Stability of Kalman filtering with Markovian packet losses

Minyi Huang*, Subhrakanti Dey

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    400 Citations (Scopus)

    Abstract

    We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. Based on the sojourn time of each visit to the failure or successful packet reception state, we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, as an estimate of filtering deterioration caused by packet losses, which describes the upper envelope of the sequence of error covariance matrices { Pt, t ≥ 1 } for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case, and obtain a sufficient and necessary condition for the scalar case. Finally, the relationship between two different types of stability notions is discussed.

    Original languageEnglish
    Pages (from-to)598-607
    Number of pages10
    JournalAutomatica
    Volume43
    Issue number4
    DOIs
    Publication statusPublished - Apr 2007

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