Parallel fast-array recursive least squares filters for active noise control with on-line system identification

Rapid convergence, fast tracking, and low computational cost are desirable characteristics for active noise control applications with rapidly changing transfer paths. Kalman filters with a forgetting factor lower than unity can give a significantly improved tracking performance but have been found to be numerically unstable for the efficient fast array form of the algorithm. A convex mixing fast-array Kalman filter can provide numerical stability. This is achieved by running two finite length growing memory recursive least squares filters in parallel and using a convex combination of the two filters when the control signal is calculated. A reset of the filter parameters with proper re-initialization is enforced periodically. In previous versions it is assumed that deviations of the secondary path from the nominal value are small. If these deviations become significant then the model of the secondary path has to be updated. In this paper we present results of a version of the algorithm with on-line adjustment of the secondary path model. One adaptive filter is used to minimize the error signal while the other adaptive filter minimizes the modeling error of the secondary path. The paper compares different adaptive filters with respect to convergence and tracking.