  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.
