Advertisement

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
  • 88 Downloads

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.

Keywords

Kernel risk-sensitive loss Bilinear forms Adaptive filter Impulsive noise 

Notes

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).

References

  1. 1.
    J. Arenas-Garcia, A.R. Figueiras-Vidal, A.H. Sayed, Mean-square performance of a convex combination of two adaptive filters. IEEE Trans. Signal Process. 54(3), 1078–1090 (2006)CrossRefzbMATHGoogle Scholar
  2. 2.
    J. Arenas-Garcia, M. Martinez-Ramon, A. Navia-Vazquez, A.R. Figueiras-Vidal, Plant identification via adaptive combination of transversal filters. Signal Process. 86(9), 2430–2438 (2006)CrossRefzbMATHGoogle Scholar
  3. 3.
    J. Benesty, C. Paleologu, S. Ciochina, On the identification of bilinear forms with the Wiener filter. IEEE Signal Process. Lett. 24(5), 653–657 (2017)CrossRefGoogle Scholar
  4. 4.
    H.K. Baik, V.J. Mathews, Adaptive lattice bilinear filters. IEEE Trans. Signal Process. 41(6), 2033–2046 (1993)CrossRefzbMATHGoogle Scholar
  5. 5.
    B. Chen, L. Xing, B. Xu, H. Zhao, N. Zheng, J.C. Príncipe, Kernel risk-sensitive loss: definition, properties and application to robust adaptive filtering. IEEE Trans. Signal Process. 65(11), 2888–2901 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    B. Chen, L. Xing, H. Zhao, N. Zheng, J.C. Principe, Generalized correntropy for robust adaptive filtering. IEEE Trans. Signal Process. 64(13), 3376–3387 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    B. Chen, L. Xing, J. Liang, N. Zheng, J.C. Principe, Steady-state mean-square error analysis for adaptive filtering under the maximum correntropy criterion. IEEE Signal Process. Lett. 21(7), 880–884 (2014)CrossRefGoogle Scholar
  8. 8.
    B. Chen, J. Wang, H. Zhao, N. Zheng, J.C. Principe, Convergence of a fixed-point algorithm under maximum correntropy criterion. IEEE Signal Process. Lett. 22(10), 1723–1727 (2015)CrossRefGoogle Scholar
  9. 9.
    P.S.R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation, 4th edn. (Springer, New York, 2013)CrossRefzbMATHGoogle Scholar
  10. 10.
    U. Forssen, Adaptive bilinear digital filters. IEEE Trans. Circuits Systems-II: Analog Digit. Signal Process. 40, 729–735 (1993)CrossRefGoogle Scholar
  11. 11.
    M. Ferrer, M.D. Diego, A. Gonzalez, G. Piñero, Convex combination of affine projection algorithms, in Proceedings of 17th European Signal Processing Conference, UK (2009), pp. 431–435Google Scholar
  12. 12.
    R. Hu, H.M. Hassan, Echo cancellation in high speed data transmission systems using adaptive layered bilinear filters. IEEE Trans. Commun. 42(234), 655–663 (1994)Google Scholar
  13. 13.
    S.M. Kuo, H.T. Wu, Nonlinear adaptive bilinear filters for active noise control systems. IEEE Trans. Circuits Syst. I Regul. Pap. 52(3), 617–624 (2005)MathSciNetCrossRefGoogle Scholar
  14. 14.
    T. Koh, E.J. Powers, Second-order Volterra filtering and its application to nonlinear system identification. IEEE Trans. Acoust. Speech Signal Process. ASSP 33(6), 1445–1455 (1985)CrossRefzbMATHGoogle Scholar
  15. 15.
    L.S. Li, V.J. Mathews, Efficient block-adaptive parallel-cascade quadratic filters. IEEE Trans. Circuits Syst. II 46(4), 468–472 (1999)CrossRefGoogle Scholar
  16. 16.
    L. Lu, H. Zhao, A novel convex combination of LMS adaptive filter for system identification, in 2014 12th International Conference on Signal Processing (ICSP), (China, Hangzhou, 2014), pp. 225–229Google Scholar
  17. 17.
    L. Lu, H. Zhao, B. Champagne, Distributed nonlinear system identification in α -stable noise. IEEE Signal Process. Lett. 25(7), 979–983 (2018)CrossRefGoogle Scholar
  18. 18.
    L. Lu, H. Zhao, Adaptive combination of affine projection sign subband adaptive filters for modeling of acoustic paths in impulsive noise environments. Int. J. Speech Technol. 19(4), 907–917 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    L. Lu, H. Zhao, B. Chen, Collaborative adaptive Volterra filters for nonlinear system identification in α-stable noise environments. J. Frankl. Inst. 353(17), 4500–4525 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    W. Liu, P.P. Pokharel, J.C. Principe, Correntropy: properties and applications in non-gaussian signal processing. IEEE Trans. Signal Process. 55(11), 5286–5298 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    G.-K. Ma, J. Lee, V. J. Mathews, A RLS bilinear filter for channel equalization, in Proceedings of IEEE ICASSP, (1994), pp. 257–260Google Scholar
  22. 22.
    S. Marsi, G.L. Sicuranza, On reduced-complexity approximation of quadratic filters, in Proceedings of 27th Asilomar Conference Signals, Systems, Computers, Pacific Grove, (CA, 1993), pp. 1026–1030Google Scholar
  23. 23.
    V.J. Mathews, G.L. Sicuranza, Polynomial Signal Processing (Wiley, Hoboken, 2000)Google Scholar
  24. 24.
    V.J. Mathews, Adaptive polynomial filters. IEEE Signal Process. Mag. 8(3), 10–26 (1991)CrossRefGoogle Scholar
  25. 25.
    V. H. Nascimento, R. C. de Lamare, A low-complexity strategy for speeding up the convergence of convex combinations of adaptive filters, in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (Kyoto, Japan, 2012), pp. 3553–3556Google Scholar
  26. 26.
    A. Navia-Vazquez, J. Arenas-Garcia, Combination of recursive least p-norm algorithms for robust adaptive filtering in alpha-stable noise. IEEE Trans. Signal Process. 60(3), 1478–1482 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    T.M. Panicker, V. John, Mathews, Parallel-cascade realizations and approximations of truncated Volterra systems. IEEE Trans. Signal Process. 46(10), 2829–2832 (1998)CrossRefGoogle Scholar
  28. 28.
    C. Paleologu, J. Benesty, S. Ciochina, An NLMS algorithm for the identification of bilinear forms, in Proceedings of EUSIPCO, (2017), pp. 2620–2624Google Scholar
  29. 29.
    C. Paleologu, S. Ciochina, J. Benesty, Analysis of an LMS algorithm for bilinear forms, in Digital Signal Processing (DSP), 2017 22nd International Conference on. IEEE, (2017), pp. 1–5Google Scholar
  30. 30.
    M.T.M. Silva, V.H. Nascimento, Improving the tracking capability of adaptive filters via convex combination. IEEE Trans. Signal Process. 56(7), 3137–3149 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    A. Singh, J. C. Principe, Using correntropy as a cost function in linear adaptive filters, in Proceedings of IEEE 2009 International Joint Conference Neural Network, (2009), pp. 2950–2955Google Scholar
  32. 32.
    L. Shi, Y. Lin, Convex combination of adaptive filters under the maximum correntropy criterion in impulsive interference. IEEE Signal Process. Lett. 21(11), 1385–1388 (2014)CrossRefGoogle Scholar
  33. 33.
    G. Sicuranza, Quadratic filters for signal processing. Proc. IEEE 80(8), 1263–1285 (1992)CrossRefGoogle Scholar
  34. 34.
    M. Schetzen, Nonlinear system modeling based on the Wiener theory. Proc. IEEE 69(12), 1557–1573 (1981)CrossRefGoogle Scholar
  35. 35.
    M. Schetzen, Volterra and Wiener Theory of the Nonlinear Systems (Wiley, New York, 1980)zbMATHGoogle Scholar
  36. 36.
    L. Tan, J. Jiang, Nonlinear active noise control using diagonalchannel LMS and RLS bilinear filters, in Proceedings of IEEE MWSCAS, (2014), pp. 789–792Google Scholar
  37. 37.
    B. Weng, K.E. Barner, Nonlinear system identification in impulsive environments. IEEE Trans. Signal Process. 53(7), 2588–2594 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    W. Wang, H. Zhao, B. Chen, Robust adaptive Volterra filter under maximum correntropy criteria in impulsive environments. Circuits Syst. Signal Process. 36(10), 4097–4117 (2017)CrossRefzbMATHGoogle Scholar
  39. 39.
    W. Wang, H. Zhao, Performance analysis of diffusion least mean fourth algorithm over network. Signal Process. 141, 32–47 (2017)CrossRefGoogle Scholar
  40. 40.
    S. Zhao, B. Chen, J. C. Principe, Kernel adaptive filtering with maximum correntropy criterion, in Proceedings of IEEE International Joint Conference on Neural Network, (2011), pp. 2012–2017Google Scholar
  41. 41.
    Y. Yu, H. Zhao, Adaptive combination of proportionate NSAF with the tap-weights feedback for Acoustic echo cancellation. Wireless Pers. Commun. 92(2), 467–481 (2017)CrossRefGoogle Scholar
  42. 42.
    Y. Yu, H. Zhao, Novel combination schemes of individual weighting factors sign subband adaptive filter algorithm. Int. J. Adapt. Contr. Signal Process. 31(8), 1193–1204 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    H. Zhao, X. Zeng, Z. He, T. Li, W. Jin, Nonlinear adaptive filter-based simplified bilinear model for multichannel active control of nonlinear noise processes. Appl. Acoust. 74(12), 1414–1421 (2013)CrossRefGoogle Scholar

Copyright information

© 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

Personalised recommendations