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The signal I'm working on includes some noise which is I assume Gaussian white noise with zero mean and an arbitrary variance. So, it is like;

y[t] = a[t]*x[t] + n[t] 

I'm searching for the unknown variance of the noise component of the signal to use in Kalman filter. My idea is using Whitening filter over observation y[k] and finding variance of noise component n[k] afterwards.

Is it a common practice to use whitening filter for noise estimation and is there any counter-argument not to use it?

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    $\begingroup$ that whitening filter will also spread a[t]*x[t], so I'm not sure you're winning anything, unless you know things about a[t]*x[t] you don't tell us! $\endgroup$ Feb 10 '20 at 12:06
  • $\begingroup$ @MarcusMüller I know x[t] is a speech envelope but you are right, whitening filter will also spread a[t]*x[t] and there will be nothing to gain. I'll find another solution. Thank you $\endgroup$
    – kubicwerke
    Feb 10 '20 at 17:26
  • $\begingroup$ But you're on a very good track! You have a model for your signal; it's a speech signal, so if you can convert it into a form that is especially good at representing speech with as few coefficients as possible, and then compare the energy in the few you need with those you don't need, you'd have a pretty good SNR estimator. However, it's even easier: specch typically has very little energy above 10 kHz, but white noise (by definition of "white") has the same power density all over the spectrum. So, high-pass filter your $y$, and you get a bandwidth with the noise power density only. $\endgroup$ Feb 10 '20 at 17:51

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