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A Quaternion Widely Linear Adaptive Filter

<12>Motivated by the success of the widely linear model in complex-valued (bivariate) signal processing and the ubiquity of vector sensors (e.g. three-dimensional body sensors, 3D anemometers), this work has enhanced the capability of this model to handle three-dimensional and four-dimensional signals. As a result, this model provides additional degrees of freedom in signal detection, estimation and separation; for instance, the various degrees of second order circularity and the enhanced dimensionality allow the identification of more than one Gaussian signal in a mixture. This quaternion-valued model has been adopted by other researchers, including Nascimento (signal processing) and.Nitta (neural computation).