The landing barge is towed into position by tugs, and once the boosters are landed I presume it is towed back out, so there will be some tug boats nearby.
It has station-keeping thrusters to stay at precise GPS coordinates. But it can't move far under own power and is towed. The name ASDS is not really to be taken literally here.
It will likely be a proper dynamic positioning system so will more than likely use two independent reference systems for position, one could be a DGPS system the other could be as basic as a taughtwire....
