I'm working on something else right now and don't feel like diving into an hour or so of research. But considering this "audience," odds are good somebody here already knows the answer off the top of their head.

Is the GPS satellite system self-contained? That is, if civilization fell, would GPS boxes (assuming you could find batteries) still work as long as the satellites were up there and operational? What lifetime does a satellite have before its fuel and such run out, and how many can you lose before the system doesn't work any more?

Or is there some central Earth-surface facility that coordinates all this in real time and without it the satellites would be useless? Something that has to control the system from the ground?

Notes for future fiction ideas...