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Spline adaptive filtering algorithm based on Heaviside step function

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Abstract

To reduce the interference of impulsive noise when the spline adaptive filter (SAF) algorithm is used to identify nonlinear systems, this paper proposes a family of SAF algorithms using the Heaviside step function (HSF). The suitability of those cost functions proposed are investigated; those cost functions are design based on some HSF’s approximate functions. Then based on that, four SAF algorithms have been developed: SAF-HSF-sigmoid, SAF-HSF-erfc, SAF-HSF-atan, and SAF-HSF-tanh. Also, the bound of the learning rate has been derived for those proposed algorithms. The proposed SAF-HSF algorithms have been evaluated for nonlinear system identification and simulation studies to demonstrate their robustness.

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Acknowledgements

The Fundamental Research Funds supported the National Natural Science Foundation of China (61871420), the Central Universities Southwest Minzu University (2021XJTD01), Natural Science Foundation of Henan Polytechnic University (B2021-38), and the Wuhu and Xidian University special fund for industry-university-research cooperation (XWYCXY-012020014).

Funding

Fundamental Research Funds for the Central Universities, 2021XJTD01, Sihai GUAN, National Natural Science Foundation of China, 61871420, Biswal Bharat, Natural Science Foundation of Henan Polytechnic University, B2021-38, Yong Zhao, the Wuhu and Xidian University special fund for industry-university-research cooperation, XWYCXY-012020014, Yong Zhao

Author information

Authors and Affiliations

  1. College of Electronic and Information, Southwest Minzu University, Chengdu, China

    Sihai Guan

  2. Key Laboratory of Electronic and Information Engineering, State Ethnic Affairs Commission, Beijing, People’s Republic of China

    Sihai Guan

  3. Sichuan Vocational College of Finance and Economics, Chengdu, China

    Qing Cheng

  4. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, China

    Yong Zhao

  5. School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China

    Bharat Biswal

  6. Department of Biomedical Engineering, New Jersey Institute of Technology (NJIT), Newark, NJ, USA

    Bharat Biswal

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  1. Sihai Guan
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  2. Qing Cheng
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  3. Yong Zhao
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  4. Bharat Biswal
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Correspondence to Sihai Guan.

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Guan, S., Cheng, Q., Zhao, Y. et al. Spline adaptive filtering algorithm based on Heaviside step function. SIViP 16, 1333–1343 (2022). https://doi.org/10.1007/s11760-021-02085-z

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  • DOI: https://doi.org/10.1007/s11760-021-02085-z

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