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The widely linear quaternion recursive total least squares


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Article

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Authors

Thanthawaritthisai, Thiannithi 
Tobar, Felipe 
Constantinides, Anthony G 
Mandic, Danilo P 

Abstract

A widely linear quaternion recursive total least squares (WLQRTLS) algorithm is introduced for the processing of Q- improper processes contaminated by noise. The total least squares for quaternions (QTLS) is a generalisation of the real-valued total least squares and is introduced rigorously, starting from the existence condition for low-rank approximation of quaternion matrices. Then, a quaternion Rayleigh quotient (QRQ) is defined to establish the link between the QTLS solution and the minimisation of the QRQ. Finally, the rank-one update formula is employed to allow for fast iterative solution based on the QRQ. Through simulations, the WL-QRTLS was shown to exhibit superior performance, under perturbations on both input and output signals, to other adaptive filtering of the same class - the widely linear quaternion least mean squares (WL-QLMS) and the widely linear quaternion recursive least squares (WL-QRLS). The experiments on both synthetic and real-world Q-improper processes supported the analysis.

Description

This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICASSP.2015.7178593

Keywords

widely linear QRTLS, total least squares, Rayleigh quotient, low-rank approximation, quaternions

Journal Title

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Publisher

IEEE