Relativistic stereometric coordinates supplied by relativistic auto-locating
positioning systems made up of four satellites supplemented by a fifth one are
defined in addition to the well-known emission and reception coordinates. Such
a constellation of five satellites defines a so-called relativistic localizing
system. The determination of such systems is motivated by the need to not only
locate (within a grid) users utilizing receivers but, more generally, to
localize any spacetime event. The angles measured on the celestial spheres of
the five satellites enter into the definition. Therefore, there are, up to
scalings, intrinsic physical coordinates related to the underlying conformal
structure of spacetime. Moreover, they indicate that spacetime must be endowed
everywhere with a local projective geometry characteristic of a so-called
generalized Cartan space locally modeled on four-dimensional, real projective
space. The particular process of localization providing the relativistic
stereometric coordinates is based, in a way, on an enhanced notion of parallax
in space and time generalizing the usual parallax restricted to space only.Comment: Preprint version of Sec. VIII in the HAL-INRIA document with
reference: hal-00945515, v1. One bibliographic reference (Blagojevic et al.)
more with respect to version
