Stationary GPS unit shows movement...

All GPS satellites, apart from the one or two geostationary Egnos / WAAS satellites, are constantly moving across the sky, GPS works by measuring the varying distances from at least 3 satellites to the GPS receiver, the satellite's movement is not the problem, Theoretically your GPS should give you a single stationary point where ever the satellites are, however inaccuracies are introduced by the GPS's clock and also by the satellites not being in the best location (the further apart they are the better). The satellites carry very accurate atomic clocks, however your GPS does not, so it is quite normal for GPSs to get the time (and it's position) slightly wrong, this shows up as a moving location when the GPS is actually stationary. All GPSs, both new and old do this to some degree, although newer GPSs have the advantage of being more sensitive, being able to use not only GPS but also Egnos / WAAS and Glonass satellites etc. all of which cuts down errors. Some GPSs also perform averaging where many readings are taken over a long period and summed into a single more accurate stationary location