Identification of Volterra kernels using interpolation

This paper presents a new method for the identification of frequency-domain Volterra kernels. Since the nonlinear kernels often play a secondary role compared to the dominant, linear component of the system, it is worth establishing a balance between the degree of liberty of these components and their effect on the overall accuracy of the model. This is necessary in order to reduce the model complexity, hence the required measurement length. Based on the assumption that frequency-domain kernels are locally smooth, the kernel surfaces can be approximated by interpolation techniques, thus reducing the complexity of the model. Similarly to the unreduced (Volterra) model, this smaller model is also i) linear in the unknowns; ii) only locally sensitive to its parameters; and iii) free of structural assumptions about the system. The parameter estimation boils down to solving a linear system of equations in the least-squares (LS) sense. The design of the interpolation scheme is described and the performance of the approximation is analyzed and illustrated by simulation. The algorithm allows a significant saving in measurement time compared to other kernel estimation methods.