Took, Mandic: A Quaternion Widely Linear Adaptive Filter


by Clive Cheong Took and Danilo P. Mandic
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 8, AUGUST 2010, pp. 4427-4431
Digital Object Identifier 10.1109/TSP.2010.2048323

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 -proper and -improper signals, leading to improved accuracies compared to the QLMS class of algorithms. Simulations on both benchmark and real world data support the analysis.

Index Terms— properness, quadrivariate processes, quaternion adaptive filtering, quaternion LMS (QLMS), quaternion second-order noncircularity, widely linear model, widely linear QLMS, Wiener model.

Source: Email by D. Mandic (d.mandicATimperial.ac.uk), 2011/01/19 0:43

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