Location Problem in Relativistic Positioning: Relative Formulation

Author:

Serrano Montesinos Ramón1ORCID,Ferrando Joan Josep12ORCID,Morales-Lladosa Juan Antonio12ORCID

Affiliation:

1. Departament d’Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain

2. Observatori Astronòmic, Universitat de València, 46980 Paterna, Spain

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. The covariant quantities associated with relativistic positioning systems are analysed relative 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.

Funder

Spanish Ministerio de Ciencia, Innovación y Universidades

Conselleria d’Educació, Universitats i Ocupació, Generalitat Valenciana

Publisher

MDPI AG

Reference35 articles.

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4. On the exact solutions of pseudorange equations;Chaffee;IEEE Trans. Aerosp. Electron. Syst.,1994

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