An H 1 - Optimal Alternative to the FxLMS Algorithm 1

We study a general setting of active noise cancellation problems from the H1 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 nite impulse response (FIR) structure on the controller, we suggest an adaptation scheme for the weight vector of an FIR lter that approximates the H1-optimal solution. Our discussions in this paper explain; (i) why and how this new adaptive scheme generalizes previous results on the H1-optimality of the LMS algorithm, (ii) why it is an alternative for the widely used Filtered-X Least-MeanSquares (FxLMS) algorithm, and (iii) 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 (approximate) H1-optimal adaptive scheme with the FxLMS algorithm.