Multivariance nonlinear system identification using Wiener basis functions and perfect sequences

Abstract

Abstract-Multivariance identification methods exploit input signals with multiple variances for estimating the Volterra kernels of nonlinear systems. They overcome the problem of the locality of the solution, i.e., the fact that the estimated model well approximates the system only at the same input signal variance of the measurement. The estimation of a kernel for a certain input signal variance requires recomputing all lower order kernels. In this paper, a novel multivariance identification method based on Wiener basis functions is proposed to avoid recomputing the lower order kernels with computational saving. Formulas are provided for evaluating the Volterra kernels from the Wiener multivariance kernels. In order to further improve the nonlinear filter estimation, perfect periodic sequences that guarantee the orthogonality of the Wiener basis functions are used for Wiener kernel identification. Simulations and real measurements show that the proposed approach can accurately model nonlinear devices on a wide range of input signal variances.

Nonlinear system identification using Wiener basis functions and multiple-variance perfect sequences

“…In this paper, differently from the classical approach based on G-functionals, the Wiener series is expressed as a linear combination of basis functions, which are orthogonal for white Gaussian inputs, as was proposed in the early conference papers [27,28].…”

Identification of Volterra Models of Tube Audio Devices using Multiple-Variance Method

“…Deterministic periodic signals, called perfect periodic sequences (PPSs), that guarantee the orthogonality of the basis functions on a finite period, can also be developed. Using a PPS input signal, the identification of an unknown nonlinear filter can be improved either by using Wiener kernels or Wiener basis functions as approximators [9,10].…”

“…The subset is obtained by delaying and reducing the memory of the identified nonlinear kernels, i.e., considering only the most relevant terms of each kernel. The estimation of the reduced kernel can still be done with the cross-correlation estimation method, as proposed in [10], since with the cross-correlation method each kernel element is estimated independently of other elements. In this way, it will be shown that it is possible to obtain a good approximation error also with a reduced number of kernel elements on an extended range of input signal variances.…”