Locating Objects Away from Earth Surface: Positioning Accuracy

Abstract

The motion of the Galileo and GPS satellite constellations is simulated in Schwarzschild space-time, whereas photons travel in Minkowski space-time. This is a good enough approach to deal with the main goal of this paper: the study of positioning accuracy in the framework of the so-called relativistic positioning. Our study is based on numerical 4D simulations. In this meeting, the contribution of J.A. Morales-Lladosa contains some basic ideas which have been important to perform our numerical calculations. For four chosen emitters (satellites) of a certain constellation, many receivers located at different distances from Earth surface and in distinct directions are considered. Thus, we verify that, in some space-time regions, the Jacobian of the transformation giving the emission coordinate in terms of the inertial ones vanishes. For receivers placed close to these regions, positioning errors due to uncertainties in the satellite trajectories are too great. Our results suggest that, given a receiver, the 4-tuple of satellites used for location must be carefully chosen to minimize positioning errors (large enough Jacobian values). © Springer-Verlag Berlin Heidelberg 2014.