About QLMS Derivations

Author

Barthelemy, Quentin ; Larue, A. ; Mars, Jerome I.

Author_Institution

Data Anal. Tools Lab., CEA, Gif-sur-Yvette, France

Volume

21

Issue

2

fYear

2014

fDate

Feb. 2014

Firstpage

240

Lastpage

243

Abstract

In this letter, a review of the quaternionic least mean squares (QLMS) algorithm is proposed. Three versions coming from three derivation ways exist: the original QLMS [1] based on componentwise gradients, HR-QLMS [2] based on a quaternion gradient operator and iQLMS [3] based on an involutions-gradient. Noting and investigating the differences between the three QLMS formulations, we show that the original QLMS suffers from a mistake in the derivation calculus. Thus, we propose to derive rigorously the criterion following the first way, giving the correct version of QLMS. A comparison with the other QLMS versions validates these results on simulated data.

Keywords

gradient methods; least mean squares methods; signal processing; HR-QLMS; componentwise gradients; derivation calculus; iQLMS; involutions-gradient; quaternion gradient operator; quaternionic least mean squares algorithm; signal processing; Calculus; Least squares approximations; Mars; Quaternions; Signal processing; Signal processing algorithms; Vectors; Adaptive filtering; QLMS; quaternionic signal processing;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2014.2299066

Filename

6705599