Stochastic modelling and analysis of filtered-x least-mean-square adaptation algorithm

• Published in: IET signal processing Vol. 7; no. 6; pp. 486 - 496
• Main Authors: Ardekani, Iman Tabatabaei, Abdulla, Waleed H
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.08.2013; The Institution of Engineering & Technology
• Subjects: Adaptation; adaptation process; adaptive control; Adaptive control systems; Algorithms; closed‐form mathematical expressions; computer simulations; Exact solutions; filtered‐x least‐mean‐square adaptation algorithm; FxLMS adaptation process; FxLMS algorithm; Learning; least mean squares methods; Mathematical analysis; Mathematical models; physical plant; real‐time control setup; Special Issue on Active Noise Control: Theory, Review, and Applications; stability; stability condition; steady‐state performance; stochastic modelling; stochastic processes; Stochasticity; FxLMS algorithm; least mean squares methods; stochastic modelling; adaptive control; adaptation process; computer simulations; adaptive control systems; FxLMS adaptation process; stability condition; filtered-x least-mean-square adaptation algorithm; physical plant; closed-form mathematical expressions; real-time control setup; steady-state performance; stochastic processes; stability
• ISSN: 1751-9675; 1751-9683; 1751-9683
• DOI: 10.1049/iet-spr.2012.0090

This study represents a stochastic model for the adaptation process performed on adaptive control systems by the filtered-x least-mean-square (FxLMS) algorithm. The main distinction of this model is that it is derived without using conventional simplifying assumptions regarding the physical plant to be controlled. This model is then used to derive a set of closed-form mathematical expressions for formulating steady-state performance, stability condition and learning rate of the FxLMS adaptation process. These expressions are the most general expressions, which have been proposed so far. It is shown that some previously derived expressions can be obtained from the proposed expressions as special and simplified cases. In addition to computer simulations, different experiments with a real-time control setup confirm the validity of the theoretical findings.