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Stability of Kalman filtering with Markovian packet losses. (English) Zbl 1261.93083
Summary: 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 \(\{P_{t},\,t\geq 1\}\) 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.

MSC:
93E11 Filtering in stochastic control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
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