Leaky-FXLMS algorithm: stochastic analysis for Gaussian data and secondary path modeling error

• Published in: IEEE transactions on speech and audio processing Vol. 13; no. 6; pp. 1217 - 1230
• Main Authors: Tobias, O.J., Seara, R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2005; Institute of Electrical and Electronics Engineers
• Subjects: Active noise/vibration control; Adaptive algorithm; Adaptive algorithms; Adaptive filters; Algorithm design and analysis; Algorithms; Applied sciences; Data analysis; Delay estimation; Detection, estimation, filtering, equalization, prediction; Error analysis; Exact sciences and technology; Gaussian; Information, signal and communications theory; leaky filtered-X LMS algorithm; Least squares approximation; LMS algorithm; Mathematical analysis; Mathematical models; Noise robustness; Signal and communications theory; Signal processing algorithms; Signal, noise; Stochastic processes; Stochasticity; Telecommunications and information theory; Vibration control; Weighting filter; Data analysis; Adaptive algorithm; leaky filtered-X LMS algorithm; Adaptive filter; Loudspeaker; Modeling; Implementation; Active noise/vibration control; Stochastic analysis; Accuracy; Theoretical model; Overload; Analytical method; LMS algorithm; Algorithm analysis; Active noise control; Least mean squares methods
• ISSN: 1063-6676
• DOI: 10.1109/TSA.2005.852018

This paper presents a stochastic analysis of the leaky filtered-X least-mean-square (LFXLMS) algorithm. The version with leakage of the adaptive algorithm is used in practical implementations aiming to reduce undesirable effects due to numerical errors in finite-precision machines, overload of the secondary source, among others. Based on new analysis assumptions, instead of the ordinary independence theory frequently used in classical LMS analysis, an analytical model for the first and second moments of the adaptive filter weights has been derived. In addition, the proposed theoretical models consider the situation in which the secondary path is imperfectly modeled. Experimental results demonstrate the accuracy of the proposed model as compared with the classical analysis.