On 2011-04-23 the National Geographic aired a TV special, in part about GPS. They said a number of things that struck me as highly unlikely. I wonder if you could confirm:
1. they said that the GPS hand held unit sends its time to 3 satellites. I would have imagined it would be reverse.
You are correct in that it is the satellites that transmit the signals. The hand held is a receiver only and must be receiving data from a minimum of three satellites to calculate a position.
2. They said the satellites do the calculation then send the position back to to hand held unit. That made no sense. That would be a huge computational burden on the satellites which are strapped for power and weight.
You are correct again.
3. They said the satellites are adjusted for relativistic effects prior to launch and suggested there is no way of adjusting their clocks ever after. That struck me as absurd. Obviously you need ways to control the satellite in may ways from ground.
Each satellite has very accurate atomic clocks but I'm not sure how much adjustment can be done from the ground or would ever be required
4. They said the hand held GPS unit has an extremely accurate clock. This seems plausible, but I would have imagined there would be some mechanism to keep it accurate so that that clock itself would not need atomic accuracy.
The handhelds do not have atomic clocks but their clocks are updated from the satellite signals and so are very accurate.
5. They said if they did not adjust for relativistic effects, GPS would be out by 7 miles each day. That sounds cool, but higher than I would have expected.
I'm not sure of the exact numbers but there are several sources of error of which clock errors are one.
6. They said something about how accurate it was. I don't remember the number, but it struck me as too high. It obviously must be accurate enough to nail down which street you are on.
The best accuracy you can expect from recreational grade GPS receivers is +/- 3 metres (10 ft) under ideal conditions. Under tree cover or in difficult topography accuracy will be much worse.
I don't own a GPS unit myself, though my brother, and my sister each let me play with theirs for a few hours. A satellite company uses my BigDate software for helping keep all the satellites in the world co-ordinated. They never told me the detail of just how they use it.
GPS signals are used for timing in a number of applications including cell phone networks.