Linear state estimation for Markov jump linear system with multi-channel observation delays and packet dropouts

ABSTRACT

This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet losses. The reorganisation method is employed to convert the delayed measurement system into an equivalent delay-free one and a new state variable is introduced, by which the original state estimation with transmission delays and data losses is transformed into the new state estimation for the reorganised delay-free system with jumping parameters and multiplicative noises. The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations. Then the original state estimation will be obtained via the jumping property. Finally, we show that the difference Riccati equations converge to a set of generalised algebraic Riccati equations under appropriate assumptions, which result in an optimal stationary filter.

KEYWORDS:

• State estimation
• Markov jumping system
• observation delay
• packet loss
• convergence

Acknowledgements

The authors are grateful to anonymous referees for their suggestions which have greatly improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 61473134, 61573220), the Postdoctoral Science Foundation of China (Grant No. 2017M622231), and the Fundamental Research Funds of Shandong University (Grant No. 2017JC009).

Notes on contributors

Chunyan Han

Chunhan Han received her Ph.D. degree in Control Theory and Control Engineering from Shandong University in 2010. She is currently an associate professor at the School of Electrical Engineering, University of Jinan. Her research interest covers optimal control and estimation, time delay systems, and Markov jump linear systems.

Wei Wang

Wei Wang received his PhD degree in control science and engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently an associate professor at Shandong University. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.