Inertia based underwater positioning system

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The killer is (as pointed out by at least @tursiops and @James79) that even a "perfect" IMU is blind to your movement due to current.

An IMU don't care about the source of the movement, current, fins, DVP,... they all have the same effect.

The issues are the quality of the initial condition, and the fact that the needed double numerical integration is unstable. And if you are thinking about a wrist mounted system, there will be a lot of noise to cancel in that double integration to get the interesting signal.
 
In the case of IN for a diver, the noise would be much greater than the signal (propulsion pulses, vector changes, depth changes, magnetic signature changes on wrecks, etc.) with some of the ‘noise’ changing very slowly (tide/current, static hovering, etc.).
 

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