A Novel Generalization of Modified LMS Algorithm to Fractional Order

In this letter, the modified least mean squares (MLMS) algorithm proposed by Kretschmer is generalized to fractional order α (0 <; α ≤ 1 ). Such generalization is achieved by replacing the first order difference of the weight updating equation with a fractional one. The convergence speed, weight...

Full description

Saved in:
Bibliographic Details
Published inIEEE signal processing letters Vol. 22; no. 9; pp. 1244 - 1248
Main Authors Tan, Yun, He, Zhiqiang, Tian, Baoyu
Format Journal Article
LanguageEnglish
Published IEEE 01.09.2015
Subjects
Calculus
Convergence
Discrete Mittag-Leffler function
Equations
fractional difference
fractional order integrator
Indexes
Least squares approximations
LMS
Noise
Signal processing algorithms
Online AccessGet full text
ISSN1070-9908
1558-2361
DOI10.1109/LSP.2015.2394301

Cover

More Information
Summary:In this letter, the modified least mean squares (MLMS) algorithm proposed by Kretschmer is generalized to fractional order α (0 <; α ≤ 1 ). Such generalization is achieved by replacing the first order difference of the weight updating equation with a fractional one. The convergence speed, weight noise and implementation issue of the generalized MLMS (GMLMS) algorithm are examined. It is shown that for smaller step size, the fractional order α functions the same as the step size, which means that a smaller α will give smaller weight noise while a bigger α will give faster convergence speed.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2015.2394301