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This paper introduces the random Fourier bias-compensated filter under general adaptive function (RFFBCGA) algorithm, which addresses the limitations of existing nonlinear adaptive filtering methods by effectively mitigating input noise and enhancing signal characterization. The RFFBCGA algorithm maintains a fixed network structure while improving robustness against non-Gaussian output noise, outperforming traditional bias-compensated kernel least mean square (BCKLMS) approaches. Extensive simulations on real-world time series prediction tasks validate the superiority of the proposed method in handling complex noise scenarios.
A novel filtering algorithm that not only combats input noise but also adapts flexibly to various output noise conditions, significantly enhancing time-series prediction accuracy.
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.