A robust adaptive filter for noise reduction problems

Classical optimum adaptive filtering assumes that some second order moments are known, so that the optimality is linked to the accurate knowledge of the letter moments. In most practical cases, this knowledge is uncertain, estimates must be utilized instead of true values, and a considerable decrease in the performance is often deplored. Thus, two related problems arise : first, a single optimization criterion must be clearly defined to provide a joint estimate of the unknown variables and the second order moments; secondly, a measure of the estimated filter performance should be used to enquire into the optimality of the estimated solution.