Signal, Image and Video Processing

, Volume 7, Issue 1, pp 197–207 | Cite as

New unbiased adaptive IIR filter: it’s robust and variable step-size versions and application to active noise control

  • S. V. NarasimhanEmail author
  • S. Veena
Original Paper


This paper proposes a robust variable step-size adaptive IIR filter realized by a new bias-free structure (BFS). Unlike equation error (EQE) method that uses a desired signal contaminated with observation noise, the BFS employs a filter driven by the output of the plant estimate and this achieves a bias-free estimate of the denominator of the system function. In addition, the adaptation is made robust to the observation noise by the Griffiths’ LMS adaptation, which uses the cross-correlation estimate between the input and the desired signal for its adaptation gradient computation. A robust variable step-size adaptation is also realized by the Griffiths’ gradient. The proposed structure is referred to as BFSGV and has good modeling capability with improved convergence rate and reduced misadjustment. For system identification, the proposed BFSGV algorithm gives a 3 dB improvement in the performance index over EQE method. The proposed BFSGV has been applied to active noise control (ANC). The BSFGV structure is used for secondary path (SP) estimation, and for the main path (MP), BFS structure with step-size varied according to Okello’s method (BSFV) is used. The new ANC system for narrowband noise field is found to be having 4 times faster convergence rate and an additional noise reduction of 15dB over that FIR for MP and the EQE for SP. Further, the use of the proposed ANC IIR algorithm achieves computational savings compared to that of FIR. For the broadband noise field, the proposed method that uses BSFV for MP and BSFGV for SP provides 18 times faster convergence rate and 2.5 dB reduction in ANC error compare to that of the ANC using FIR for MP and the EQE for SP estimation.


Equation error IIR adaptive filters Bias-free equation error IIR adaptive filters Griffiths’ LMS algorithm Robust and variable step-size algorithms Active noise control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Farhang-Boroujeny B.: Adaptive Filters Theory and Applications. Wiely, Chichester (1999)Google Scholar
  2. 2.
    Treichler J.R., Johnson C.R. Jr, Larimore M.G.: Theory and Design of Adaptive Filters. Prentice Hall, New Delhi (2000)Google Scholar
  3. 3.
    Douglas S.C., Rupp M.: On bias removal and unit norm constraints in equation error adaptive IIR adaptive filters. In: IEEE Asilomar Conf. Signals Syst. Comput. 2, 1093–1097 (1996)Google Scholar
  4. 4.
    Kim, H.-N., Song, W.-J.: Unbiased equation-error adaptive IIR filtering based on monic normalization. In: IEEE Signal Process. Lett. 6(2), 35–37 (1999, Feb)Google Scholar
  5. 5.
    Dunne B.E., Williamson G.A.: QR based iterative unbiased equation error filtering. Acoust. Speech Signal Process. (In: IEEE ICASSP) 6, 3757–3760 (2001)Google Scholar
  6. 6.
    Okello, J., Kinugasa, Y., Itoh, Y., Fukui, Y., Kobayashi, M.: A new unbiased equation error algorithm for IIR ADF and its application to ALP. ICASSP (2002)Google Scholar
  7. 7.
    Shin H.-C., Song W.-J.: Pole-cancellation error adaptive IIR filtering. IEEE Signal Process. Lett. 10(9), 280–282 (2003)CrossRefGoogle Scholar
  8. 8.
    Okello J. et al.: A new modified variable step-size for the LMS algorithm. IEEE Int. Symp. Circuits Syst. 5, 170–173 (1998)Google Scholar
  9. 9.
    Zhang, Y., Li, N., Chambers, J.A., Hao, Y.: New gradient based variable step-size LMS algorithms. EURASIP J. Adv. Signal Process. (2008), Article ID 529480Google Scholar
  10. 10.
    Narasimhan, S.V., Veena, S., Lokesha: Variable step-size Griffiths’ algorithm for improved performance of Feedforward/feedback active noise control. Signal Image Video Process. (2009, June)Google Scholar
  11. 11.
    Kuo S.M., Morgan D.R.: Active Noise Control System. Wiley, New York (1996)Google Scholar
  12. 12.
    Sun X., Meng G.: Steiglitz-Mcbride type adaptive IIR algorithm for active noise control. J. Sound Vib. 273, 441–450 (2004)CrossRefGoogle Scholar
  13. 13.
    Veena S., Narasimhan S.V.: Improved active noise control performance based on Laguerre lattice. Signal Process. 84, 695–707 (2004)zbMATHCrossRefGoogle Scholar
  14. 14.
    Veena S., Narasimhan S.V.: Laguerre escalator lattice and Feedforward / feedback active noise control. Signal Process. 87(4), 725–738 (2007)zbMATHCrossRefGoogle Scholar
  15. 15.
    Akhtar, M.T., et al.: A new variable step-size LMS algorithm based method for improved online secondary path modeling in active noise control systems. In: IEEE Trans. Audio Speech Lang. Process. 14(2), 720–726 (2006, March)Google Scholar
  16. 16.
    Netto S.L., Agathoklis P.: Efficient lattice based realization of adaptive IIR algorithms. In: IEEE Trans. Signal Process. 46(1), 223–227 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.National Aerospace Laboratories (Council of Scientific and Industrial Research, New Delhi)BangaloreIndia

Personalised recommendations