Minkowskian Approach to the Pseudorange Navigation Equations

Ramón Serrano Montesinos; Juan Antonio Morales-Lladosa

doi:10.20944/preprints202403.0106.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 1 March 2024 / Approved: 4 March 2024 / Online: 4 March 2024 (06:00:42 CET)

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space-time, which maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered and the subjacent elements are geometrically interpreted. The case of four static beacons is analized as a clarifying situation.

Relativistic Positioning Systems; pseudorange navigation equations; Bancroft’s closed-form solution

Physical Sciences, Other

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Minkowskian Approach to the Pseudorange Navigation Equations

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