Adaptive second-order Volterra filtered-X RLS algorithms with sequential and partial updates for nonlinear active noise control

In this paper, we propose adaptive second-order Volterra filtered-X recursive least square (RLS) algorithms using sequential and partial updates for nonlinear active noise control. Recent research advancement has demonstrated that nonlinear active control is feasible for applications where the noise to be controlled may be a nonlinear and deterministic noise process such as chaotic noise rather than a stochastic, or white or tonal noise process, and both primary and secondary paths in an active noise control (ANC) system may exhibit a nonlinear behavior. To accommodate nonlinear active noise control, the standard second-order Volterra filtered-X recursive least square (VFXRLS) or least mean square (VFXLMS) algorithms are usually applied. The second-order VFXRLS algorithm offers fast convergence performance but suffers a huge computational burden. On the other hand, the standard second-order VFXLMS algorithm requires less computational complexity but behaves at a slow convergence rate. The proposed second-order VFXRLS algorithms with sequential and partial updates could significantly reduce the computational complexity required by the standard second-order VFXRLS algorithm with a compromised performance.