Subs dive to the Titanic and other sites of interest that are very deep in the ocean (and they mostly make it back. Mostly.). In those kinds of depths, GPS doesn’t work. Compasses may tell you north, but it’s hard to know which way to go if you don’t know where you currently are.
So suppose I descend to see the Titanic. In the course of descending 12,5 feet from the surface, I somehow drift a half-mile or more away from the wreck site by the time I reach the sea floor. How do I find my way to the wreck?
Along the same lines, how are the coordinates of the wreck (or any other point of interest at that depth) determined?
Seems promising in theory, except the drift rate looks like it could be a problem. From your link:
All inertial navigation systems suffer from integration drift: small errors in the measurement of acceleration and angular velocity are integrated into progressively larger errors in velocity, which are compounded into still greater errors in position.[7][8] Since the new position is calculated from the previous calculated position and the measured acceleration and angular velocity, these errors accumulate roughly proportionally to the time since the initial position was input. Even the best accelerometers, with a standard error of 10 micro-g, would accumulate a 50-meter (164-ft) error within 17 minutes.[9] Therefore, the position must be periodically corrected by input from some other type of navigation system.
It takes about three hours to descend to the Titanic, so even assuming you start your descent directly above the wreck, you’d probably end up being off by at least half a kilometer by the time you hit bottom.
Zero-velocity updates - in which the vehicle is brought to a dead stop, and all existing velocity readings are reset to zero - won’t be possible during the descent, because you won’t know whether your sub has actually come to a dead stop until you get all the way down to the sea floor.
Submersibles work in conjunction with surface support ships, which I would presume have sonar beacons so the sub knows where it is in relation to the support ship.
For ROV submersibles, the answer is above - ultra short baseline acoustic. That works when the mothership knows where it is and thus relative position to the mothership provides absolute position.
When you don’t have a mothership, and really don’t want to surface - any naval submarine - it gets a lot harder. Inertial systems is one solution. But as noted, they can drift, and errors accumulate.
The fascinating technology is full tensor magnetic gradiometric sensors. Very sensitive magnetometers that measure the 3D magnetic field and also measure the rate of change in field. You end up with 6 separate values at each location. (The tensor is symmetric, so 3 of the 9 possible values are duplicates.) Subs could cruise about the sea and and watch the magnetic field change to remarkable precision, and thus continuously plot their location. Won’t tell you where you are from nothing, but allows for navigation starting from a known location. Requires existing FTMG maps, but they could be surveyed by airborne or surface vessels.
The technology was declassified a while ago, and is now a mainstay of potential fields geological survey. With a modern SQUID based sensor you can hang one from a helicopter and get a silly accurate picture of the geology.