Active noise control with fast array recursive least squares filters using a parallel implementation for numerical stability

Significant noise reduction in feedforward active noise control systems with a rapidly changing primary path requires rapid convergence and fast tracking performance. This can be accomplished with a fast-array Kalman method which uses an efficient rotation matrix technique to calculate the filter parameters. However, finite precision effects lead to unstable behavior. In this paper results of a recent algorithm [1] are presented, which exhibits the fast convergence, tracking properties and the linear calculation complexity of the fast array Kalman method, but which does not suffer from the numerical problems. This is achieved by using a convex combination of two parallel finite length growing memory recursive least squares filters. A periodic reset of the filter parameters with proper initialization is enforced, preventing the numerical instability. The performance of the algorithm is demonstrated in numerical simulations and in real-time experiments. Convergence rate and tracking performance are similar to that of a fast-array sliding window recursive least squares algorithm, while eliminating the numerical issues. It is shown that the new algorithm provides significantly improved convergence and tracking as compared to more traditional algorithms, such as based on the filtered reference least mean squares algorithm. [1] S. van Ophem and A. P. Berkhoff, A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control, International Journal of Adaptive Control and Signal Processing, 2014, submitted.