A Kalman filter approach to active noise control

Most Active Noise Control (ANC) systems use some form of the LMS [5] [9] algorithm due to its reduced computational complexity. However, the problems associated with it are well-known, namely slow convergence and high sensitivity to the eigenvalue spread [3] [9]. To overcome these problems the RLS algorithm is often used, but it is now widely known, that the RLS loses many of its good properties for a forgetting factor lower than one. Namely, it has been shown that in some applications the LMS algorithm is actually better in tracking non-stationary systems than the RLS algorithm [2] [3]. One approach, which works well with non-stationary systems, is to use some specialized form of the Kalman filter, which can be interpreted as a generalization of the RLS algorithm [1][3][4]. The Kalman filter has a high computational complexity, similar to that of the RLS algorithm, which can make it costly for some applications. Nevertheless, for narrow-band ANC, the number of taps is not very large [9], and the application of the Kalman filter in ANC may be easily handled by today DSP´s. In this paper, a specialized version of the Kalman filter fitted to ANC is developed; both control filter adaptation and secondary path modeling. It is shown, throw computer experiments, that a large reduction in the residual noise can be achieved in non-stationary environments, compared with the LMS and RLS based algorithms, especially when on-line secondary path modeling is used.