Either show my location or don't. Randomizing in a four-mile radius is both compromising and useless.
( ) Accurate location
( ) Fuzzy location (within 4 miles)
( ) Super-fuzzy location (state/country and time zone)
( ) No location
So something like
shown_pos(t) = mode(quantize(pos(t-j)),...,quantize(pos(t-j-k)))
For some delay j and hysteresis k.