Robust Filtering for Linear Discrete-Time Systems with Parametric Uncertainties

A Krein Space Estimation Approach

Tea Hoon Lee, Won Sang Ra, Tae Sung Yoon, Jin Bae Park, Soo Yul Jung, Joong Eon Seo

Research output: Contribution to journalConference article

11 Citations (Scopus)

Abstract

A new unified robust filtering algorithm is proposed for discrete-time linear systems with uncertainties described by sum quadratic constraints. The proposed method extends the existing Krein space estimation theory to robust filtering problem. It is shown that the robust filtering problem can be cast into the minimization problem of an indefinite quadratic form. By interpreting the uncertainties as another noise sources, the Krein space approach converts the minimization problem into the generalization of the Krein space Kalman filtering problem with an additional condition. This approach can be applied to H2 (Kalman) filtering problem and to H filtering problem as well. Moreover, the resulting robust filters have the similar recursive structures to various forms of the conventional Kalman filter, which makes the filters easy to design. Numerical examples verify the performances and the robustness of the proposed filters.

Original languageEnglish
Pages (from-to)1285-1290
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
Publication statusPublished - 2003 Dec 1
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: 2003 Dec 92003 Dec 12

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Robust Filtering
Krein Space
Discrete-time Linear Systems
Parametric Uncertainty
Kalman filters
Kalman Filtering
Linear systems
Filter
Minimization Problem
Uncertainty
Estimation Theory
Quadratic Constraint
Quadratic form
Kalman Filter
Convert
Filtering
Verify
Robustness
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

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abstract = "A new unified robust filtering algorithm is proposed for discrete-time linear systems with uncertainties described by sum quadratic constraints. The proposed method extends the existing Krein space estimation theory to robust filtering problem. It is shown that the robust filtering problem can be cast into the minimization problem of an indefinite quadratic form. By interpreting the uncertainties as another noise sources, the Krein space approach converts the minimization problem into the generalization of the Krein space Kalman filtering problem with an additional condition. This approach can be applied to H2 (Kalman) filtering problem and to H∞ filtering problem as well. Moreover, the resulting robust filters have the similar recursive structures to various forms of the conventional Kalman filter, which makes the filters easy to design. Numerical examples verify the performances and the robustness of the proposed filters.",
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Robust Filtering for Linear Discrete-Time Systems with Parametric Uncertainties : A Krein Space Estimation Approach. / Lee, Tea Hoon; Ra, Won Sang; Yoon, Tae Sung; Park, Jin Bae; Jung, Soo Yul; Seo, Joong Eon.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2, 01.12.2003, p. 1285-1290.

Research output: Contribution to journalConference article

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AU - Ra, Won Sang

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AU - Jung, Soo Yul

AU - Seo, Joong Eon

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AB - A new unified robust filtering algorithm is proposed for discrete-time linear systems with uncertainties described by sum quadratic constraints. The proposed method extends the existing Krein space estimation theory to robust filtering problem. It is shown that the robust filtering problem can be cast into the minimization problem of an indefinite quadratic form. By interpreting the uncertainties as another noise sources, the Krein space approach converts the minimization problem into the generalization of the Krein space Kalman filtering problem with an additional condition. This approach can be applied to H2 (Kalman) filtering problem and to H∞ filtering problem as well. Moreover, the resulting robust filters have the similar recursive structures to various forms of the conventional Kalman filter, which makes the filters easy to design. Numerical examples verify the performances and the robustness of the proposed filters.

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