  We explore, in the general relativistic context, the properties of the
recently introduced GPS coordinates, as well as those of the associated frames
and coframes. We show that they are covariant, and completely independent of
any observer. We show that standard spectroscopic and astrometric observations
allow any observer to measure (i) the values of the GPS coordinates at his
position, (ii) the components of his [four-]velocity and (iii) the components
of the metric in the GPS frame. This provides to this system an unique value
both for conceptual discussion (no frame dependence) and for practical use
(involved quantities are directly measurable): localisation, motion monitoring,
astrometry, cosmography, tests of gravitation theories. We show explicitly, in
the general relativistic context, how an observer may estimate its position and
motion, and reconstruct the components of the metric. This arises from two main
results: the extension of the velocity fields of the probes to the whole
(curved) spacetime; and the identification of the components of the observer's
velocity in the GPS frame with the (inversed) observed redshifts of the probes.
Specific cases (non relativistic velocities; Minkowski and
Friedmann-Lema\^{i}tre spacetimes; geodesic motions) are studied in details.
