The rate and direction of tectonic movements can be measured by comparing the coordinates of the same GPS receiver over time. The coordinates are obtained using trilateration.
All materials I could find on the topic of GPS geolocating implicitly assume that the obliquity and precession of Earth would not change over the period when tectonic movements are measured. This assumption may be right as obliquity and precession change in long enough cycles so that they can be seen as fixed even since the start of space age (1957).
It is still interesting to figure out whether and how obliquity and precessional changes of Earth affect the accuracy of GPS-based measurements of tectonic shifts. Let's picture a scenario where as a result of tectonic plates movement, Earth's obliquity and / or precession suddenly change due to redistribution of the planet's mass. Would it be plausible for the new coordinates of GPS receivers to be wrongly calculated? After all, if obliquity and / or precession change, satellites' orbits would intersect the Earth's grid (or graticule) at different positions and angles. The satellites may not be sufficiently adjusted to this new situation, and measured movements of tectonic plates may end up either larger or smaller than the actual values.
