Estimating device height from 3-axis accelerometer data (possibly by supervised learning)
Any tiny offset error will cause a double integration to fly off quadratically in time.  Even if you manage to calibrate out this error for one sample test setup, any drift in offset due to change in temperature, orientation, age, power fluctuations, etc., will eventually render that calibration useless.

Continuous recalibration (airspeed, compass, optical fix, etc.) is likely required for a more useful result over a sufficiently long time period.