A Stable Total Least Square Adaptive Algorithm for the Nonlinear Volterra Filter

Aiming at the nonlinear filtering problem that exists when the input and output observation data are both corrupted by noises, a stable total least square adaptive algorithm for the nonlinear Volterra filter is proposed in this paper. Taking the minimum Rayleigh Quotient of the augmented Volterra weight vectors and a constraint to the last element of the augmented Volterra weight vectors via a Lagrange multiplier as the overall cost function, the recursive formula of the Volterra weight vector is derived. The stability property of the algorithm is analyzed and the step-size parameter to guarantee the stability of the algorithm is educed. The proposed algorithm is implemented without requiring normalization. The simulation results have shown that, in addition to the fine convergence, the robust anti-noise performance and the stable convergence precision of the proposed algorithm are remarkably higher than other total least square algorithms for the nonlinear system.