A Family of Robust Generalized Adaptive Filters and Application for Time-series Prediction

TL;DR

This paper introduces a robust generalized adaptive filter (RGA-AF) that adapts smoothly to changing noise environments, enhancing performance in diverse scenarios, and extends the framework to address asymmetric noise and nonlinear filtering.

Contribution

The paper proposes a novel RGA-AF framework with flexible cost functions, along with variants for asymmetric noise and nonlinear filtering, improving adaptability and robustness over existing adaptive filters.

Findings

Simulations show superior performance in linear system identification.

Effective in time-series prediction under varying noise conditions.

Addresses asymmetric noise and nonlinear filtering challenges.

Abstract

The continuous development of new adaptive filters (AFs) based on novel cost functions (CFs) is driven by the demands of various application scenarios and noise environments. However, these algorithms typically demonstrate optimal performance only in specific conditions. In the event of the noise change, the performance of these AFs often declines, rendering simple parameter adjustments ineffective. Instead, a modification of the CF is necessary. To address this issue, the robust generalized adaptive AF (RGA-AF) with strong adaptability and flexibility is proposed in this paper. The flexibility of the RGA-AF's CF allows for smooth adaptation to varying noise environments through parameter adjustments, ensuring optimal filtering performance in diverse scenarios. Moreover, we introduce several fundamental properties of negative RGA (NRGA) entropy and present the negative asymmetric RGA-AF (NAR-GA-AF) and kernel recursive NRGA-AF (KRNRGA-AF). These AFs address asymmetric noise distribution and nonlinear filtering issues, respectively. Simulations of linear system identification and time-series prediction for Chua's circuit under different noise environments demonstrate the superiority of the proposed algorithms in comparison to existing techniques.