I was reading about the Allan-variance method and I have a question and I need some help to understand it. Since the Allan is about analyzing the frequency stability and it can characterize the IMU sensor (for sure the oscillators too), so it calculates the bias instability (the dynamic one), my question is if the Allan is capable of calculating the bias (the static one) or not?
thanks in advance
No, the Allan Variance as a differencing computation will not calculate a static offset. A static offset will simply be removed in the difference operation. The Allan Variance will indicate how stable the waveform under evaluation is over time regardless of any offset.
I explain the details of the Allan Variance (and Allan Deviation or ADEV) computation at this post showing the differencing operation specifically.
What the ADEV plot will conveniently do with regards to computing the bias, is it will indicate the optimum averaging time over which the mean can be computed for which the standard deviation of that error will be minimized. This would be the time $\tau$ for which the bias stability reaches a minimum (the bias stability floor, or when used with oscillators; the flicker floor).
