I have a quasi stationary but time varying stochastic signal of which I would like to recursively (adapting to its time dependence) estimate the variance. I believe the signal could be modeled like white noise filtered through a narrow-banded band pass filter. I’ll describe two options that I’ve tried with some success, but that have some drawbacks.

  1. Recursively compute the variance with a (fixed) forgetting factor. Like V[k+1]=Alpha*V[k]+(1-alpha)*u[k]*u[k]
  2. Use RLS to estimate an AR(2) model from which I then use the whitened innovations to compute the input noise variance. This variance I then multiply with the factor implied by the AR(2) model.

The drawback with option 1 is that with a fixed forgetting factor one gets oscillating variance when the corresponding forgetting time constant is small compared to one over the dominant frequency in the signal.

I don’t quite understand why option 2 is not working better than it is. My hope was that by using the whitened noise I would get a much less oscillating variance estimation. My question is if the second approach seems reasonable and if you know of any other approaches that I could try.

The mention factor for AR(2) is discussed here: https://stats.stackexchange.com/questions/256437/variance-of-a-stationary-ar2-model



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