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

arXiv: https://arxiv.org/abs/1808.00613 · HTML: https://mlsanity.com/paper/1808.00613/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2018.

## Built on by (most cited first, 3 of 3)

- [FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator](https://mlsanity.com/paper/2409.13978/) (2024)
- [Study of Robust Sparsity-Aware RLS algorithms with Jointly-Optimized Parameters for Impulsive Noise Environments](https://mlsanity.com/paper/2204.08990/) (2022)
- [Design and Analysis of Robust Resilient Diffusion over Multi-Task Networks Against Byzantine Attacks](https://mlsanity.com/paper/2206.12749/) (2022)

## Abstract (arXiv)

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.