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Robust Nonlinear Adaptive Filter Based on Kernel Risk-Sensitive Loss for Bilinear Forms

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Abstract

In this paper, a robust adaptive filter based on kernel risk-sensitive loss for bilinear forms is proposed. The proposed algorithm, called minimum kernel risk-sensitive loss bilinear form (MKRSL-BF), is derived by minimizing the cost function based on the minimum kernel risk-sensitive loss (MKRSL) criterion. The proposed algorithm can obtain the excellent performance when the system is corrupted by the impulsive noise. In addition, to further improve the performance of the MKRSL-BF algorithm, the novel algorithm based on the convex scheme is proposed, which can suppress the confliction between the fast convergence rate and the low steady-state error. Finally, simulations are carried out to verify the advantages of the proposed algorithms.

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Notes

  1. For any matrices \( \left\{ {{\mathbf{A}},{\mathbf{B}},{\mathbf{C}}} \right\} \) of compatible dimensions, the Kronecker product has the properties

    \( {\text{vec}}\left( {{\mathbf{ABC}}} \right) = \left( {{\mathbf{B}}^{T} \otimes {\mathbf{A}}} \right){\text{vec}}\left( {\mathbf{C}} \right) \),

    \( {\text{tr}}\left( {{\mathbf{BA}}} \right) = {\text{tr}}\left( {{\mathbf{AB}}} \right) = \left( {{\text{vec(}}{\mathbf{A}}^{T} )} \right)^{T} {\text{vec(}}{\mathbf{B}} )n \).

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Acknowledgements

This work was partially supported by the Doctoral Innovation Fund Program of Southwest Jiaotong University (Grant: D-CX201715) and the National Science Foundation of P.R. China (Grant: 61271340, 61571374 and 61433011).

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Authors and Affiliations

  1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, Chengdu, China

    Wenyuan Wang & Haiquan Zhao

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Wenyuan Wang & Haiquan Zhao

  3. College of Electronics and Information Engineering, Sichuan University, Chengdu, 610065, China

    Lu Lu

  4. School of Information Engineering, Southwest University of Science and Technology, Mianyang, 621010, China

    Yi Yu

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  1. Wenyuan Wang
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Correspondence to Haiquan Zhao.

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Wang, W., Zhao, H., Lu, L. et al. Robust Nonlinear Adaptive Filter Based on Kernel Risk-Sensitive Loss for Bilinear Forms. Circuits Syst Signal Process 38, 1876–1888 (2019). https://doi.org/10.1007/s00034-018-0928-z

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  • DOI: https://doi.org/10.1007/s00034-018-0928-z

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