Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this paper, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

The Volterra-PARAFAC (VP) nonlinear system model, which consists of a FIR filterbank followed by a memoryless nonlinearity, aims at offering a good compromise between accuracy and parametric complexity. Here, for an even better compromise, we propose a generalization with IIR filters (VPI model) and evaluate both models. For the evaluation, we consider the concrete case of two audio loudspeakers and initially compute reference Volterra kernels from their known physical state-space models, using an efficient procedure. Then, VP and VPI models are derived and their accuracy is tested. As shown, the VPI models have in this case only 15 to 26 % of the parametric complexity of VP models with the same accuracy, which points to a great potential for accurate and efficient nonlinear system modeling.