The solution is called Differential GPS or ‘DGPS’ and its concept ... known location should be able to act as a DGPS over IP base station, right? In theory, yes. In practice… fail.

two of these Piksi boards – one base station and one on a vehicle, connected via radio link – can make for a very exacting high-accuracy GPS receiver. Previously, commercial RTK GPS systems ...

Also called a "differential GPS" (DGPS), an augmentation system compensates for those discrepancies by transmitting corrections to the GPS receivers either via satellite or terrestrial radio.