Steiglitz-McBride adaptive notch filter based on a variable-step-size LMS algorithm and its application to active noise control

This paper proposes a new Steiglitz–McBride (SM) adaptive notch filter (SM-ANF) based on a robust variable-step-size least-mean-square algorithm and its application to active noise control (ANC). The proposed SM-ANF not only has fast convergence but also has small misadjustment. The variable-step-size algorithm uses the sum of the squared cross correlation between the error signal and the delayed inputs corresponding to the adaptive weights. The cross correlation provides robustness to the broadband signal, which plays the role of noise. The proposed SM-ANF is computationally simpler than the existing Newton/recursive least-squares-type ANF. The frequency response of the new SM-ANF has a notch depth of about −25 dB (for each of the three frequencies considered) and has spectral flatness within 5 dB (peak to peak). This robust notch filter algorithm is used as an observation noise canceller for the secondary path estimation of an ANC system based on the SM method. The ANC with proposed SM-ANF provides not only faster convergence but also an 11-dB improvement in noise attenuation over the SM-based ANC without such a SM-ANF. Copyright © 2015 John Wiley & Sons, Ltd.