Phase-based order separation for Volterra series identification

This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates nonlinear homogeneous order contributions from which Volterra kernels can be identified independently. Unlike existing separation methods that use amplitude relations between test signals, we propose another order separation method based on phase. This method gives access to a new type of complex-valued output signals, which can be used to improve kernel identification. First, the underlying ideas are introduced via the presentation of a theoretical method using complex-valued test signals. Second, the proposed order separation method using real-valued signals is described. Third, a new identification process is given, combining existing least-squares identification method with the previous results. Finally, numerical experiments are used to compare the proposed order separation method with state-of-the-art, as well as to evaluate the new Volterra series identification process.