If GPS timing is bad, a lot of people will notice that their position on the map is incorrect, because that's the whole purpose of the GPS network.
A 1 microsecond error is 300 meters.
While the speed-of-light propagation is about 300 meters in a microsecond, isn't the final position error possibly much greater? For calculating position on Earth, you can think about a sphere expanding at the speed of light from each satellite. The 1 microsecond error here corresponds to a radius 300m bigger or smaller, which only corresponds to 300m horizontal distance on the ground if the satellite is on the horizon (assuming that Earth is locally a flat plane for simplicity here). For a satellite directly overhead, the 300m error is a vertical distance. Calculating the difference in horizontal position from this error is then finding the length of a leg of a right triangle with other leg length D and hypotenuse length D+300m, where D is the orbital distance from the satellite (according to Wikipedia, 20180km). The final horizontal distance error is then sqrt((D+300)^2 - D^2), or about 110km.
Of course, this is just the effect of a 1us error in a single satellite, I'm sure there's ways to detect and compensate for these errors.
As another sanity check, if the error for 1 us is 110 km, the error for 1 ns would be 110 m, and I suspect 1 ns error is not unusual for consumer electronics:
> To reduce this error level to the order of meters would require an atomic clock. However, not only is this impracticable for consumer GPS devices, the GPS satellites are only accurate to about 10 nano seconds (in which time a signal would travel 3m)
Right, I was basically calculating where that signal would just be reaching the surface at the same time it was 300m under you. This is a circle around you with a radius of ~110km (again using the approximation of the ground as a flat plane). Thinking about it more, there's not much reason to do this (GPS isn't really tied to the surface of the Earth, it gives you 3-D coordinates). I guess my point was that the 300m of distance from 1us of light propagation should not be thought of as a horizontal distance.
https://www.gps.gov/systems/gps/performance/2016-UTC-offset-...
* Air and sea port operators and navigators
* Military personal running supply lines
* Military personal on foot in operations and training
* Space-X
* NASA
* River boats
* Fresh water fishermen
* Etc
Out of all the possible users who would notice a 300m deviation just based on visual reconciliation, I personally would not say it would be so rare that the USAF would not find out very quickly. Of course, this is ignoring the equipment that would likely detect the issue way before somebody in the Army started phoning the USAF.
There's not so many GPS satellites out there that you're going to be bouncing around them all the time - even if only one is affected, it would be very noticeable for extended periods of time.
I am not so sure about that. The most common use of GPS is in satnav in cars. Satnavs typically show a map, and typically it is very easy to confirm your position on a map. Any inaccuracy by more than the usual few meters would be quickly noticed by the majority of GPS users.