Second-order Volterra filtering and its application to nonlinear system identification

Some recent results on the design and implementation of second-order Volterra filters are presented. The (second-order) Volterra filter is a nonlinear filter with the filter structure of (second-order) Volterra series. A simple minimum mean-square error solution for the Volterra filter is derived, based on the assumption that the filter input is Gaussian. Also, we propose an iterative factorization technique to design a subclass of the Volterra filters, which can alleviate the complexity of the filtering operations considerably. Furthermore, an adaptive algorithm for the Volterra filter is investigated along with its mean convergence and asymptotic excess mean-square error. Finally, the utility of the Volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves.