Estimating the autocorrelation function of an arbitrarily time-variant system response

We present a technique for determining the autocorrelation of an arbitrarily time-variant system response. Our approach relies on a key relation, introduced in [1], between the system response autocorrelation function and certain 2nd and 4th order moments of the system input and (noisy) output signals, with no other prior information about the dynamics of the system response required. We introduce a “Wiener problem” interpretation of this key relation, which enables us to benefit from the wealth of existing results about the dynamics and performance of standard adaptive filters. In particular, we propose time-recursive estimates for the system response autocorrelation, with significantly reduced computational cost, as compared to previously proposed (nonrecursive) estimates. Moreover, our procedure can also be customized to track (slow) variations in the system response autocorrelation when such variations are present. We use an example to demonstrate the advantage of applying standard adaptive algorithms such as LMS, NLMS or RLS to obtain an estimate of the desired system response autocorrelation.