Re: Estimate Observation Noise Variance

On 23 Jun, 19:35, Chris Maryan <kmar...@xxxxxxxxx> wrote:
Can anyone give some pointers on estimating observation noise variance
from an observed set.

I have an process (ARMA) that I am estimating the parameters of (blind
estimation, I don't know the input sequence, I only see the output),
it would be useful to be able to have an estimate of the variance of
the added white Gaussian observation noise.

My understanding was that the following would work, but my
understanding of this is sparse (can't find the reference for this
anymore):

Estimate the covariance matrix of the signal
Ryy = 1/N sum over i (y(i)*y(i)'), i=1 to N, for many N
for some block of observed data y(i), where the length of y(i) is
longer than the AR and MA filters of the original process.

then take the SVD: USV' = Ryy, and my understanding is that the
variance of the added noise should come out in the lower singular
values, but despite tinkering with this, I haven't had any luck.

Am I on the right track?

You are certainly on the right track, at least for AR
and sum-of-sine models. This is the basis for MUSIC,
ESPRIT and those sorts of methods.

One problem with most derivations of MUSIC & al
is that they ignore certain 1/N scaling terms.
If you find a good derivation of MUSIC and
retain the scaling terms, you might be able
to estimate the noise variance.

Can anyone suggest any other method, I'll
take anything that gets me the noise variance?

Another method would be the Levinson recursion
to find the prediction filter for the AR process.
The prediction residual will be the noise. Square
it to find the variance.

Rune
.

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