0
$\begingroup$

I just have a question about using an least-mean-squares algorithim adaptive filter for system identification. Consider the following enter image description here

I am told that as the error converges to a small value, the adaptive filter coefficients w[k] will indeed repersent the unknown system h[k]. Now, that doesn't make sense to me since the n[k] is being used in the error calculation.

Won't the adaptive filter coefficients w[k] now repersent the unknown system coefficients h[k] AND the noise n[k]?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

Because an LMS estimator will, over time, "average out" uncorrelated zero-mean noise. It's pretty much in the name.

But yes, you're right, there is a noise component in the estimate; one of the qualities of an estimator is how little the noise variance influences the estimate variance after a given length of observation.

That's the case, however, for all estimators: you measure signal + noise, and you estimate parameters from that. The parameters must be somewhat noisy; otherwise, there's something broken with your noise model.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Ah. I assume, this would work without the noise too then. $\endgroup$
    – AlfroJang80
    Commented Dec 5, 2018 at 16:55
  • $\begingroup$ it probably does in this case, but there's estimators which need the noise to work. $\endgroup$
    – Marcus Müller
    Commented Dec 5, 2018 at 16:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.