Doppler and fixed reference points is the better way. But ........ expensive, complex, and hence not useful for us.
Inertial navigation is a true option, and the only independent from external sources avilable by now.
Inertial Navigation has only a partiallly common part with the classic Dead Reckonig.
The classic way, worked almost only from speeds and times. Time can be accurately measured, but speeds are another "song".
Speed measurement is always relative and hence big uncertainties arrive if all "noise" factors are not known.
I'll use the same example I used in my last class about this subject........
If Im onboard a train running at 100m/s, walking with my friend A, at 10m/s along and with respect to the train, while you are standing on the platform.
From your point of view, we'd be moving at 90m/s or at 110m/s
But from A point of view, Im not moving (we're walking togheder). True ?
Speed measurements are always relative. If there is no knowledge about all speeds, it would be impossible to know where will A and me be after a time t with repect to any of the reference frames.
Let's now go with another situation. Inside the train again. Same observers, same conditions, but at this time, at a given time, I'll stop walking and will start running.
Let's say my speed changes from 10m/s to 20m/s in one second.
What would any observer measure ?
You, from the platform, with no knowledge of the train's, A`s or my speed, would hence realize that my speed has changed, and would measure a change of 10 m/s in 1 second.
From A point of view, the change in my speed would be the same.
And ....what about me? I'd measure the same change by means of INERTIA that would exert a force against the motion that would be proportional to the moving mass(me).
Inside Newtonian environments(Non measurable Relativistic effects) accelerations are ABSOLUTE.
In the old times, there was no way for accelerations measurements, but nowadays, we can get highly accurate lectures of it.
Inertial Navigation could be, from the theoretical point of view, the DERIVATIVE with respect to time of the old classic Dead Reckoning.
Drift caused from winds(surface vessels) or currents, can be directly measured from any chosen reference frame, from only the Inertial effects due to changes in the motion state of the moving body. In our case, the ROV.
We could even get a better approach, as we are able to measure not only accelerations(changes in speed), but changes in the acceleration itself. It means a third derivative can be used, that by comparison (integration) with the actual value of acceleration (second derivative) can be used for accuracy improvement.
With six degrees of freedom (DOF) accelerometers(linear-angular X,Y,Z) a nice approach to the real location is not "complex" to be computed.
The key is in the filtering algorithm design. I posted the simpler one, but we could refine it.
The Kalman filter looks a good point for starting.
Albeit calling Dead Reckoning to this system makes it easier to understand, Inertial Navigation has really a little thing to do with it.
Would like to start seriously working on this project. Who is for joining a team for the works ?