7_Eschaton_:
The problem is that even when the module I'm using is completely stationary in relation to Earth's surface, both latitude and longitude drift by 0.4 ms - 1.25 ms (which means a constant few centimeter drift per measurement).
Either the device is faulty or the problem description is.
If there was constant drift the GPS would eventually show you on the other side of a continent or an ocean - which would be daft.
Some uncertainty in the position should average out over several readings.
The uncertainty will be greater if fewer satellites are visible to the GPS but, as long as there are enough satellites visible to get a fix there should be no constant drift.
...R