Scubacastor:The principle of multi-pingers is already used in the oceanographic industry. In fact, the receiver estimates its relative position to the different pingers. Assuming the precise position of each pinger is known (lat/lon), is not very complicated to triangulate the lat/lon position of the receiver.
Unfortunately, these method is dependant of an emitter underwater. A real underwater GPS would be independant of any emitter except the satellites. A solution would be to have a surface calibration with lat/lon and then measure the displacement underwater. Not at all simple but some offshore/military solutions exist with the same principle.
I have seen the on land versoin of it using both pingers and GPS.
For GPS to work, we need to recieve relatively clear signals from 3 satellites which is not always possible, when this happen, the system would then switch to use the pingers -- measuring the relative strengths from the closest pingers to approx. the locatoin of the target instead.