I once did a gps experiment in the context of a golf device - it comes with the location of the greens, etc and tells you how far you are from those points. I just programmed in 4 points all 100-200 yards from a fixed location in my yard. I then took 3 or 4 readings (spread out across the day) for a month or so. While I had no idea how far each of these points were from me, they certainly should not change. I found the readings to vary about plus or minus 5 yards.
From what I have read atmospheric variations are the major source of error. And the WAAS system was designed to adjust for that. And note that measurements taken close together in time and space are way more repeatable than this. This was back in 2010, so maybe things have changed.
dave