Performance Bounds of Quaternion Estimators

The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventiona...

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Published in:IEEE transaction on neural networks and learning systems 2015-12, Vol.26 (12), p.3287-3292
Main Authors: Yili Xia, Jahanchahi, Cyrus, Nitta, Tohru, Mandic, Danilo P.
Format: Article
Language:English
Subjects:
Analytical models
Augmented quaternion statistics
Covariance matrices
Estimation
Learning systems
mean square error (MSE)
Mean square errors
quaternion widely linear (WL) model
Quaternions
semi-WL (SWL) model
Vectors
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cited_by cdi_FETCH-LOGICAL-c487t-c6fa1a95a2d5e4d4ad0ff890023a5ff4c4fda8f6313a57f083666c1bad550dd63
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Jahanchahi, Cyrus
Nitta, Tohru
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description The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventional strictly linear (SL) as well as the semi-WL (SWL) estimators for improper data. However, rigorous theoretical and practical performance bounds are still missing in the literature, yet this is crucial for the development of quaternion valued learning systems for 3-D and 4-D data. To this end, based on the orthogonality principle, we introduce a rigorous closed-form solution to quantify the degree of performance benefits, in terms of the mean square error, obtained when using the WL models. The cases when the optimal WL estimation can simplify into the SWL or the SL estimation are also discussed.
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source IEEE Electronic Library (IEL) Journals
subjects Analytical models
Augmented quaternion statistics
Covariance matrices
Estimation
Learning systems
mean square error (MSE)
Mean square errors
quaternion widely linear (WL) model
Quaternions
semi-WL (SWL) model
Vectors
title Performance Bounds of Quaternion Estimators
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