An adaptive nonlinear digital filter with lattice orthogonalization

A novel approach to nonlinear filtering with minimum mean square error criterion is presented. This method considers the class of nonlinear filters with Volterra series structures under the assumption that filter inputs are Gaussian, and a relatively simple solution results which is directly applicable in many practical situations. Moreover, two simple parameter adaption algorithms for the second order Volterra filter are presented and it is shown that their convergence speeds depend on the squared ratio of maximum to minimum eigenvalues of the input autocovariance matrix. Finally, the lattice orthogonalization of filter input is considered for faster convergence.