H 1 Adaptive Filtering

H 1 optimal estimators guarantee the smallest possible estimation error energy over all possible disturbances of xed energy, and are therefore robust with respect to model uncertainties and lack of statistical information on the exoge-nous signals. We have recently shown that if prediction error is considered, then the celebrated LMS adaptive l-tering algorithm is H 1 optimal. In this paper we consider prediction of the lter weight vector itself, and for the purpose of coping with time-variations, exponentially weighted, nite-memory and time-varying adaptive ltering. This results in some new adaptive ltering algorithms that may be useful in uncertain and non-stationary environments. Simulation results are given to demonstrate the feasiblity of the algorithms and to compare them with well-known H 2 (or least-squares based) adaptive lters.