A split quaternion nonlinear adaptive filter

A split quaternion learning algorithm for the training of nonlinear finite impulse response filters for the modelling of hypercomplex signals is proposed. A rigorous derivation takes into account the non-commutativity of the quaternion product, an aspect not taken into account in the existing nonlinear architectures, such as the Quaternion Multilayer Perceptron (QMLP). It is shown that the additional information present within the proposed algorithm provides an improved performance over QMLP. Simulation on both benchmark and real-world signals support the approach.