Monday, January 11, 2010

Coordinate Systems for Global Positioning

Relativistic versus Newtonian frames: emission coordinates
Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian spacetime, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his(her) null emission coordinates from the emitters which provide him his(her) trajectory.

A null frame for spacetime positioning by means of pulsating sources
We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat spacetime. As a prototypical case, we show how pulsars can be used to define such a positioning system. The reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user's coordinates and spacetime trajectory, in the reference frame where the sources are at rest. In doing so, the phases of the received pulses play the role of coordinates in the null frame. We describe our approach in flat Minkowski spacetime, and discuss the valididty of this and other approximations considered

No comments: