Nonlinear Filtered‐X LMS (NLFXLMS) is an indirect adaptive control algorithm for nonlinear active noise control (NANC) system. The algorithm has been developed for both Hammerstein and Wiener secondary paths where the nonlinearity is represented by scaled error function (SEF) and tangential hyperbolic function (THF). NLFXLMS algorithm is limited in practical application because the degree of nonlinearity has to be known in advance. This limitation leads to the development of the THF‐NLFXLMS algorithm where the degree of nonlinearity is estimated by modelling the secondary path. In this work, the NLFXLMS and THF‐NLFXLMS are extended to Wiener‐Hammerstein system. The performance of the proposed Wiener‐Hammerstein THF‐NLFXLMS is compared with NLFXLMS algorithm which is considered as the benchmark and second order Volterra algorithm of comparable computational complexity. Simulation results show that the THF‐NLFXLMS has a similar performance to NLFXLMS and outperforms the second order Volterra algorithm as the system becomes more nonlinear.
Filtered-X least mean square (FXLMS) algorithm is widely used in active noise control (ANC) systems when the secondary path is linear. However, the performance of FXLMS reduces when nonlinearity is present. Leaky FXLMS (LFXLMS) and minimum output variance FXLMS (MOVFXLMS) algorithms are effective in compensating the nonlinearity effects in nonlinear ANC (NANC). When using optimum leakage factors, these algorithms show close performance with benchmark nonlinear FXLMS (NLFXLMS) algorithm. In all three algorithms, the degree of nonlinearity must be known in advance and are usually assumed. In previous works, Tangential Hyperbolic Function NLFXLMS (THF-NLFXLMS) algorithm has been developed whereby the degree of nonlinearity is estimated using tangential hyperbolic function (THF). In this work, the performance of LFXLMS and MOVFXLMS based on optimum leakage factors calculated using the estimated degree of nonlinearity is compared with THF-NLFXLMS for Hammerstein structure. The results show that optimum MOVFXLMS performs similarly to optimum LFXLMS and THF-NLFXLMS.
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