In the context of Global Navigation Satellite Systems (GNSS), a modern approach is that of relativistic positioning. In Minkowski space-time, a relativistic positioning system (RPS) can be thought of as a set of four emitters broadcasting their respective proper times by means of electromagnetic signals. In a RPS, the basic observable is the set of four proper times received at an event x by the user: these are the user’s emission coordinates. Solving the positioning problem involves mapping the user’s emission coordinates to its coordinates in an inertial reference frame (the RPS coordinate transformation).
The purpose of this talk is to bring the (non-relativistic) theoretical foundations of current GNSSs closer to the RPS approach, by recovering from the RPS coordinate transformation equation one of the classical solutions to the problem which is still in use today: Bancroft’s closed-form solution (with four emitters).
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