JimEli:
Don't you need a surveyed point for the GPS to compare with to do differential?
You should only need a surveyed position if you want absolute coordinates. If you just want relative coordinates ("Where am I relative to the lawn boundary?") I think you just need a fixed location that both agree on. I would think that once both units have current ephemeris data they would agree on where they are.
If the base station is going to be in the same place each time you could calculate a long-term median position to use as the 'known' position.