Abstract
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.
Similar content being viewed by others
References
Farhang-Boroujeny B.: Adaptive Filters Theory and Applications. Wiely, Chichester (1999)
Treichler J.R., Johnson C.R. Jr, Larimore M.G.: Theory and Design of Adaptive Filters. Prentice Hall, New Delhi (2000)
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)
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)
Dunne B.E., Williamson G.A.: QR based iterative unbiased equation error filtering. Acoust. Speech Signal Process. (In: IEEE ICASSP) 6, 3757–3760 (2001)
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)
Shin H.-C., Song W.-J.: Pole-cancellation error adaptive IIR filtering. IEEE Signal Process. Lett. 10(9), 280–282 (2003)
Okello J. et al.: A new modified variable step-size for the LMS algorithm. IEEE Int. Symp. Circuits Syst. 5, 170–173 (1998)
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 529480
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)
Kuo S.M., Morgan D.R.: Active Noise Control System. Wiley, New York (1996)
Sun X., Meng G.: Steiglitz-Mcbride type adaptive IIR algorithm for active noise control. J. Sound Vib. 273, 441–450 (2004)
Veena S., Narasimhan S.V.: Improved active noise control performance based on Laguerre lattice. Signal Process. 84, 695–707 (2004)
Veena S., Narasimhan S.V.: Laguerre escalator lattice and Feedforward / feedback active noise control. Signal Process. 87(4), 725–738 (2007)
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)
Netto S.L., Agathoklis P.: Efficient lattice based realization of adaptive IIR algorithms. In: IEEE Trans. Signal Process. 46(1), 223–227 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Narasimhan, S.V., Veena, S. New unbiased adaptive IIR filter: it’s robust and variable step-size versions and application to active noise control. SIViP 7, 197–207 (2013). https://doi.org/10.1007/s11760-011-0284-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-011-0284-y