Combined Sparse Regularization for Nonlinear Adaptive Filters

TL;DR

This paper introduces an adaptive combined regularization scheme for nonlinear adaptive filters that leverages multiple regularization norms to improve performance in nonlinear system identification tasks.

Contribution

It proposes a novel block-based combined regularization approach that adaptively integrates two nonlinear filters with different regularizations for enhanced performance.

Findings

Outperforms individual regularization rules in nonlinear system identification

Effectively leverages online combined regularization for better modeling

Demonstrates robustness across various nonlinear scenarios

Abstract

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear filters to leverage sparsity of their coefficients. However, the choice of the norm penalty of the cost function may be not always appropriate depending on the problem. In this paper, we introduce an adaptive combined scheme based on a block-based approach involving two nonlinear filters with different regularization that allows to achieve always superior performance than individual rules. The proposed method is assessed in nonlinear system identification problems, showing its effectiveness in taking advantage of the online combined regularization.