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

arXiv: https://arxiv.org/abs/2607.19902 · HTML: https://mlsanity.com/paper/2607.19902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy Input](https://mlsanity.com/paper/1711.08677/) (2017)
- [Online Optimization with Costly and Noisy Measurements using Random Fourier Expansions](https://mlsanity.com/paper/1603.09620/) (2016)
- [A Family of Robust Generalized Adaptive Filters and Application for Time-series Prediction](https://mlsanity.com/paper/2506.00397/) (2025)

## Abstract (arXiv)

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.