Circuits, Systems, and Signal Processing

, Volume 38, Issue 12, pp 5651–5664 | Cite as

Robust Adaptive Filter Algorithms Against Impulsive Noise

  • Jae Jin JeongEmail author
  • SeungHun Kim


This paper proposes a prefiltered observation-based adaptive filter algorithm that is robust against impulsive noise. Previous impulsive noise rejection algorithms were based on output error stochastic, so there was a trade-off relationship between impulsive noise detection and tracking performances. The proposed rejection algorithm is derived by using the statistics of the observed signal and the inequality such as the Schwarz and Young inequality in the absence of impulsive noise. From this, the proposed algorithm updates the weight vector only when the observed signal is not corrupted by impulsive noise. The proposed algorithm achieves the good tracking performance because it distinguishes between the system change and interruption of impulsive noise. In addition, the proposed algorithm has same performance without impulsive noise, compared with the normalized least-mean-square-type algorithm. Further, the proposed rejection algorithm could expand to various adaptive filtering structures, which suffer the performance degradation with impulsive noise, because it is easy to implement. Hence, the proposed algorithm is combined with the NLMS algorithm for dispersive systems and the proportionate NLMS algorithm for sparse systems. Simulation results show that the proposed algorithm achieves fast convergence rate, good tracking performance, and robustness under the impulsive noise environment.


Outliers NLMS Sparse systems PNLMS 



  1. 1.
    O. Arikan, A. Enis Cetin, E. Erzin, Adaptive filtering for non-gaussian stable processes. IEEE Signal Process. Lett. 1(11), 163–165 (1994)CrossRefGoogle Scholar
  2. 2.
    J. Benesty, H. Rey, L. Rey Vega, S. Tressens, A nonparametric VSS NLMS algorithm. IEEE Signal Process. Lett. 13(10), 581–584 (2006)CrossRefGoogle Scholar
  3. 3.
    M.Z.A. Bhotto, A. Antoniou, Robust quasi-Newton adaptive filtering algorithms. IEEE Trans. Circuits Syst. II Express Briefs 58(8), 537–541 (2011)CrossRefGoogle Scholar
  4. 4.
    J. Chambers, A. Avlonitis, A robust mixed-norm adaptive filter algorithm. IEEE Signal Process. Lett. 4(2), 46–48 (1997)CrossRefGoogle Scholar
  5. 5.
    Y. Chen, Y. Gu, A.O. Hero, Sparse LMS for system identification. IEEE Int. Conf. Acoust. Speech Signal Process. 3125–3128 (2009)Google Scholar
  6. 6.
    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
  7. 7.
    Y. Chien, J. Li-You, Convex combined adaptive filtering algorithm for acoustic echo cancellation in hostile environments. IEEE Access. 6, 16138–16148 (2018)CrossRefGoogle Scholar
  8. 8.
    S. Ciochină, C. Paleologu, J. Benesty, An optimized NLMS algorithm for system identification. J. Signal Process. 118, 115–121 (2016)CrossRefGoogle Scholar
  9. 9.
    Y. Gu, J. Jin, S. Mei, \( l\_ \{0\}\) norm constraint LMS algorithm for sparse system identification. IEEE Signal Process. 16(9), 774–777 (2009)Google Scholar
  10. 10.
    S.S. Haykin, Adaptive filter theory (Pearson Education India, Bengaluru, 2008)zbMATHGoogle Scholar
  11. 11.
    S. Jo, S.W. Kim, Consistent normalized least mean square filtering with noisy data matrix. IEEE Trans. Signal Process. 53(6), 2112–2123 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    S.H. Kim, G. Koo, J.J. Jeong, S.W. Kim, An adjusting-block based convex combination algorithm for identifying block-sparse system. Signal Process. 143, 1–6 (2018)CrossRefGoogle Scholar
  13. 13.
    K.A. Lee, W.S. Gan, S.M. Kuo, Subband adaptive filtering: theory and implementation (Wiley, Hoboken, 2009)CrossRefGoogle Scholar
  14. 14.
    C. Paleologu, J. Benesty, S. Ciochină, An improved proportionate NLMS algorithms based on the \(l_0\) norm. IEEE international conference on acoustics, speech and signal processing (ICASSP), (2010), pp. 309–312Google Scholar
  15. 15.
    A.H. Sayed, Fundamentals of adaptive filtering (Wiley, Hoboken, 2003)Google Scholar
  16. 16.
    M. Sayin, N. Vanli, S. Kozat, A novel family of adaptive filtering algorithms based on the logarithmic cost. IEEE Trans. Signal Process. 62(17), 4411–4424 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    G. Strang, Linear algebra and its applications (Cengage learning, Boston, 2006)zbMATHGoogle Scholar
  18. 18.
    A.I. Sulyman, A. Zerguine, Convergence and steady-state analysis of a variable step-size NLMS algorithm. Signal Process. 83, 1255–1273 (2003)CrossRefGoogle Scholar
  19. 19.
    Y. Taso, H. Chu, S. Fang, J. Lee, C. Lin, Adaptive noise cancellation using deep cerebellar model articulation controller. IEEE Access. 6, 37395–37402 (2018)CrossRefGoogle Scholar
  20. 20.
    N.V. Thakor, Y.S. Zhu, Applications of adaptive filtering to ecg analysis: noise cancellation and arrhythmia detection. IEEE Trans. Biomed. Eng. 38(8), 785–794 (1991)CrossRefGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    Z. Yang, Y.R. Zheng, S.L. Grant, Proportionate affine projection sign algorithms for network echo cancellation. IEEE Trans. Audio Speech Lang. Process. 19(8), 2273–2284 (2011)CrossRefGoogle Scholar
  23. 23.
    A. Zemouche, A. Alessandri, A new LMI condition for decentralized observer-based control of linear systems with nonlinear interconnections. IEEE conference on decision and control, (2014), pp. 3125–3130Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.1st C4ISR Systems Team, C4ISR Systems CenterDefense Agency for Technology and Quality (DTaQ)DaeguKorea
  2. 2.Electrical EngineeringPohang University of Science and Technology (POSTECH)GyeongbukKorea

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