  The relativity of Global Positioning System (GPS) pseudorange measurements is
explored within the geometrical optics approximation in the curved space-time
near Earth. A space-time grid for navigation is created by the discontinuities
introduced in the electromagnetic field amplitude by the P-code broadcast by
the GPS satellites. We compute the world function of space-time near Earth, and
we use it to define a scalar phase function that describes the space-time grid.
We use this scalar phase function to define the measured pseudorange, which
turns out to be a two-point space-time scalar under generalized coordinate
transformations. Though the measured pseudorange is an invariant, it depends on
the world lines of the receiver and satellite. While two colocated receivers
measure two different pseudoranges to the same satellite, they obtain correct
position and time, independent of their velocity. We relate the measured
pseudorange to the geometry of space-time and find corrections to the
conventional model of pseudorange that are on the order of the gravitational
radius of the Earth.
