Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

Abstract

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emission coordinate region and co-region. In a second application, a GPS (Galileo) satellite is considered as the receiver and its emission coordinates are given by four Galileo (GPS) satellites. The bifurcation problem (double localization) in the positioning of the receiver satellite is then pointed out and discussed in detail.

16 pages, 9 figures, published (online) in Astrophys. Space Sci

References in corpus (3)

• General post-Minkowskian expansion of time transfer functions
• Measuring emission coordinates in a pulsar-based relativistic positioning system
• Positioning in a flat two-dimensional space-time: the delay master equation

Cited by in corpus (6)

• Chronometric geodesy: methods and applications
• Positioning systems in Minkowski space-time: Bifurcation problem and observational data
• Relativistic positioning: errors due to uncertainties in the satellite world lines
• Approaches to relativistic positioning around Earth and error estimations
• Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth's oblateness on Galileo satellites
• Relativistic location algorithm in curved spacetime