  Relativity is an integral part of positioning systems, and this is taken into
account in today's practice by applying many "relativistic corrections" to
computations performed using concepts borrowed from Galilean physics. A
different, fully relativistic paradigm can be developed for operating a
positioning system. This implies some fundamental changes. For instance, the
basic coordinates are four times (with a symmetric meaning, not three space
coordinate and one time coordinate) and the satellites must have cross-link
capabilities. Gravitation must, of course, be taken into account, but not using
the Newtonian theory: the gravitation field is, and only is, the space-time
metric. This implies that the positioning problem and the gravimetry problem
can not be separated. An optimization theory can be developed that, because it
is fully relativistic, does not contain any "relativistic correction". We
suggest that all positioning satellite systems should be operated in this way.
The first benefit of doing so would be a clarification and a simplification of
the theory. We also expect, at the end, to be able to run the positioning
systems with increased accuracy.
