Recursive Geman-McClure method for implementing second-order Volterra filter
For nonlinear system modeling, this work offers a robust adaptive filtering algorithm that handles impulsive noise better than prior methods, though it is an incremental improvement.
The paper proposes a recursive Geman-McClure algorithm for second-order Volterra filters, achieving improved performance over existing methods in Gaussian and impulsive noise environments, with analytical stability proofs.
The second-order Volterra (SOV) filter is a powerful tool for modeling the nonlinear system. The Geman-McClure estimator, whose loss function is non-convex and has been proven to be a robust and efficient optimization criterion for learning system. In this paper, we present a SOV filter, named SOV recursive Geman-McClure, which is an adaptive recursive Volterra algorithm based on the Geman-McClure estimator. The mean stability and mean-square stability (steady-state excess mean square error (EMSE)) of the proposed algorithm is analyzed in detail. Simulation results support the analytical findings and show the improved performance of the proposed new SOV filter as compared with existing algorithms in both Gaussian and impulsive noise environments.