Recursive Geman-McClure method for implementing second-order Volterra filter

TL;DR

This paper introduces a recursive second-order Volterra filter using the Geman-McClure estimator, enhancing robustness and stability in nonlinear system modeling under various noise conditions.

Contribution

It proposes a novel adaptive recursive SOV filter based on the Geman-McClure estimator, with detailed stability analysis and improved performance over existing methods.

Findings

Demonstrates stability of the proposed algorithm

Shows improved performance in Gaussian noise

Achieves robustness in impulsive noise environments

Abstract

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.