@SouthernSharktoothDiver, search the interweb for an intro to Kalman filters to fill in the basics: many intros start with navigation as the first example. An IMU requires periodic independent, external sample data to correct/control/limit the accumulation of sample error (i.e. drift).
I've sorta/kinda napkin-designed/built something like you're asking about - if I understand your use-case correctly. What I have/had in mind is a dive track recorder to produce a 3d track of the dive that can be added to the dive log after the fact, and used as the basis for a better dive site map. A system for safe reliable navigation during the dive is WAY more - not conceptually, but costwise and risk of use. So, not an INU like
@James79 is referring to; just a logger using an IMU and whatever external data inputs are possible.
My cobbled-together prototype had significant limitations/requirements - notably:
1. require some underwater structure "in view" (eg, bottom, coral wall, wreck, etc.) at least "most" of the time.
2. (really a corollary of point 1): require relatively good visibility.
3. require stable (no, obviously not fixed) mounting w.r.t the environment.
In the theme of "if you have a hammer everything looks like a nail", what I did was add a laser and camera to detect travel (distance and direction) against stationary structure (eg bottom). Why the "hammer/nail" analogy? I spent a lot of my career implementing, later designing, later architecting both passive and active vision systems for various 3-d measure/profile/track/target tasks. I tried to interest one employer in the project but the response (as expected) was "a cool idea is neither a product nor a business plan."
Anyway, in use, the laser/camera data, pressure (depth), and the inertial data from the IMU were all logged, along with GPS start/stop location. There was no processing on board (not budget possible as a diy project at the time). Kalman filter based processing was done offline on a desktop computer. These days an embedded system might be able to do the job in real time for a navigation system, but that's another level.
My one and only prototype seemed to generate nice data in shallow super-easy conditions, but the first (only) test with any challenges resulted in:
1. A leak in the housing about 1 minute after reaching planned bottom (12m).
2. Shorted and sparking/smoking electronics as soon as the salt water made it to the circuit board.
3. A brief fire (nice thing about a housing underwater - very limited O2).
4. No data.
I think I still have before/after pictures of the unit. It's kinda funny.
So bottom line, I think a system like that is possible, and I think about a Mk2 once in a while now that I'm retired. Given the giant advances in multiview photogrammetry it can (and should) be done without the laser. Of course, any other method that gets periodic distance and direction travelled independent of the IMU should also in principle be possible.