High end civilian IMU's typically use mechanical gyros which have been obsolete for decades. Also, a phone isn't typically moving constantly like the oceans so error rates would be lower.
Even if we could make that cheap and small enough it would still need regular corrections far more frequently than a week to be as good as a GPS is now.
If your acceleration sensor is off by 1 part per million, 9.8 m/s^2 (i.e. gravity) will turn into a positioning error of ~73km in one day.
And because of a long fly time or imprecise initial reference point (a submarine is floating) some do corrections. One of the coolest one for ICBMs is to use celestial navigation to correct errors. They'd have a window with a camera and would "look" for a few stars.
- GPS; widespread, low accuracy
- INS; always available, high short-term accuracy, terrible long-term accuracy
- terrain-matching: large-scale corrections.
The different characteristics allow one sensor to correct another to a degree to produce an overall stable position.
Of course, that was the proposal. There's more datapoints if you're willing to get creative, wifi networks (already used for this), cooperative comparison with other mobile devices in a local meshnet, acoustic cues from the environment, machine analysis of captured images, etc. Obviously dead reckoning without gps is going to require a multi-pronged approach.
Please explain how this will work?
You don't think such a system is practical, or you don't think such a system is technologically feasible?
Or you just don't understand the system I'm describing?
If you really care you could sketch out what exactly it is and how it'd work for yourself for a couple of devices (or more) and see what issues you uncover.