Gaussian information matrix for Wiener model identification

TL;DR

This paper derives a closed-form expression for the information matrix in Wiener model identification with Gaussian inputs, enabling optimal experiment design for such models.

Contribution

It provides a novel, explicit formula for the information matrix in Wiener models with arbitrary linear and nonlinear components, facilitating optimal experiment design.

Findings

Explicit formula for the information matrix derived

Expression for the determinant of the information matrix provided

Application demonstrated in optimal experiment design

Abstract

We present a closed form expression for the information matrix associated with the Wiener model identification problem under the assumption that the input signal is a stationary Gaussian process. This expression holds under quite generic assumptions. We allow the linear sub-system to have a rational transfer function of arbitrary order, and the static nonlinearity to be a polynomial of arbitrary degree. We also present a simple expression for the determinant of the information matrix. The expressions presented herein has been used for optimal experiment design for Wiener model identification.