Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1876–1888 | Cite as

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

  • Wenyuan Wang
  • Haiquan ZhaoEmail author
  • Lu Lu
  • Yi Yu
Short Paper


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.


Kernel risk-sensitive loss Bilinear forms Adaptive filter Impulsive noise 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Magnetic Suspension Technology and Maglev VehicleMinistry of EducationChengduChina
  2. 2.School of Electrical EngineeringSouthwest Jiaotong UniversityChengduChina
  3. 3.College of Electronics and Information EngineeringSichuan UniversityChengduChina
  4. 4.School of Information EngineeringSouthwest University of Science and TechnologyMianyangChina

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