Lattice algorithms for recursive least squares adaptivesecond-order Volterra filtering

摘要

This paper presents two computationally efficient recursivenleast-squares (RLS) lattice algorithms for adaptive nonlinear filteringnbased on a truncated second-order Volterra system model. The latticenformulation transforms the nonlinear filtering problem into annequivalent multichannel, linear filtering problem and then generalizesnthe lattice solution to the nonlinear filtering problem. One of thenalgorithms is a direct extension of the conventional RLS latticenadaptive linear filtering algorithm to the nonlinear case. The othernalgorithm is based on the QR decomposition of the prediction errorncovariance matrices using orthogonal transformations. Severalnexperiments demonstrating and comparing the properties of the twonalgorithms in finite and “infinite” precision environmentsnare included in the paper. The results indicate that both the algorithmsnretain the fast convergence behavior of the RLS Volterra filters and arennumerically stable