I have read here and elsewhere of different techniques of estimating tilt angle, rate of change of tilt angle.
Many of these use a combination of an accelerometer and rate gyroscope. There is also extensive use of Kalman filtering with both of these sensor types.
I may be a little naive, but I think this could be over complicated.
Surely a single accelerometer can be used to derive the instantaneous angle of a body and also the rate of change of angle?