Q:

How are GPS satellite clocks synchronized with each other in the earth's frame of reference?

I have been looking at different threads. It seems like the receiver clock on Earth doesn't have to be synchronized with the satellite clocks.
But I believe the satellite clocks need to be synchronized with each other in the earth's frame of reference.
How is this achieved?

A:

The satellites' location is very accurately determined using ranging techniques, where a pulse is sent from a ground station to the satellite and the satellite responds very quickly, with a known time between receive/transmit. This allows one to determine exactly how far away the satellite is. Combining this information with orbital tracks allows one to determine exactly where the satellite is.
The amount of time required to do a time update from the time the signal is sent to the time it is received and in use is also well known. What is actually sent to the satellite is the time deltas, to tell the clock to jump forward or backward a certain amount of time. For GPS, this update can occur every 8 hours, but in practice is done every 24 hours.
The satellites each have onboard atomic clocks, for very accurately determining the time. Relativity is managed in essence by correcting for the clock based on the expected time. They slowed the clocks down to correct for this effect.
Signals are sent up to the satellite via the GPS ground network.
The time standard used for GPS clocks is a whole number of seconds from UTC. GPS time does not account for leap seconds, thus the whole number of seconds time difference. 

A:

Receiver clock synchronisation:
GPS or GNSS applications are only dependend on the travel time of the signal. To put it simply: You only need the travel time of four GNSS satellites to calculate the position. Three satellites for determination of the position (x,y,z) and one for the receiver clock error. This clock error is the synchronisation between the receiver (e.g. car navigation) and the GNSS satellites.
Satellite clock synchronisation:
The satellite clocks are synchronised regularly by an associated ground station of the provider.
For example Galileo: There is a ground station (Galileo Mission system) and there are several Sensor stations worldwide. 

The GMS ( Galileo Mission System ) will use the GSS ( Galileo Sensor
  Stations ) network in two independent ways. The first is the
  Orbitography Determination and Time Synchronisation (OD&TS) function,
  which will provide batch processing every ten minutes of all the
  observations of all satellites over an extended period and calculates
  the precise orbit and clock offset of each satellite, including a
  forecast of predicted variations (SISA - Signal-in-Space Accuracy)
  valid for the next hours. The results of these computations for each
  satellite will be up-loaded into that satellite nominally every 100
  minutes using a scheduled contact via a Mission Up-link Station

Stolen here
Best regards 
Ben

