Nonlinear Bias-Compensated Adaptive Filter and Its Application for Time-Series Prediction

2026-07-22

AI Summary

This work addresses the limitations of existing nonlinear adaptive filtering algorithms, which often neglect input noise and exhibit insufficient robustness under non-Gaussian output noise. To overcome these issues, the paper proposes the RFFBCGA algorithm, which synergistically integrates random Fourier features, a bias-compensation mechanism, and a generalized adaptive function within a fixed network architecture. This integration effectively mitigates the adverse effects of input noise while enhancing signal representation capability. By transcending the constraints of conventional fixed dictionaries, the method significantly improves robustness against both input perturbations and non-Gaussian output noise. Experimental results demonstrate that RFFBCGA consistently achieves superior performance, stability, and adaptability across a range of simulated and real-world time series prediction tasks.

Abstract

Most existing nonlinear adaptive filtering algorithms only account for output noise, neglecting the fact that input noise is also prevalent in practice. Although the recently proposed bias-compensated kernel least mean square (BCKLMS) algorithm addresses input noise in the nonlinear errors-in-variables (EIV) model, it still suffers from two major limitations. First, the use of a fixed-size dictionary restricts network growth but also prevents it from fully capturing the characteristics of the input signal. Second, as an least mean square (LMS) based algorithm, it exhibits poor robustness in the presence of non-Gaussian noise in the output signal. To overcome these issues, this paper proposes the random Fourier bias-compensated filter under general adaptive function (RFFBCGA) algorithm. Within the random Fourier feature based bias-compensated (RFFBC) framework, the proposed algorithm not only maintains a fixed network structure and effectively mitigates input noise interference through the BC term, but also achieves improved characterization of the input signal. Moreover, by leveraging the flexible form of the general adaptive (GA) function, the algorithm's robustness across various noise scenarios is further enhanced. Extensive simulations, including real-world time series prediction tasks, demonstrate the superiority of the proposed method.

Problem

• nonlinear adaptive filtering
• input noise
• errors-in-variables model
• non-Gaussian noise
• robustness

Innovation

• bias-compensated adaptive filtering
• random Fourier features
• general adaptive function
• nonlinear time-series prediction
• errors-in-variables model