Split quaternion nonlinear adaptive filtering

Authors:
Bukhari Che Ujang;Clive Cheong Took;Danilo P. Mandic
Affiliations:
Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK;Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK;Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Venue:
Neural Networks
Year:
2010

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Abstract

A split quaternion learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of three- and four-dimensional signals is proposed. The derivation takes into account the non-commutativity of the quaternion product, an aspect neglected in the derivation of the existing learning algorithms. It is shown that the additional information taken into account by a rigorous treatment of quaternion algebra provides improved performance on hypercomplex processes. A rigorous analysis of the convergence of the proposed algorithms is also provided. Simulations on both benchmark and real-world signals support the approach.