Just a slight nitpick: Your GPSr doesn't have a hyper accurate atomc clock. Which is why it needs a signal from minimum four satellites, not three, to resolve your position in three dimensions.
True, but then it's not a one to one comparison of a system with three buoys triangulating a position
With GPS there's also some intentional jitter in the signals to inherently degrade the accuracy, and some other limited situations where it won't function at all, which all keep it "good enough" for most civilian purposes, but not so good that it's easy to use for nefarious purposes.
So, pondering on this last night as I was waiting for my puppy to do his business outside, it dawned on me that Bluetooth may actually be the
perfect technology for this application. I obviously don't know specifics of their system, but the bluetooth standard is 100mW of power, or 0.1 watt. Let's call the distance from a diver's tank to their hands 60cm just for argument's sake. This is probably conservative, and would definitely be limiting, but play along for now. A 2.4GHz signal with 0.1w source power will be attenuated to ~0.0000000000001153w, or 1.15x10^-13 over 60cm of water. That's an impossibly weak signal, and you'd need an incredibly sensitive receiver to pick anything up.
But the environment is actually helpful in this scenario. If you had a 1.0x10^-13w signal you were trying to find while sitting in your living room, you'd have absolutely no hope. Bluetooth, wifi, cordless telephones, baby monitors, car alarms, even your microwave oven all use 2.4GHz. There's a
ton of interference on the surface. You'd need not only some incredibly sensitive instruments to receive such a weak signal in the first place, but some really fancy discrimination to "see past" all the very loud interference. The same reason I said it can't be used underwater may actually help in this case. Because water is so attenuating to 2.4GHz, you can assume with near certainty that you'll have essentially zero interference at depth, which would actually make it easier to "hear" a very weak signal from a nearby source. You also shouldn't have significant multipath interference issues.
I still have my doubts that there's enough sensitivity in a receiver to pick up a signal that low, but I'm not as confident it's impossible.
A somewhat analogous situation: NASA's Voyager spacecraft use 23 watt transmitters. By comparison, a fixed mount marine radio you'll see on a dive boat is legally limited to 25watts. Your Boston Whaler has a more powerful radio than the only human-constructed objects to travel into interstellar space. That's pretty cool. Just as cool; we still talk to them regularly. I had to look this up, but Voyager(s) use 8GHz radio, which is pretty interference free, just as the underwater 2.4GHz situation would be. We can hear the incredibly weak signals coming back from Voyager by using massive antennas (like 100+ft diameter). Voyager 1 is currently 13.8 BILLION miles from Earth, and we still communicate with it precisely because of the low interference. That big FM radio station you can only pick up from the next county on a clear day is transmitting near 100,000 watts, but there's too much interference for a clear signal to carry even a few dozen miles.
All that to say "maybe Bluetooth
could work for them." I still think it's unlikely, but again, I'm no expert. If I'm simply remembering the loss characteristics through water incorrectly, I wouldn't have to be far off for my math to fall apart and render all of my assumptions completely irrelevant.