Kalman filter for discrete-time stochastic linear systems subject to intermittent unknown inputs

IEEE Transactions on Automatic Control

Volumn 58, Issue 7, 2013, Pages 1882-1887

  Keller, Jean Yves ^a   Sauter, Dominique D J ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Covariance matrices; intermittent unknown inputs; kalman filter; linear system

Indexed keywords

COVARIANCE MATRICES; DISCRETE TIME LINEAR SYSTEMS; ESTIMATION ERRORS; NECESSARY AND SUFFICIENT STABILITY CONDITIONS; PREDICTION ERRORS; STOCHASTIC LINEAR SYSTEMS; TECHNICAL NOTES; UNKNOWN INPUTS;

COVARIANCE MATRIX; KALMAN FILTERS; LINEAR SYSTEMS; STOCHASTIC SYSTEMS;

STATE ESTIMATION;

EID: 84879904618     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2013.2264739     Document Type: Article

References (31)

1. A. T. Alouani, T. R. Rice, andW.D. Blair, "Atwo-stage filter for state estimation in the presence of dynamic stochastic bias," in Proc. Amer. Control Conf., Chicago, IL, 1992, pp. 1784-1788. (Pubitemid 23556314)
2. M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswieki, Diagnosis and Fault Tolerant Control. Berlin, Germany: Springer, 2006.
3. A. Censi, "On the performance of Kalman filtering with intermittent observations:Ageometric approachwith fractals," in Proc. Amer. Control Conf., St Louis, MO, 2009, pp. 3806-3812.
4. J. Chen and R. J. Patton, "Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances," Control Theory Appl., vol. 143, no. 1, pp. 31-36, 1996. (Pubitemid 126760260)
5. J. Chen and R. J. Patton, Robust Model Based Fault Diagnosis for Dynamic Systems. Norwell, MA: Kluwer Academic Publishers, 1999.
6. M. Darouach, M. Zasadzinski, and J. Y. Keller, "State estimation for discrete systems with unknown inputs using state estimation of singular systems," in Proc. Amer. Control Conf., Chicago, IL, 1992, pp. 3014-3015. (Pubitemid 23579629)
7. M. Darouach and M. Zasadzinski, "Unbiased minimum variance estimation for systems with unknown exogenous inputs," Automatica, vol. 33, no. 4, pp. 717-719, 1997. (Pubitemid 127417107)
8. H. Fang, Y. Shi, and J. Yi, "On stable simultaneous input and state estimation for discrete-time linear systems," Int. J. Adaptive Control Signal Processing, pp. 671-686, 2011.
9. A. Fletcher, S. Rangan, and V. Goyal, "Estimation from lossy sensor data: Jump linear modeling and Kalman filtering," in Proc. Int. Symp. Inform. Processing Sensor Netw., 2004, pp. 251-258.
10. B. Friedland, "Treatment of bias in recursive filtering," IEEE Trans. Autom. Control, vol. 14, no. 4, pp. 359-367, Apr. 1969.
11. S. Gillijns and B. De Moor, "Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough," Automatica, vol. 43, no. 5, pp. 934-937, 2007. (Pubitemid 46509773)
12. F. B. Hmida, K. Khémiri, J. Ragot, andM. Gossa, "Robust filtering for state and fault estimation of linear stochastic systems with unknown disturbance," Math. Problems Eng., 2010, 591639.
13. M. Hou and P. C. Müller, "Disturbance decoupled observer design: A unified viewpoint," IEEE Trans. Autom. Control, vol. 39, no. 6, pp. 1338-1341, Jun. 1994.
14. M. Hou and R. J. Patton, "Input observability and input reconstruction," Automatica, vol. 34, no. 6, pp. 789-794, 1998. (Pubitemid 128400405)
15. M. Hou and R. J. Patton, "Optimal filtering for systems with unknown inputs," IEEE Trans. Autom. Control, vol. 43, no. 3, pp. 445-449, Mar. 1998. (Pubitemid 128737368)
16. J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, "Survey of recent results in networked control systems," Proc. IEEE, vol. 95, no. 1, pp. 138-162, Jan. 2007.
17. C. S. Hsieh and F. C. Chen, "Optimal solution of the two stage Kalman estimator," IEEE Trans. Autom. Control, vol. 44, no. 1, pp. 194-199, Jan. 1999.
18. M. Ignagni, "Optimal and suboptimal separate-bias Kalman filter estimators of a stochastic bias," IEEE Trans. Autom. Control, vol. 45, no. 3, pp. 547-551, Mar. 2000.
19. T. Kailath, A. Sayed, and B. Hassibi, Linear Estimation. Upper Saddle River, NJ: Prentice-Hall, 2000.
20. J. Y. Keller and M. Darouach, "Optimal two-stage Kalman filter in the presence of random bias," Automatica, vol. 33, no. 9, pp. 1745-1748, 1997. (Pubitemid 127378851)
21. J. Y. Keller and D. Sauter, "Restricted diagonal detection filter and updating strategy for multiple fault detection and isolation," Adaptive Control Signal Processing, vol. 25, no. 1, pp. 68-87, 2011.
22. Y. Kim and J. Park, "Noise response of detection filters: Relation between detection space and completion space," Control Theory Appl., vol. 150, no. 4, pp. 443-447, 2003.
23. K. H. Kim, J. G. Lee, and C.G. Park, "Adaptive two-stage Kalman filter in the presence of unknown random bias," Adaptive Control Signal Processing, vol. 20, no. 6, pp. 305-319, 2006. (Pubitemid 44351635)
24. P. K. Kitanidis, "Unbiased minimum-variance linear state estimation," Automatica, vol. 23, no. 6, pp. 775-778, 1987.
25. Y. Liang, L. Zhang, D. Zhou, and Q. Pan, "Estimation of systems with statistically-constrained inputs," Appl. Math. Computat., vol. 217, no. 6, pp. 2644-2656, 2010.
26. J. Park and G. Rizzoni, "A new interpretation of the fault detection filter," Int. J. Control, vol. 60, no. 6, pp. 1339-1351, 1994.
27. L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, and S. Sastry, "Foundations of control and estimation over lossy networks," Proc. IEEE, vol. 95, no. 1, pp. 163-187, Jan. 2007.
28. L. Shi, L. Xie, and R. M. Murray, "Kalman filtering over a packeddelaying network: A probabilistic approach," Automatica, vol. 45, no. 9, pp. 2134-2140, 2009.
29. D. Simon, Optimal State Estimation: Kalman, , and Nonlinear Approaches. New York: Wiley-Interscience, 2006.
30. B. Sinopoli, L. Schenato,M. Franceschetti, K. Poolla,M. Jordan, and S. Sastry, "Kalman filtering with intermittent observations," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1453-1464, Sep. 2004.
31. A. Censi, "Kalman Filtering with intermittent observations: Convergence for semi-Markov chains and an intrinsic performance measure," IEEE Trans. Autom. Control, vol. 56, no. 2, pp. 376-381, Feb. 2011.