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
221-226
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
23 October 2002
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
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.
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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
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Date deposited: 05 Oct 2018 16:30
Last modified: 18 Mar 2024 03:48
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