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Kalman Filtering Over Gilbert-Elliott Channels: Stability Conditions and Critical Curve
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
Australian Natl Univ, Res Sch Engn, Canberra, ACT 0200, Australia..
Australian Natl Univ, Res Sch Engn, Canberra, ACT 0200, Australia..
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 4, p. 1003-1017Article in journal (Refereed) Published
Abstract [en]

This paper investigates the stability of Kalman filtering over Gilbert-Elliott channels where random packet drops follow a time-homogeneous two-state Markov chain whose state transition is determined by a pair of failure and recovery rates. First of all, 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 further show that the condition can be interpreted using 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 connection between the two stability notions holds for any random packet drop process. We prove that there exists a critical curve in the failure-recovery rate plane, below which the Kalman filter is mean-square stable and no longer mean-square stable above. 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-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 63, no 4, p. 1003-1017
Keywords [en]
Estimation, Kalman filtering, Markov processes, stability, stochastic systems
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-228143DOI: 10.1109/TAC.2017.2732821ISI: 000429056000007OAI: oai:DiVA.org:kth-228143DiVA, id: diva2:1207076
Note

QC 20180518

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-18Bibliographically approved

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Wu, Junfeng

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