An efficient implementation of maximum likelihood identification of LTI state-space models by local gradient search

N.H. Bergboer; V. Verdult; M.H.G. Verhaegen

An efficient implementation of maximum likelihood identification of LTI state-space models by local gradient search

N.H. Bergboer, V. Verdult, M.H.G. Verhaegen

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Abstract

We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parameter space. The output error identification problem is discussed, and its extension to maximum likelihood identification is explained. We show that the maximum likelihood framework yields parameter errors that converge to the Cramer-Rao bound. Furthermore, the implementation is shown to be fast and able to handle large sample size problems.

Original language	Undefined
Pages	616-621
Publication status	Published - 2002
Event	41st IEEE Conference on Decision and Control, CDC 2002 - Las Vegas, United States Duration: 10 Dec 2002 → 13 Dec 2002 Conference number: 41

Conference

Conference	41st IEEE Conference on Decision and Control, CDC 2002
Abbreviated title	CDC
Country/Territory	United States
City	Las Vegas
Period	10/12/02 → 13/12/02

Keywords

Identification
search problems
least squares approximations
Maximum likelihood estimation
Linear systems
multivariable systems
State-spacemethods
IR-55873

Access to Document

01184569

Cite this

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title = "An efficient implementation of maximum likelihood identification of LTI state-space models by local gradient search",

abstract = "We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parameter space. The output error identification problem is discussed, and its extension to maximum likelihood identification is explained. We show that the maximum likelihood framework yields parameter errors that converge to the Cramer-Rao bound. Furthermore, the implementation is shown to be fast and able to handle large sample size problems.",

keywords = "Identification, search problems, least squares approximations, Maximum likelihood estimation, Linear systems, multivariable systems, State-spacemethods, IR-55873",

author = "N.H. Bergboer and V. Verdult and M.H.G. Verhaegen",

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note = "41st IEEE Conference on Decision and Control, CDC 2002 ; Conference date: 10-12-2002 Through 13-12-2002",

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T1 - An efficient implementation of maximum likelihood identification of LTI state-space models by local gradient search

AU - Bergboer, N.H.

AU - Verdult, V.

AU - Verhaegen, M.H.G.

N1 - Conference code: 41

PY - 2002

Y1 - 2002

N2 - We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parameter space. The output error identification problem is discussed, and its extension to maximum likelihood identification is explained. We show that the maximum likelihood framework yields parameter errors that converge to the Cramer-Rao bound. Furthermore, the implementation is shown to be fast and able to handle large sample size problems.

AB - We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parameter space. The output error identification problem is discussed, and its extension to maximum likelihood identification is explained. We show that the maximum likelihood framework yields parameter errors that converge to the Cramer-Rao bound. Furthermore, the implementation is shown to be fast and able to handle large sample size problems.

KW - Identification

KW - search problems

KW - least squares approximations

KW - Maximum likelihood estimation

KW - Linear systems

KW - multivariable systems

KW - State-spacemethods

KW - IR-55873

M3 - Paper

SP - 616

EP - 621

T2 - 41st IEEE Conference on Decision and Control, CDC 2002

Y2 - 10 December 2002 through 13 December 2002

ER -