Kalman filtering over a packet dropping network: A probabilistic approach

We consider the problem of state estimation of a discrete time process over a packet dropping network. Previous pioneering work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k les M], i.e., the probability that P_k is bounded by a given M, and we derive lower and upper bounds on Pr[P_k les M]. We are also able to recover the results in the literature when using Pr[P_k les M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper.