A NOVEL FILTERED-X LMS ALGORITHM AND ITS APPLICATION TO ACTIVE NOISE CONTROL

Abstract

The conventional filtered-x LMS (Least Mean Square) algorithm [1, p. 288] was derived based on the assumption of a slow adaptation. This prevents an adaptive system from achieving a faster convergence, which is of importance to many applications. A novel filtered-x LMS algorithm is proposed in this paper without the aforementioned assumption. Therefore a more favourable convergence rate is achieved at the cost of a slight increase in computation complexity. In the novel algorithm, a so called virtual system is constructed. The algorithm thus tries to minimize the mean square value of the output error of the virtual system instead of that of the original problem. If a certain condition is met, the optimal solution of this minimization however also leads to the optimal solution of the original problem. A comparison is made between the performance of the novel algorithm and that of the conventional one. The novel algorithm is found to converge more rapidly while retaining the same robustness of the conventional algorithm. A practical implementation of the algorithm is presented for an active noise control (ANC) system, where the analysis and simulation results are confirmed by the experiments.