Yes, satellites are tracked by ground stations, and receive an update every 24 hours with information about their project positions in the future.
GPS satellites transmit this data in the form of an almanac which includes all the high level parameters for estimating the location of every satellite, and ephemeris data which allows you to calculate the precise location of the satellite, when used in tandem with the almanac.
The almanac doesn’t change too often, but ephemeris data is only valid for a few hours. The satellites recalculate the ephemeris data themselves, and normally have a few months of needed data stored on board, just in case they can’t get updates. But the expectation is they’re updated every 24 hours.
This is also why, in a zombie apocalypse type scenario, GPS would become inaccurate past the point of usability within a few weeks, maybe a few months max.
Amongst other things, the clocks need to be corrected for relativistic effects.
Due to the net effect of both kinetic and gravitational time dilation, clocks onboard a satellite advance more quickly than they would on Earth (when observed from Earth).
They use atomic clocks, so it's accurate to something like 1 part in 10^16, or about 1 second in a billion years! A friend of mine is working on the next generation, which will be even more accurate.
In contrast, the force of gravity experienced by the satellite is known to much less accuracy. In fact, changes on a monthly basis due to rainfall/rivers and tides. The GRACE satellites measure the change, although I couldn't find any information on how accurate their measurements are, except that they can measure the distance between the two satellites to within a micrometer (10^-6), so substantially less precision than the clock!
Not quite that accurate. Apparently it’s more like 3 seconds per million years for a rubidium atomic clock, and 1 second per 3 million years for a hydrogen maser. (Caesium atomic clocks are somewhere in between)
Is it a similar problem? I hadn't thought about how GPS satellites know where they are. Do they need regular correction?