There has been some talk here before about the RTK-Lib project, which allows much greater GPS positional accuracy. Now someone has ported RTK-Lib the Android and it's in the Google PlayStore for free:
So apart from an Android device (or Android-x86 image) you need a raw capable GPS (Skytraq S1315F-RAW or something fancier) with decent antenna and a correction feed (or second GPS)... and volia cm level accuracy for your robotics projects.
Don't know for certain whether this can run headless once configured.
There's also a 'report GGA to base' function, which might allow the computation to be done in 'moving base' mode and then the solution's position relayed to the rover.... if you don't want to put extra processing on the drone.