Skip to main content
SpringerLink
Log in

Improved Filtered-x Least Mean Kurtosis Algorithm for Active Noise Control

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The least mean kurtosis (LMK) algorithm has been successfully applied to linear system identification. It outperforms the conventional least mean square method for Gaussian and non-Gaussian noises. The purpose of this work is to apply the LMK algorithm to active noise control (ANC) systems, i.e., to develop a filtered-x LMK (FxLMK) algorithm. The proposed FxLMK algorithm is robust against the attenuation of various noise interferences in ANC system. To further improve the noise reduction performance, a recursive sampled variance method is incorporated into the FxLMK algorithm, resulting in an improved FxLMK (IFxLMK) algorithm without significantly increasing the computational burden. Simulations in the various noise inputs show the effectiveness of the proposed algorithms. Moreover, the traction substation noise control problem is considered in our simulations, and an overall system scheme and simulation studies are conducted. Simulation results demonstrate that the IFxLMK algorithm can improve the convergence rate of adaptive filter and improve the performance of noise reduction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. M.T. Akhtar, W. Mitsuhashi, Variable step-size based online acoustic feedback neutralization in multiple-channel ANC systems, in Proc. 53rd IEEE Int. Midwest Symp. Circuits Syst., pp. 1073–1076 (2010)

  2. M. Bergamasco, F.D. Rossa, L. Piroddi, Active noise control with on-line estimation of non-Gaussian noise characteristics. J. Sound Vib. 331(1), 27–40 (2012). doi:10.1016/j.jsv.2011.08.025

    Article  Google Scholar 

  3. M. Ferrer, A. Gonzalez, M.D. Diego, G. Pinero, Convex combination filtered-x algorithms for active noise control systems. IEEE Trans. Audio Speech Lang. Process. 21(1), 156–167 (2013). doi:10.1109/TASL.2012.2215595

    Article  Google Scholar 

  4. N.V. George, G. Panda, A robust filtered-s LMS algorithm for nonlinear active noise control. Appl. Acoust. 73(8), 836–841 (2012). doi:10.1016/j.apacoust.2012.02.005

    Article  Google Scholar 

  5. B. Huang, Y. Xiao, J. Sun, G. Wei, A variable step-size FXLMS algorithm for narrowband active noise control. IEEE Trans. Audio Speech Lang. Process. 21(2), 301–312 (2013). doi:10.1109/TASL.2012.2223673

    Article  Google Scholar 

  6. J.K. Hwang, Y.P. Li, A gradient-based variable step-size scheme for kurtosis of estimated error. IEEE Signal Process. Lett. 17(4), 331–334 (2010). doi:10.1109/LSP.2010.2040929

    Article  Google Scholar 

  7. N. Kunchakoori, A. Routray, D.P. Das, An energy function based fuzzy variable step size FxLMS algorithm for active noise control, in Proc. IEEE Region 10 and 3rd Int. Conf. Indust. Inf. Syst., pp. 1–7 (2008)

  8. S.M. Kuo, D.R. Morgan, Active Noise Control Systems: Algorithms and DSP Implementations (Wiley, New York, 1996)

    Google Scholar 

  9. Y.H. Lee, J.D. Mok, S.D. Kim, S.H. Cho, Performance of least mean absolute third (LMAT) adaptive algorithm in various noise environments. Electron. Lett. 34(3), 241–242 (1998). doi:10.1049/el:19980181

    Article  Google Scholar 

  10. L. Lu, H. Zhao, Adaptive Volterra filter with continuous lp-norm using a logarithmic cost for nonlinear active noise control. J. Sound Vib. 364, 14–29 (2016). doi:10.1016/j.jsv.2015.11.029

    Article  Google Scholar 

  11. L. Lu, H. Zhao, B. Chen, Improved-variable-forgetting-factor recursive algorithm based on the logarithmic cost for Volterra system identification. IEEE Trans. Circuits Syst. II 63(6), 588–592 (2016). doi:10.1109/TCSII.2016.2531159

    Article  Google Scholar 

  12. A. Papoulis, Random Variables and Stochastic Processes (McGraw Hill Inc, New York, 1965)

    MATH  Google Scholar 

  13. D.I. Pazaitis, A.G. Constantinides, LMS+F algorithm. Electron. Lett. 31(17), 1423–1424 (1995). doi:10.1049/el:19951026

    Article  Google Scholar 

  14. X. Qiu, L. Xun, Y. Ai, C.H. Hansen, A waveform synthesis algorithm for active control of transformer noise: implementation. Appl. Acoust. 63(5), 467–469 (2002). doi:10.1016/S0003-682X(01)00060-3

    Article  Google Scholar 

  15. H. Qu, W. Ma, J. Zhao, B. Chen, Kernel least mean kurtosis based online chaotic time series prediction. Chin. Phys. Lett. 30(11), 1–5 (2013). doi:10.1088/0256-307X/30/11/110505

    Article  Google Scholar 

  16. L. Tan, J. Jiang, Active control of impulsive noise using a nonlinear companding function. Mech. Syst. Signal Process. 58–59, 29–40 (2015). doi:10.1016/j.ymssp.2015.01.010

    Article  Google Scholar 

  17. O. Tanrikulu, A.G. Constantinides, Least-mean kurtosis: a novel higher-order statistics based adaptive filtering algorithm. Electron. Lett. 30(3), 189–190 (1994). doi:10.1049/el:19940129

    Article  Google Scholar 

  18. E. Walach, B. Widrow, The least mean fourth (LMF) adaptive algorithm and its family. IEEE Trans. Inf. Theory 30(2), 275–283 (1984). doi:10.1109/TIT.1984.1056886

    Article  Google Scholar 

  19. L. Wu, X. Qiu, Active impulsive noise control algorithm with post adaptive filter coefficient filtering. IET Signal Process. 7(6), 515–521 (2013). doi:10.1049/iet-spr.2012.0164

    Article  Google Scholar 

  20. L. Wu, H. He, X. Qiu, An active impulsive noise control algorithm with logarithmic transformation. IEEE Trans. Audio Speech Lang. Process. 19(4), 1041–1044 (2011). doi:10.1109/TASL.2010.2061227

    Article  Google Scholar 

  21. L. Zhang, J. Tao, X. Qiu, Active control of transformer noise with an internally synthesized reference signal. J. Sound Vib. 331(15), 3466–3475 (2012). doi:10.1016/j.jsv.2012.03.032

    Article  Google Scholar 

  22. H. Zhao, A practical wavelet domain LMK algorithm for predicting multimedia traffic, in IEEE ICC’08, pp. 515–519 (2008)

  23. H. Zhao, X. Zeng, J. Zhang, Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes. Signal Process. 90(3), 834–847 (2010). doi:10.1016/j.sigpro.2009.09.001

    Article  MATH  Google Scholar 

  24. H. Zhao, X. Zeng, X. Zhang, Z. He, T. Li, W. Jin, Adaptive extended pipelined second-order Volterra filter for nonlinear active noise controller. IEEE Trans. Audio Speech Lang. Process. 20(4), 1394–1399 (2012). doi:10.1109/TASL.2011.2175383

    Article  Google Scholar 

  25. H. Zhao, X. Zeng, Z. He, S. Yu, B. Chen, Improved functional link artificial neural network via convex combination for nonlinear active noise control. Appl. Soft Comput. 42, 351–359 (2016). doi:10.1016/j.asoc.2016.01.051

    Article  Google Scholar 

  26. Y. Zhou, Y. Yin, Q. Zhang, An optimal repetitive control algorithm for periodic impulsive noise attenuation in a non-minimum phase ANC system. Appl. Acoust. 74(10), 1175–1181 (2013). doi:10.1016/j.apacoust.2013.04.008

    Article  Google Scholar 

  27. Y. Zhou, Q. Zhang, Y. Yin, Active control of impulsive noise with symmetric \(\alpha \)-stable distribution based on an improved step-size normalized adaptive algorithm. Mech. Syst. Signal Process. 56–57, 320–339 (2015). doi:10.1016/j.ymssp.2014.10.002

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by National Natural Science Foundation of China (Grants: 61271340, 61571374, 61433011).

Author information

Authors and Affiliations

  1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education and School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China

    Lu Lu & Haiquan Zhao

Authors
  1. Lu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haiquan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haiquan Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, L., Zhao, H. Improved Filtered-x Least Mean Kurtosis Algorithm for Active Noise Control. Circuits Syst Signal Process 36, 1586–1603 (2017). https://doi.org/10.1007/s00034-016-0379-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0379-3

Keywords

Search

Navigation