I expect that we'll see great improvements in the near future as GPS is still a relatively young technology (the 1990 gulf war was the first time it was widely used in a conflict) and we've already seen the price of GPS receivers dropping significantly. This gps tracker, for example, is less than $USD25.
Differential GPS (DGps) is commonly used by surveyers, marine navigators and aircraft as a way to increase the accuracy of GPS from a nominal 15m to more like 100-150mm. This is achieved by using ground based station, at a known position, to broadcast corrections. These corrections are the difference between the known position and the position calculated by the GPS.
Based on the assumption that all receivers in a given area have the same positional error, receivers in unknown locations can correct their calculated position by knowing the error caculated by the fixed station. For example, if the known location of the fixed station differs from its received GPS location by 3m to the east, a receiver at an unknown location can correct its position by 3m to the east to calculate its actual position.

The first step is to confirm my assumption that all GPS receivers in a given area have the same positional error. I'll confirm this by placing my laptop GPS receiver next to my phone and see what the difference in displayed position is.