Positioning systems in Minkowski space-time: from emission to inertial coordinates
arXiv:0910.2568 · doi:10.1088/0264-9381/27/6/065013
Abstract
The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of an emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a `central' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.
20 pages; 1 figure
References in corpus (6)
- Two-dimensional approach to relativistic positioning systems
- Relativistic Positioning Systems: The Emission Coordinates
- Positioning with stationary emitters in a two-dimensional space-time
- Emission vs Fermi coordinates: applications to relativistic positioning systems
- Relativistic Positioning Systems
- Relativistic Positioning Systems: current status
Cited by in corpus (12)
- A comprehensive analysis of the geometry of TDOA maps in localisation problems
- Positioning systems in Minkowski space-time: Bifurcation problem and observational data
- Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
- TDOA--based localization in two dimensions: the bifurcation curve
- Positioning in a flat two-dimensional space-time: the delay master equation
- Pulsar Positioning System: A quest for evidence of extraterrestrial engineering
- Relativistic positioning: errors due to uncertainties in the satellite world lines
- The algebro-geometric study of range maps
- Geometric approach to the definition of emission coordinates
- Approaches to relativistic positioning around Earth and error estimations
- Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth's oblateness on Galileo satellites
- Relativistic location algorithm in curved spacetime