I was looking into implementing an Inertial Navigation System for an Android phone, which I realise is hard given the accelerometer accuracy, and constant fluctuation of rea
You are making the assumption that the accelerometer readings in the X and Y directions, which in this case is entirely hardware noise, would form a normal distribution around your average. Apparently that is not the case.
One thing you can try is to plot these values on a graph and see whether any pattern emerges. If not then the noise is statistically random and cannot be calibrated against--at least for your particular phone hardware.