...you measure the tilt angle T against the vertical line and if your function f(t) also contains the typical DC offset of Vdd/2 of such an acceleration sensor.

Usually pitch and roll is measured against the horizon and so your formula becomes

Uout = c x g x sin(roll) + Vdd/2 + noise

where "g" is the gravitational acceleration, "c" a gain factor, "roll" the roll angle against the horizon and noise the sum of electronic noise, drifts and additional unwanted tangential and centripetal accelerations.

The component of gravity acceleration in line to the sensor, i.e. the acceleration the sensor is actually measuring, is a = g x sin(roll).

The following scheme shows how pitch and roll are defined:



And yes, a good low pass filtering is absolutely crucial!

Kai