Abstract
We consider the Kalman filtering problem in a networked environment where there are partial or entire packet losses described by a two state Markovian process. Based on random packet arrivals of the sensor measurements and the Kalman filter updates with partial packet, the statistical properties of estimator error covariance matrix iteration and stability of the estimator are studied. It is shown that to guarantee the stability of the Kalman filter, the communication network is required to provide for each of the sensor measurements an associated throughput, which captures all the rates of the successive sensor measurements losses. We first investigate a general discrete-time linear system with the observation partitioned into two parts and give sufficient conditions of the stable estimator. Furthermore, we extend the results to a more general case where the observation is partitioned into n parts. The results are illustrated with some simple numerical examples.
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This work is supported by National Natural Science Foundation of China (No. 60504017), Fok Ying Tong Education Foundation (No. 111066), and Program for New Century Excellent Talents in University (No.NCET-04-0982).
Bao-Feng Wang received the B. Sc. degree in mathematics and applied mathematics at Nanchang University of Aeronautics and Astronautics, Nanchang, PRC in 2003, and the M. Sc. degree in computer application at Dalian Maritime University, Dalian, PRC in 2006. She is currently a Ph.D. candidate in control theory and control applications at Dalian Maritime University, Dalian, PRC.
Her research interests include state estimation and filtering design of networked control systems.
Ge Guo received the B. Sc. and Ph.D. degrees from Northeastern University, Shenyang, PRC in 1994 and 1998, respectively. He joined Lanzhou University of Technology (LUT), PRC in 1999, where he was an associate professor and the director of the Institute of Intelligent Control and Robots from 2000 to 2004. Since 2004, he has been a professor in LUT and then in Dalian Maritime University, PRC since 2005. He is the editor-in-chief of International Journal of Systems, Control and Communications, and an editorial board member of several other international journals. He was the honoree of the New Century Excellent Talents in University, Ministry of Education, PRC, the nominee of Gansu Top Ten Excellent Youths, and the recipient of the Outstanding Teacher Prize, both from Gansu Province, PRC.
His research interests include networked control system theory, process control, hybrid vehicle, and mobile robot control.
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Wang, BF., Guo, G. Kalman filtering with partial Markovian packet losses. Int. J. Autom. Comput. 6, 395–400 (2009). https://doi.org/10.1007/s11633-009-0395-x
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DOI: https://doi.org/10.1007/s11633-009-0395-x