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Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

Xiang, Min, Cheong Took, Clive and Mandic, Danilo P. (2016) Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing Signal Processing, 136. pp. 81-91.

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Abstract

Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper and improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the use of augmented variables and statistics. To reduce the computation cost while maintaining the performance level, we propose a four-channel estimation framework as an efficient alternative to quaternion widely linear estimation. This is achieved by using four linear models to estimate the four components of quaternion signals. We also show that any of the four channels is able to replace a strictly linear quaternion estimator when estimating strictly linear systems. The proposed method is shown to reduce computational complexity and provide more flexible algorithms, while preserving the physical meaning inherent in the quaternion domain. The proposed framework is next applied to quaternion minimum mean square error estimation to yield the reduced-complexity versions of the quaternion least mean square (QLMS), quaternion recursive least squares (QRLS), and quaternion nonlinear gradient decent (QNGD) algorithms. For the proposed QLMS algorithm, an adaptive step-size strategy is also explored. The effectiveness of the so introduced estimation techniques is validated by simulations on synthetic and real-world signals.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Xiang, MinUNSPECIFIEDUNSPECIFIED
Cheong Took, CliveUNSPECIFIEDUNSPECIFIED
Mandic, Danilo P.UNSPECIFIEDUNSPECIFIED
Date : 14 October 2016
Identification Number : 10.1016/j.sigpro.2016.10.007
Copyright Disclaimer : © 2016 Elsevier B.V. All rights reserved.
Uncontrolled Keywords : Quaternion filter; Mean square error; Widely linear estimation; Four-channel model; Computational complexity
Depositing User : Clive Harris
Date Deposited : 01 Sep 2017 08:10
Last Modified : 01 Sep 2017 08:10
URI: http://epubs.surrey.ac.uk/id/eprint/842097

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