LATTICE ALGORITHMS FOR RECURSIVE LEAST-SQUARES ADAPTIVE 2ND-ORDER VOLTERRA FILTERING

This paper presents two computationally efficient recursive least-squa res (RLS) lattice algorithms for adaptive nonlinear filtering based on a truncated second-order Volterra system model. The lattice formulati on transforms the nonlinear filtering problem into an equivalent multi channel, linear filtering problem and then generalizes the lattice sol ution to the nonlinear filtering problem. One of the algorithms is a d irect extension of the conventional RLS lattice adaptive linear filter ing algorithm to the nonlinear case. The other algorithm is based on t he QR decomposition of the prediction error covariance matrices using orthogonal transformations. Several experiments demonstrating and comp aring the properties of the two algorithms in finite and ''infinite'' precision environments are included in the paper. The results indicate that both the algorithms retain the fast convergence behavior of the RLS Volterra filters and are numerically stable.