Imperial College London
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ProfessorDaniloMandic

Faculty of Engineering, Department of Electrical and Electronic Engineering

Professor of Machine Intelligence
 
 
 
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Contact

 

+44 (0)20 7594 6271d.mandic Website

 
 
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Assistant

 

Miss Vanessa Rodriguez-Gonzalez +44 (0)20 7594 6267

 
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Location

 

813Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Xiang:2017:10.1109/TSP.2017.2787102,
author = {Xiang, M and Kanna, S and Mandic, DP},
doi = {10.1109/TSP.2017.2787102},
journal = {IEEE Transactions on Signal Processing},
pages = {1566--1579},
title = {Performance analysis of quaternion-valued adaptive filters in nonstationary environments},
url = {http://dx.doi.org/10.1109/TSP.2017.2787102},
volume = {66},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Quaternion adaptive filters have been widely used for the processing of three-dimensional (3-D) and 4-D phenomena, but complete analysis of their performance is still lacking, partly due to the cumbersomeness of multivariate quaternion analysis. This causes difficulties in both understanding their behavior and designing optimal filters. Based on a thorough exploration of the augmented statistics of quaternion random vectors, this paper extends an analysis framework for real-valued adaptive filters to the mean and mean square convergence analyses of general quaternion adaptive filters in nonstationary environments. The extension is nontrivial, considering the noncommutative quaternion algebra, only recently resolved issues with quaternion gradient, and the multidimensional augmented quaternion statistics. Also, for rigor, in order to model a nonstationary environment, the system weights are assumed to vary according to a first-order random-walk model. Transient and steady-state performance of a general class of quaternion adaptive filters is provided by exploiting the augmented quaternion statistics. An innovative quaternion decorrelation technique allows us to develop intuitive closed-form expressions for the performance of quaternion least mean square (QLMS) filters with Gaussian inputs, which provide new insights into the relationship between the filter behavior and the complete second-order statistics of the input signal, that is, quaternion noncircularity. The closed-form expressions for the performance of strictly linear, semiwidely linear, and widely linear QLMS filters are investigated in detail, while numerical simulations for the three classes of QLMS filters with correlated Gaussian inputs support the theoretical analysis.
AU  - Xiang,M
AU  - Kanna,S
AU  - Mandic,DP
DO  - 10.1109/TSP.2017.2787102
EP  - 1579
PY  - 2017///
SN  - 1053-587X
SP  - 1566
TI  - Performance analysis of quaternion-valued adaptive filters in nonstationary environments
T2  - IEEE Transactions on Signal Processing
UR  - http://dx.doi.org/10.1109/TSP.2017.2787102
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000425050700013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/58490
VL  - 66
ER  -
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