title: Split quaternion nonlinear adaptive filtering.
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.
authors.affiliation: Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. che.che-ujang07@imperial.ac.uk
authors.forename: Bukhari Che
authors.initials: BC
authors.lastname: Ujang
authors.forename: Clive Cheong
authors.initials: CC
authors.lastname: Took
authors.forename: Danilo P
authors.initials: DP
authors.lastname: Mandic
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D016208:Databases, Factual; D017711:Nonlinear Dynamics; D013269:Stochastic Processes; D014919:Wind