How do GPS satellites keep their on board clocks accurate? I assume that they need to get update from a base station. But how do you make sure that after the update all the satellites are synchronized, i.e. there isn't any phase shift.
You have your base station on earth, and assume that all the satellites you want to update are in line of sight. You send an update command. But, each satellite is a different distance from the base station. There will also be a delay from receiving the command, to updating the internal clock. Some satellites may have newer hardware, which is faster.
If you update the satellites separately, you would need to ensure that your timings of the commands that you send are very accurate. This seems like a difficult thing to get right. Is there a better method that is used in practice?
I guess what I am interested in is say you have a clock at location A. How do you synchronize it with a clock at location B, which is far away from A? You have the message flight time delay, processing delay in B etc.
Answer
Clock errors are not corrected, they are compensated in two steps.
1. Error determination
The GPS control segment uses reference receivers in well known locations to determine the actual orbital elements and the clock error of space vehicles. The reference for position is the WGS84 reference frame, for time it is the international atomic time. Even the smallest effects like continental drift and relativistic time dilatation are taken into account.
2. Error Compensation
The onboard clock (in fact, the SV Z-Count, see IS-GPS-200 3.3.4) is not tuned, slewed or reset to compensate for the error. Citing IS-GPS, 20.3.4.2:
Each SV operates on its own SV time
Instead, the offset between UTC and this spacecraft's clock ("GPS-Time") is broadcast in the navigation message (see IS-GPS 20.3.3.3.1.8). This does not only include the current offset, but also different forecasts ("fit intervals", 20.3.4.4). Normally, only the highly precise short term forecast is relevant, the others would be used if the control segment is inoperable and no uplink is possible.
Likewise, the position error (deviation from nominal orbit) is left uncorrected (this would deplete precious fuel), but is broadcast to receivers by uploading ephemeris data (orbital elements) to the spacecraft.
Time of flight is no issue for the uplink, as the new fit interval data has already been determined in the previous step.
The actual compensation is then done in the receiver (user segment). It applies corrections when relating the observed signal/code phase of different SV.
Exceptional situations
Sometimes, old spacecraft behave in unexpected ways, for example their clocks begin to drift unpredictably. AGI has a website with performance data of onboard clocks. You can see, that USA-151s clock (sending PRN28) is a little bit shaky and needs frequent compensations.
If a clock goes wild or a powered maneuver makes the SV unusable for navigation the SV sends an "inoperable flag" in its navigation message and is ignored by end users' receivers.
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