A fast-array Kalman filter solution to active noise control

A Kalman filter solution to active control and its fast-array implementation are provided. The adaptive control problem is formulated as a state-estimation problem and no interchanging of the adaptive filter and the secondary-path is imposed. Moreover, no estimate of the disturbance signal is needed, and we exploit the structure in the state–space matrices to derive a fast-array implementation. A minimum variance estimate of the controller coefficients and the secondary path state is obtained. When there is no uncertainty in the secondary path, state equivalence with the modified filtered-RLS algorithm is proven. Using exponential forgetting, the analysis shows that in the generation of the filtered reference signal in the modified filtered-RLS, exponential forgetting should be incorporated too. Simulations show the superiority in convergence of the fast-array Kalman algorithm over the fast-array modified filtered-RLS algorithm. Copyright # 2004 John Wiley & Sons, Ltd.