I found not so much literature to the topic, this is why I ask here. Does someone know some ways to estimate the drift rate of the gyrometer. I was thinking about basically two approaches. One would be to use a low pass filter with a low cut-off frequency to estimate the drift of the angular velocity. Second would be to use the accelerometer, calculate the attitude dcm and by this also the angular velocity. The difference between the acc angular velocity and gyrometer would be maybe also a drift rate. Nevertheless, I am not so sure whether this is a good way to get reliable drift rates :D
If your drift is expected to be a constant bias then you should be able to measure it while the gyroscope is static. Many systems employ a feature that measures the bias for a couple of seconds when the device is powered on so that it can be subtracted from future gyroscope measurements.
However, if the drift is more of a random walk that wobbles up and down, then you will need something a bit more sophisticated. Your suggestion of using the accelerometer is good but you will need a magnetometer as well if you want to determine the attitude -- the accelerometer won't pick up any rotation if the angular velocity is aligned with the gravity vector. But overall, a sensor fusion approach is almost always better since all of your sensors will have some inherent uncertainty.