Adaptive filtering with a H∞ criterion

H^∞ optimal estimators guarantee the smallest possible estimation error energy over all possible disturbances of fixed energy, and are therefore robust with respect to model uncertainties and lack of statistical information on the exogenous signals. We have previously shown that if the prediction error is considered, then the celebrated LMS adaptive filtering algorithm is H^∞ optimal. In this paper we consider prediction of the filter weight vector itself, and for the purpose of coping with time-variations, exponentially weighted, finite-memory and time-varying adaptive filtering. This results in some new adaptive filtering algorithms that may be useful in uncertain and non-stationary environment. Simulation results are given to demonstrate the feasibility of the algorithm and to compare them with well-known H² (or least-squares based) adaptive filters