by Bukhari Che Ujang, Clive Cheong Took, Danilo P. Mandic
Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus,
London SW7 2AZ, UK
Neural Networks 23 (2010) pp. 426-434.
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.
Quaternion-valued adaptive filters, Nonlinear adaptive filtering, Cauchy-Riemann-Fueter equation, Quaternion Multilayer Perceptron, Wind modelling