Abstract
A robust Kalman filter is proposed for the discrete-time system with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e. the sum quadratic constraint (SQC). It is shown that the SQC can be converted into an indefinite quadratic cost function to be minimised in the Krein space, and it is found that the Krein space Kalman filter is a solution of the minimisation problem. After introducing a Krein space state-space model, which includes the uncertainty, one can easily write a robust version of the Krein space Kalman filter by modifying the measurement matrix and the variance of measurement noises in the original Krein space Kalman filter. Since the resulting robust Kalman filter has the same recursive structure as a conventional Kalman filter, a robust filtering scheme can be readily designed using the proposed method. A numerical example demonstrates that the proposed filter achieves robustness against parameter variation and improvement in performance when compared with a conventional Kalman filter and an existing robust Kalman filter, respectively.
| Original language | English |
|---|---|
| Pages (from-to) | 59-64 |
| Number of pages | 6 |
| Journal | IEE Proceedings: Control Theory and Applications |
| Volume | 151 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2004 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Instrumentation
- Electrical and Electronic Engineering
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Robust Kalman filtering via Krein space estimation. / Lee, T. H.; Ra, W. S.; Yoon, T. S.; Park, J. B.
In: IEE Proceedings: Control Theory and Applications, Vol. 151, No. 1, 01.01.2004, p. 59-64.Research output: Contribution to journal › Article
TY - JOUR
T1 - Robust Kalman filtering via Krein space estimation
AU - Lee, T. H.
AU - Ra, W. S.
AU - Yoon, T. S.
AU - Park, J. B.
PY - 2004/1/1
Y1 - 2004/1/1
N2 - A robust Kalman filter is proposed for the discrete-time system with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e. the sum quadratic constraint (SQC). It is shown that the SQC can be converted into an indefinite quadratic cost function to be minimised in the Krein space, and it is found that the Krein space Kalman filter is a solution of the minimisation problem. After introducing a Krein space state-space model, which includes the uncertainty, one can easily write a robust version of the Krein space Kalman filter by modifying the measurement matrix and the variance of measurement noises in the original Krein space Kalman filter. Since the resulting robust Kalman filter has the same recursive structure as a conventional Kalman filter, a robust filtering scheme can be readily designed using the proposed method. A numerical example demonstrates that the proposed filter achieves robustness against parameter variation and improvement in performance when compared with a conventional Kalman filter and an existing robust Kalman filter, respectively.
AB - A robust Kalman filter is proposed for the discrete-time system with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e. the sum quadratic constraint (SQC). It is shown that the SQC can be converted into an indefinite quadratic cost function to be minimised in the Krein space, and it is found that the Krein space Kalman filter is a solution of the minimisation problem. After introducing a Krein space state-space model, which includes the uncertainty, one can easily write a robust version of the Krein space Kalman filter by modifying the measurement matrix and the variance of measurement noises in the original Krein space Kalman filter. Since the resulting robust Kalman filter has the same recursive structure as a conventional Kalman filter, a robust filtering scheme can be readily designed using the proposed method. A numerical example demonstrates that the proposed filter achieves robustness against parameter variation and improvement in performance when compared with a conventional Kalman filter and an existing robust Kalman filter, respectively.
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UR - http://www.scopus.com/inward/citedby.url?scp=1542476647&partnerID=8YFLogxK
U2 - 10.1049/ip-cta:20040064
DO - 10.1049/ip-cta:20040064
M3 - Article
AN - SCOPUS:1542476647
VL - 151
SP - 59
EP - 64
JO - IEE Proceedings: Control Theory and Applications
JF - IEE Proceedings: Control Theory and Applications
SN - 1350-2379
IS - 1
ER -