Model-free active noise control using second-order simultaneous perturbation stochastic approximation algorithm for periodic noise

Model-free active noise control (ANC) using simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted interest of researchers since it avoids the problem of secondary path modeling (SPM). However, the existing SPSA-based ANC methods are all based on the first-order SPSA algorithm and the convergence rate of these methods are significantly lower than that of the Filtered-x least mean square (FxLMS) algorithm. In order to enhance the convergence performance, this paper introduces the second-order SPSA algorithm into the ANC system. During the implementation of the second-order SPSA algorithm, a novel method of matrix positive definite transformation based on eigenvalue decomposition (EVD) is proposed to make the algorithm applicable to the ANC system. Convergence performance and tracking performance of ANC using the second-order SPSA algorithm are compared with ANC using the FxLMS algorithm and the standard SPSA through simulation and experimental verification. Simulation and experimental verification results show that ANC using the second-order SPSA algorithm can not only achieve the convergence rate comparable to that of ANC using the FxLMS algorithm, but also track the secondary path change.