From what I have read the atomic clocks onboard the GPS satellites are adjusted to run 38 microseconds slower per day prior to being launched into space. After the adjustments the satellites are launched into space and the clocks stay synchronized with each other and with clocks on the ground. Since the satellites are in motion relative to each other shouldn't the clocks fall out of synch with each other due to special relativity?
Anyone who understands the working principle of satellite navigation system positioning knows that the current satellite navigation system uses the pseudo-range difference method to achieve positioning for ground users.
Pseudorange means that the measured distance data also includes error items, and these errors are the same for each satellite. In practical applications, the satellite navigation system will use 4 satellites to measure 4 pseudo-ranges, and then make a difference to offset the same error term, and finally obtain the user's final positioning coordinates.
In fact, accurate positioning is guaranteed, as long as the atomic clocks of all satellites in orbit are synchronized. This is because the more precise the time measurement, the more accurate the position calculation, given the speed at which the signal travels (the speed of light) is known. The atomic clock used by my country's Beidou has sufficient accuracy and stability, with an error of only one second in 3 million years. In addition, the ground measurement and control will perform routine secondary time-frequency corrections every day.
In addition to achieving precise positioning, the same is true in the field of school time. The method of pseudo-range difference is also used to realize the clock synchronization of the ground user and the system time synchronization of the satellite navigation system.
In other words, whether it is from the positioning angle of the satellite navigation system or the timing angle of the satellite navigation system, the deviation proposed in the "relativistic correction" can be eliminated through the principle of pseudo-range difference. No matter whether the relativistic effect exists or not, the existing satellite navigation system can be canceled in the process of measuring pseudo-range and difference.
Therefore, it can be said that the "relativistic effect" of the satellite navigation system can be discussed, but the satellite navigation system does not need to make special corrections to the theory of relativity, let alone use the application of the satellite navigation system to prove or deny the theory of relativity.