Abstract
In this chapter, we study the Kalman filtering problem with Markovian packet losses with the focus on the stability of estimation error covariance matrices.
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- 1.
This notation means that there is a positive definite \(\bar{P}\) such that \(\mathbb {E}[{P_{k}}]<\bar{P}\) for all \(k\in \mathbb {N}\). Similar meaning applies to the notation \(\sup _{k\in \mathbb {N}}\mathbb {E}[{M_{k}}]<\infty \).
References
S. Meyn, R. Tweedie, J. Hibey, Markov Chains and Stochastic Stability (Springer, London, 1996)
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan, S. Sastry, Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49(9), 1453–1464 (2004)
M. Huang, S. Dey, Stability of Kalman filtering with Markovian packet losses. Automatica 43(4), 598–607 (2007)
L. Xie, L. Xie, Stability of a random Riccati equation with Markovian binary switching. IEEE Trans. Autom. Control 53(7), 1759–1764 (2008)
Y. Mo, B. Sinopoli, Towards finding the critical value for Kalman filtering with intermittent observations (2010). http://arxiv.org/abs/1005.2442
K. Plarre, F. Bullo, On Kalman filtering for detectable systems with intermittent observations. IEEE Trans. Autom. Control 54(2), 386–390 (2009)
R. Singer, Estimating optimal filter tracking performance for manned maneuvering targets. IEEE Trans. Aerosp. Electron. Syst. 6(4), 473–483 (1970)
V. Solo, One step ahead adaptive controller with slowly time-varying parameters. Technical report, Department of ECE (John Hopkins University, Baltimore, 1991)
R. Ash, C. Doléans-Dade, Probability and Measure Theory (Academic Press, San Diego, 2000)
R. Horn, C. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985)
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You, K., Xiao, N., Xie, L. (2015). Kalman Filtering with Packet Losses. In: Analysis and Design of Networked Control Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6615-3_13
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DOI: https://doi.org/10.1007/978-1-4471-6615-3_13
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