Reduced complexity Volterra model of non-linear MISO system

In this paper, we propose a new dynamic non-linear MISO system model using discrete-time Volterra series. To provide a reduced complexity model, each Volterra kernel is expanded on independent generalised orthonormal bases (GOBs) associated to the inputs to develop a new black-box non-linear MISO-GOB-Volterra model. However, this reduction is ensured once the poles characterising each independent generalised orthonormal basis (GOB) are set to their optimal values. For the selection of optimal GOBs poles, we develop two new general approaches based on Gauss-Newton and exhaustive algorithms, the performances of which are illustrated and compared in simulation.