H∞ Adaptive Filtering

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 shown that if the prediction error is considered, then the celebrated LMS adaptive filtering algorithm is H∞ optimal. 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 environments. Simulation results are given to demonstrate the feasibility of the algorithms and to compare them with well-known H^2 (or least-squares based) adaptive filters.