Improving the approximation ability of Volterra series identified with a cross-correlation method

Simone Orcioni

doi:10.1007/s11071-014-1631-7

Abstract

This paper proposes an improvement in cross-correlation methods derived from the Lee–Schetzen method, in order to obtain a lower mean square error in the output for a wider range of the input variances. In particular, each Wiener kernel is identified with a different input variance and new formulas for conversion from Wiener to Volterra representation are presented.

Highlights

Volterra series is a polynomial functional series for nonlinear system representation and identification
In order to test the previous statement, we identified a nonlinear system of infinite order with a second-order Volterra series, using (10) and a LMS identification algorithm, in the implementation reported in [3]
The truncation error was excluded by choosing, as test systems, Volterra systems of finite order that can ideally approximated with no error with Volterra series of the same order

Summary

Introduction

Volterra series is a polynomial functional series for nonlinear system representation and identification. In [4], Fréchet showed that a sum of a finite number of terms of Volterra series can approximate continuous realvalued mappings, defined on compact aggregates, e.g., on functions defined over intervals. This is an important limitation when forcing signals are defined over an infinite (or semi-infinite) time interval The supplementary material regards previous work by the author on Volterra series identification. Electronic supplementary material The online version of this article (doi:10.1007/s11071-014-1631-7) contains supplementary material, which is available to authorized users.

Methods

Results

Conclusion