Ashby is widely recognized expert regarding the GPS. This paper tells you more than you'd ever want to know about the GPS and how it works, and has lots of math for those who love math. I'm just quoting pertinent excerpts.
Relativity in the Global Positioning System
Neil Ashby, Living Reviews in Relativity December 2003, 6:1
The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work.
The purpose of this article is to explain how relativistic effects are accounted for in the GPS. Although clock velocities are small and gravitational fields are weak near the earth, they give rise to significant relativistic effects. These effects include first- and second-order Doppler frequency shifts of clocks due to their relative motion, gravitational frequency shifts, and the Sagnac effect due to earth’s rotation. If such effects are not accounted for properly, unacceptably large errors in GPS navigation and time transfer will result.
Almost all users of GPS are at fixed locations on the rotating earth, or else are moving very slowly over earth’s surface. This led to an early design decision to broadcast the satellite ephemerides in a model earth-centered, earth-fixed, reference frame (ECEF frame), in which the model earth rotates about a fixed axis with a defined rotation rate...
Although the ECEF frame is of primary interest for navigation, many physical processes (such as electromagnetic wave propagation) are simpler to describe in an inertial reference frame. Certainly, inertial reference frames are needed to express Eqs. (1), whereas it would lead to serious error to assert Eqs. (1) in the ECEF frame.
The time transformation t = t′ in Eqs. (3) is deceivingly simple. It means that in the rotating frame the time variable t′ is really determined in the underlying inertial frame. It is an example of coordinate time.
Now consider a process in which observers in the rotating frame attempt to use Einstein synchronization to establish a network of synchronized clocks...Observers fixed on the earth, who were unaware of earth rotation, would use just ƒ dσ′/c for synchronizing their clock network. Observers at rest in the underlying inertial frame would say that this leads to significant path-dependent inconsistencies, which are proportional to the projected area encompassed by the path.
Synchronization is thus performed in the underlying inertial frame in which self-consistency can be achieved.... For atomic clocks in satellites, it is most convenient to consider the motions as they would be observed in the Earth-Centered Inertial (ECI) Frame. Then the Sagnac effect becomes irrelevant...For the GPS it means that synchronization of the entire system of ground-based and orbiting atomic clocks is performed in the local inertial frame, or ECI coordinate system.
Anyone who understands that, and who also understands the basic premises of SR (who I've yet to run across in this forum) would immediately understand that the GPS system rejects SR and adopts a Preferred Frame Theory of relativistic motion, with the ECI serving as the preferred frame.
SR simply will not work in the "real world."
A PFT treats all motion, simultaneity, and time as absolute, not relative. It has to, for the GPS to be a viable practical system. Although SR cannot be used, the Lorentz transformations can and are, of course. The GPS abandons SR's formulation of the LR, and implements them in the way Lorentz designed them. This of course means that the speed of light is not constant in every inertial frame. The speed of light is variable in GR, too, of course.
Edited by Moronium, 05 March 2019 - 01:49 PM.