The GPS satellites carry only enough propellant for small corrections and orbit at about 12,500 miles. Spy satellites used to (probably, in the main, still do) carry much more fuel (to sustain height and to change orbit to cover different areas) and orbit at a few hundred miles, for detail of pictures obtained.
While it is certainly possible that GPS satellites also carry spy cameras, it seems unlikely, being high up and stuck on fixed orbits.
They used to have "Selective Availability", they declared they won't use that again, and newer replacement satellites are supposedly incapable of using it ...
You can get GPS RTK modules for about £300 that give you 1cm precision relative to either your own base-station, or to a commercial network of base-stations.
Differential GPS. You calculate the difference between the GPS provided location of a fixed reference point and your GPS provided location. You usually transmit the fixed to the mobile with a radio link.
Simple in principle. But both receivers need to be seeing exactly the same satellites, which is tricky/impossible to do with COTS equipment. Hence the cost.
(Pre-GPS, we'd lug a pair of lorry batteries to remote clifftop locations to power two or more Decca Trisponders for maybe a couple of days. These used time-of-flight coded pulses picked up on the survey vessel. Lots of TTL. Later, I automated this by hooking the receiver to an HP-85 via a GPIO card and wrote HP BASIC software to plot position every second on an A3 flatbed plotter. The first time, the skipper couldn't get the hang of steering when the plotter was going 'backwards' until I made a tiny paper boat which I sat on the plotter pen and rotated as needed. Lightbulb moment for skipper.)
In message snipped-for-privacy@pvr2.lan, Rod Speed snipped-for-privacy@gmail.com writes
I'm pretty sure that there have previously occasionally been localised military trials to test the effectiveness of disruption to GPS signals - prior to which have been announcements to warn members of the public that they should temporarily not rely on their satnavs to give correct readings (or even to work at all).
But it is much more likely that the turnip's smartphone is at fault than he happened to encounter another trial like that which didnt have any warning to the general public that GPS was being deliberately compromised that day.
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