Lag-recursive estimation of the average autocorrelation of an arbitrarily time-variant system response

Several techniques have been proposed for identifying the impulse response of arbitrarily time-variant systems. The majority of such techniques rely on a statistical characterization of the time-variant impulse response in terms of its average power spectrum or, equivalently, its average autocorrelation. We present here a computationally-efficient lag-recursive method for estimating the desired average autocorrelation over a wide range of lag values, and using only measurements of the input and output signals of the system of interest. Our method involves L sets of M² linear equations each, where L is the number of distinct lag values, and M is the length of the system´s impulse response. We rely on two distinct types of lag-recursive shift invariance to reduce the cost of setting up these equations by a factor of M² and the cost of solving them by a factor of M, as compared with a non-structured solution.