Article
Version 1
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Location Problem in Relativistic Positioning: Relative Formulation
Version 1
: Received: 4 June 2024 / Approved: 5 June 2024 / Online: 6 June 2024 (11:29:08 CEST)
A peer-reviewed article of this Preprint also exists.
Serrano Montesinos, R.; Ferrando, J.J.; Morales-Lladosa, J.A. Location Problem in Relativistic Positioning: Relative Formulation. Universe 2024, 10, 299. Serrano Montesinos, R.; Ferrando, J.J.; Morales-Lladosa, J.A. Location Problem in Relativistic Positioning: Relative Formulation. Universe 2024, 10, 299.
Abstract
A relativistic positioning system is a set of four emitters broadcasting their proper times by means of light signals. The four emitter times received at an event constitute the emission coordinates of the event. Covariant quantities associated with relativistic positioning systems are analysed relatively to an observer in Minkowski space-time by splitting them in their relative space-like and time-like components. The location of a user in inertial coordinates from a standard set of emission data (emitted times and satellite trajectories) is solved in the underlying 3+1 formalism. The analytical location solution obtained by Kleusberg for the GPS system is recovered and interpreted in a Minkowskian context.
Keywords
Relativistic Positioning Systems; pseudorange navigation equations; Kleusberg’s solution
Subject
Physical Sciences, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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