A Quaternion Widely Linear Adaptive Filter

Author

Took, Clive Cheong ; Mandic, Danilo P.

Author_Institution

Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK

Volume

58

Issue

8

fYear

2010

Firstpage

4427

Lastpage

4431

Abstract

A quaternion widely linear (QWL) model for quaternion valued mean-square-error (MSE) estimation is proposed. The augmented statistics are first introduced into the field of quaternions, and it is demonstrated that this allows for capturing the complete second order statistics available. The QWL model is next incorporated into the quaternion least mean-square (QLMS) algorithm to yield the widely linear QLMS (WL-QLMS). This allows for a unified approach to adaptive filtering of both Q-proper and Q-improper signals, leading to improved accuracies compared to the QLMS class of algorithms. Simulations on both benchmark and real world data support the analysis.

Keywords

adaptive filters; higher order statistics; Q-improper signals; Q-proper signals; adaptive filtering; augmented statistics; quaternion valued mean-square-error estimation; quaternion widely linear adaptive filter; quaternion widely linear model; second order statistics; widely linear QLMS; $BBQ$-properness; Wiener model; quadrivariate processes; quaternion LMS (QLMS); quaternion adaptive filtering; quaternion second-order noncircularity; widely linear QLMS; widely linear model;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2010.2048323

Filename

5447699