A universal modified LMS algorithm with iteration order hybrid switching

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.