Numerical modeling of a Global Navigation Satellite System in a general relativistic framework
arXiv:1003.5836 · doi:10.1016/j.asr.2010.07.007
Abstract
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no \emph{a priori} realization of a terrestrial reference frame. We show that the calculation is very fast and could be implemented in a real GNSS, as an alternative to usual post-Newtonian corrections. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system.
17 pages, 11 figures
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Cited by in corpus (10)
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- Positioning in a flat two-dimensional space-time: the delay master equation
- Relativistic positioning: errors due to uncertainties in the satellite world lines
- Geometric approach to the definition of emission coordinates
- Approaches to relativistic positioning around Earth and error estimations
- A relativistic and autonomous navigation satellite system
- Relativistic location algorithm in curved spacetime