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I have some simulated outputs from a model of a sensor that a teammate wrote. I'm attempting to verify, using Allan deviation, that random walk and bias instability were modelled correctly.

To do this, I'm following this mathworks tutorial: https://www.mathworks.com/help/fusion/ug/inertial-sensor-noise-analysis-using-allan-variance.html

To measure instability, that tutorial fits a line with 0 slope to a well defined critical point in the tail of the Allan deviation curve. However, my case has some wonky tails with multiple critical points:

enter image description here

Notice the green curve in particular (z-axis sensor) is super weird. How would I modify the techniques outlined in that tutorial to derive the instability for these three sensors?

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    $\begingroup$ I'm not confident I get enough of the big picture, but if you're doing the 2-sample average variance (in other words, the Allan variance), then you are incorporating a lot of different times into every point in the curve you're getting. If afterwards the curve is still not smooth, that either beans your phenomenon just actually changes systematically at these delays, or your observation was not long enough to support the statistics you're trying to do here. Either way, the statement you could make would be "this data does not support the claim that things are stable". That is a weak statement. $\endgroup$ Commented Aug 23, 2023 at 8:29
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    $\begingroup$ But if your curve simply doesn't have that low point where the mathworks guide defined the bias instability to be visible, then it doesn't. It might come at larger delays then what you calculated the Allan deviation graph for (again, possibly limited by the number of time samples you have, or physically limited), or it might simply never come. Physics has little compassion for mathworks guides, and nose can make it so that a clear minimum, zero-slope region like in that example never manifests. $\endgroup$ Commented Aug 23, 2023 at 8:35
  • $\begingroup$ As Marcus said, you need about 100x more samples to have sufficient confidence in the result...so if you want to measure the ADEV at 10 seconds, you need 1000 seconds worth of data. Ultimately this is a guideline but comes down to the confidence you would want in your result. All the results to the far right will be "super wierd" and different with each run, consistent with a low confidence interval. $\endgroup$ Commented Aug 26, 2023 at 23:33
  • $\begingroup$ @DanBoschen when you say 100x more samples, do you mean 100x more averaging intervals? Because I increased the number of samples by well over 100x by first increasing the sample rate then the duration of the simulation, then both at the same time. This had exactly zero affect on the tail of the deviation plot. $\endgroup$ Commented Aug 28, 2023 at 15:47
  • $\begingroup$ @rocksNwaves I mean 100x the time duration regardless of the sampling rate used. So if you want an ADEV at 1 sec, I recommend collecting 100 seconds worth of data to reduce the error in the result. (The longer the capture, the lower the error). To get a 1 sec ADEV, you will also need to sample at least once per second. $\endgroup$ Commented Aug 29, 2023 at 16:50

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