The University of Southampton
University of Southampton Institutional Repository

The Fisher information matrix for linear systems

The Fisher information matrix for linear systems
The Fisher information matrix for linear systems

Estimation of parameters of linear systems is a problem often encountered in applications. The Cramer Rao lower bound gives a lower bound on the variance of any unbiased parameter estimation method and therefore provides an important tool in the assessment of a parameter estimation method and for experimental design. Here we study the calculation of the Fisher information matrix, the inverse of the Cramer Rao lower bound, from a system theoretic point of view. A number of results appear in the literature that deal with the case where the stationary data is given as the output of a linear system driven by Gaussian noise. The non-stationary situation where the data is the output of a linear system with Gaussian measurement noise is rarely considered despite its importance in applications. A general description will be given for Fisher information for such data in terms of a derivative system. For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.

Cramer Rao lower bound, Fisher information matrix, Linear non-stationary system, Lyapunov equation, Parameter estimation, System identification
0167-6911
221-226
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Ober, Raimund J. (2002) The Fisher information matrix for linear systems. Systems and Control Letters, 47 (3), 221-226. (doi:10.1016/S0167-6911(02)00190-1).

Record type: Article

Abstract

Estimation of parameters of linear systems is a problem often encountered in applications. The Cramer Rao lower bound gives a lower bound on the variance of any unbiased parameter estimation method and therefore provides an important tool in the assessment of a parameter estimation method and for experimental design. Here we study the calculation of the Fisher information matrix, the inverse of the Cramer Rao lower bound, from a system theoretic point of view. A number of results appear in the literature that deal with the case where the stationary data is given as the output of a linear system driven by Gaussian noise. The non-stationary situation where the data is the output of a linear system with Gaussian measurement noise is rarely considered despite its importance in applications. A general description will be given for Fisher information for such data in terms of a derivative system. For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.

This record has no associated files available for download.

More information

e-pub ahead of print date: 13 September 2002
Published date: 23 October 2002
Keywords: Cramer Rao lower bound, Fisher information matrix, Linear non-stationary system, Lyapunov equation, Parameter estimation, System identification

Identifiers

Local EPrints ID: 424925
URI: http://eprints.soton.ac.uk/id/eprint/424925
ISSN: 0167-6911
PURE UUID: 83bfced1-9aba-41c6-8b55-8479e244901c
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 05 Oct 2018 16:30
Last modified: 18 Mar 2024 03:48

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×