Before the days of GPS we used to use what was called a taut-wire system for maintaining position of our floating offshore oil platform. An anchor point was fixed to the seabed and a wire was kept under constant tension to the platform. The angle was measured between the anchor and the platform, plus a measure of water depth. From these a calculation was made of platform position relative to the anchor. OK an interesting story but of no use to a scuba diver.
One of the "normal" ways for doing underwater position sensing is to place at least three sonar transmitters at "known" reference positions on the seabed then triangulate your position on a receiver which measure time differences between signal arrival times. You could turn the whole idea upside down. Three fixed floating buoys each with a sonar transmitter. One the basis that the sea is level (not crashing waves) then you can triangulate your position from the time it takes signals to arrive. Note that all sonar transmitters will have to be synchronised so that they transmit at identical times.
Now I leave it to someone else to do the hard bits !!