A universal modified LMS algorithm with iteration order hybrid switching

• Published in: ISA transactions Vol. 67; pp. 67 - 75
• Main Authors: Cheng, Songsong, Wei, Yiheng, Chen, Yuquan, Liang, Shu, Wang, Yong
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.03.2017
• Subjects: Convergence speed; Fractional order calculus; Iteration order; Modified least mean square; Response speed; Switching; 99-00; Iteration order; 00-01; Fractional order calculus; Modified least mean square; Switching; Response speed; Convergence speed
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2016.11.019

This paper presents a fractional order modified least square algorithm(FOMLMS), which involves an iteration order switch strategy. A FOMLMS scheme whose iteration order can be extended into α∈(0,2) is investigated. The performance of FOMLMS with the iteration order in different interval (0<α<1or1<α<2) is separately analyzed. It turns out that, both of a larger iteration order (0<α<2) and iteration step size can always result in a faster response speed and convergence speed. Therefore, in order to obtain a satisfying convergence speed without sacrificing other performance, a hybrid switch law of iteration order is naturally developed. Finally, the validity of this proposed algorithm is illustrated by three numerical examples. •A fractional order modified least square algorithm (FOMLMS) with (0<α<2) is proposed.•The performance of FOMLMS with α in two interval (0<α<1 or 1<α<2) is separately analyzed.•A hybrid switch law of α is developed to obtain a better convergence speed.