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Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value

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2 Author(s)
Yilin Mo ; ECE Department, Carnegie Mellon University, Pittsburgh, PA, USA ; Bruno Sinopoli

In this paper, we analyze the performance of Kalman filtering for discrete-time linear Gaussian systems, where packets containing observations are dropped according to a Markov process modeling a Gilbert-Elliot channel. To address the challenges incurred by the loss of packets, we give a new definition of non-degeneracy, which is essentially stronger than the classical definition of observability, but much weaker than one-step observability, which is usually used in the study of Kalman filtering with intermittent observations. We show that the trace of the Kalman estimation error covariance under intermittent observations follows a power decay law. Moreover, we are able to compute the exact decay rate for non-degenerate systems. Finally, we derive the critical value for non-degenerate systems based on the decay rate, improving upon the state of the art.

Published in:

IEEE Transactions on Automatic Control  (Volume:57 ,  Issue: 3 )