Efficient adaptive Volterra filters for active nonlinear noise control with a linear secondary-path

Using a nonlinear filter to control a linear device has been studied in Strauch and Mulgrew (1998), and been proved to be effective in active noise control (ANC) when: i) the secondary path has a linear and nonminimum phase transfer function, and the reference noise is a nonlinear, predictable noise or non-Gaussian noise; ii) the primary path has a nonlinear effect. Tan et al. (2001) reinforced these statements and successfully implemented this idea with an adaptive Volterra filter, and developed an algorithm called the Volterra filtered-x LMS (VFXLMS) algorithm. However this VFXLMS suffers from a heavy computational burden as well as stability problems. In this paper, we provide several alternatives to VFXLMS: the modified Volterra LMS algorithm that increases the convergence rate by slightly increasing the computational burden, the filtered-error Volterra LMS algorithms (including the adjoint Volterra LMS algorithm and the secondary-path equalization Volterra LMS algorithm) that greatly reduce the computational complexity and improves the convergence rate. Analysis and simulation results prove the effectiveness of our proposed adaptive algorithms.