected by Earth's curved space-time, providing a relativistic model that accounts for gravitational effects on measurement accuracy.

Contribution

It introduces a relativistic framework for GPS pseudorange measurements using space-time scalar functions, highlighting corrections due to Earth's gravity.

Findings

Measured pseudorange is a two-point scalar invariant.

Corrections to conventional pseudorange models are on the order of Earth's gravitational radius.

Different receivers measure different pseudoranges but obtain correct positions independently.

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 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 pseudorange that are on the order of the gravitational radius of the Earth.