GPS satellites don’t correct for relativistic effects. They just set the Earth as the preferred frame, which is a great choice for a terrestrial positioning system.
I’ll see if I can find the paper it’s quite interesting.
Edit: I can't find the specific paper I'm thinking of. It's one that discusses how when other orbiting bodies want to use GPS they have to make a bunch of complex corrections that terrestrial users don't. But a search for Earth Centerered Inertial Frame will find you plenty of papers discussing the general concept.
I’ll see if I can find the paper it’s quite interesting.
Edit: I can't find the specific paper I'm thinking of. It's one that discusses how when other orbiting bodies want to use GPS they have to make a bunch of complex corrections that terrestrial users don't. But a search for Earth Centerered Inertial Frame will find you plenty of papers discussing the general concept.