GPS satellites do not transmit their position. They transmit a mathematical equation that, when time is input as an independent variable, can be solved to resolve position. This is the almanac.
In theory the equation need never change, so the satellite would only need to transmit a time signal. However, in practice the satellites' orbits do change slightly on a regular basis, so the current (updated) almanac is continuously re-broadcast.
With a current orbital equation (almanac) and an accurate time, you can generate a pseudo-range between the receiver and the satellite. Given at least four pseudo-ranges, you can solve for position in 3D.
It is important to note that the satellites do not transmit position. They transmit an equation and a time signal.
An example would be a B747 travelling on a great circle path between the Brisbane VOR and the SFO VOR at precisely 400kts GS.
- Can you find its position? Yes, if you know the time it set heading from BNE VOR.
- Did the B747 transmit its position? No, never. Just the equation of motion and the time of set heading.
Hope this helps.