An H∞-optimal alternative to the FxLMS algorithm

We study a general setting of active noise cancellation problems from the H_∞ point of view and present a solution that optimally limits the worst case energy gain from the interfering measurement errors, external disturbances, and initial condition uncertainty to the residual noise. The optimal bounding of this energy gain is the main characteristic of the proposed solution. To impose a finite impulse response structure on the controller, we suggest an adaptation scheme for the weight vector of an FIR filter that approximates the H_∞-optimal solution. Our discussions explain: 1) why and how this new adaptive scheme generalizes previous results on the H_∞-optimality of the LMS algorithm; 2) why it is an alternative to the widely used filtered-X least-mean-squares (FxLMS) algorithm; and 3) how the formulation provides an appropriate framework to address the issues of modeling error and robustness. Simulations are used to compare the performance of the proposed H_∞-optimal adaptive scheme with the FxLMS algorithm