Active non-linear noise control with non-linearities in the secondary path

The filtered-X LMS algorithm is successfully applied in linear active noise control and linear active vibration control. However, when it comes to non-linear noise or vibration control, or when the secondary path has a non-linearity, this algorithm must be modified to ensure that it converges and that it is unbiased. Some modified algorithms have been proposed for active control of nonlinear noise with a linear secondary path [L.Z. Tan and J. Jiang, Aug. 2001] or a weakly non-linear secondary path [V. DeBrunner and D. Zhou, 2002]. In this paper, we extend 'a non-linear filtered-X LMS' algorithm to solve the active non-linear noise control (ANNC) and active non-linear vibration control (ANVC) with non-linearities in the secondary path using an adaptive Volterra filter for the first time. Two improved versions of the non-linear adaptive filters that improve the stability and reduce the computational complexity are proposed and discussed in detail. Simulations show their effectiveness.