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Stability conditions and phase transition for Kalman filtering over Markovian channels
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0001-9940-5929
2015 (English)In: Chinese Control Conference, CCC, IEEE Computer Society, 2015, 6721-6728 p.Conference paper (Refereed)Text
Abstract [en]

This paper investigates the stability of Kalman filtering over Gilbert-Elliott channels where the random packet drop follows a time-homogeneous two-state Markov chain whose state transition is determined by a pair of failure and recovery rates. First, we establish a relaxed condition guaranteeing peak-covariance stability described by an inequality in terms of the spectral radius of the system matrix and transition probabilities of the Markov chain. We show that this condition can be rewritten as a linear matrix inequality feasibility problem. Next, we prove that the peak-covariance stability implies mean-square stability, if the system matrix has no defective eigenvalues on the unit circle. This implication holds for any random packet drop process, and is thus not restricted to Gilbert-Elliott channels. We prove that there exists a critical curve in the failure-recovery rate plane, below which the Kalman filter is mean-square stable and above is unstable for some initial values. Finally, a lower bound for this critical failure rate is obtained making use of the relationship we establish between the two stability criteria, based on an approximate relaxation of the system matrix.

Place, publisher, year, edition, pages
IEEE Computer Society, 2015. 6721-6728 p.
Keyword [en]
estimation, Kalman filtering, Markov processes, stability, stochastic system
National Category
Signal Processing
URN: urn:nbn:se:kth:diva-181518DOI: 10.1109/ChiCC.2015.7260700ScopusID: 2-s2.0-84946599917ISBN: 9789881563897OAI: diva2:911365
34th Chinese Control Conference, CCC 2015, 28 July 2015 through 30 July 2015

QC 20160311

Available from: 2016-03-11 Created: 2016-02-02 Last updated: 2016-03-11Bibliographically approved

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Wu, JunfengJohansson, Karl Henrik
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