Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

Karim Khémiri; Fayçal Ben Hmida; José Ragot; Moncef Gossa

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 4, page 629-637
  • ISSN: 1641-876X

Abstract

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This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.

How to cite

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Karim Khémiri, et al. "Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances." International Journal of Applied Mathematics and Computer Science 21.4 (2011): 629-637. <http://eudml.org/doc/208075>.

@article{KarimKhémiri2011,
abstract = {This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.},
author = {Karim Khémiri, Fayçal Ben Hmida, José Ragot, Moncef Gossa},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Kalman filtering; minimum-variance estimation; state estimation; fault estimation; unknown disturbances; linear discrete-time systems},
language = {eng},
number = {4},
pages = {629-637},
title = {Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances},
url = {http://eudml.org/doc/208075},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Karim Khémiri
AU - Fayçal Ben Hmida
AU - José Ragot
AU - Moncef Gossa
TI - Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 4
SP - 629
EP - 637
AB - This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.
LA - eng
KW - Kalman filtering; minimum-variance estimation; state estimation; fault estimation; unknown disturbances; linear discrete-time systems
UR - http://eudml.org/doc/208075
ER -

References

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  2. Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin/Heidelberg. Zbl1126.93004
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  13. Jamouli, H., Keller, J. and Sauter, D. (2003). Fault isolation filter with unknown inputs in stochastic systems, Proceedings of Safeprocess, Washington, DC, USA, pp. 531-536. 
  14. Kailath, T., Sayed, A. and Hassibi, B. (2000). Linear Estimation, Prentice Hall, Englewood Cliffs, NJ. Zbl0980.93077
  15. Keller, J. (1998). Fault isolation filter design for linear stochastic systems with unknown inputs, 37th IEEE Conference on Decision and Control, Tampa, FL, USA, pp. 598-603. 
  16. Keller, J. (1999). Fault isolation filter design for linear stochastic systems, Automatica 35(10): 1701-1706. Zbl0933.93066
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