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Keywords = Bancroft’s closed-form solution

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22 pages, 1626 KB  
Article
Minkowskian Approach to the Pseudorange Navigation Equations
by Ramón Serrano Montesinos and Juan Antonio Morales-Lladosa
Universe 2024, 10(4), 179; https://doi.org/10.3390/universe10040179 - 12 Apr 2024
Cited by 1 | Viewed by 1427
Abstract
Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that 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 [...] Read more.
Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that 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 analysed as a clarifying situation. Full article
(This article belongs to the Section Gravitation)
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