Public GPS only has a 100M precision from the satellites. Cheap GPS systems use averaging to eventually narrow this down to less than a meter or so. You can also use differential systems which broadcast correction data that can be used to improve accuracy as well, but still down to just sub 1m resolution, although you have to subscribe to them. With both you might get sub decimeter resolution.
Vertical resolution is a bit less due to the lateral differential of the satellites being much less than their horizontal difference, but again, with averaging and other techniques, you can still get quite precise. They are not in a flat plane, but in a medium level orbit. It's just the fact that we only see part of the orbital sphere that makes vertical resolution less, but not that much.
Miltary GPS systems have 1m resolution, and with averaging and differential systems, can easily get down to sub-centimeter precision.
It would be easiest to just measure the rotation of the drive train, just like real cars do.