Relativistic Positioning Systems: Numerical Simulations
- Diego Sáez
Dept. of Astronomía y Astrofísica, Universidad de Valencia
The motion of satellite constellations similar to the GPS and Galileo ones is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true location may be found using additional information (angles or times). The region where the Jacobian, J, of the transformation from emission to inertial coordinates vanishes is also represented and interpreted. It is shown that the uncertainties in the satellite world lines produce positioning errors, which depend on the value of |J|. The smaller this quantity the greater the resulting positioning errors. Among all the available 4-tuples of satellites, the most appropriate one - for a given location - should minimize positioning errors (large enough |J| values) avoiding bifurcation.