Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective

We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[Pk], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[Pk ¿ M], i.e., the probability that Pk is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[Pk ¿ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[Pk ¿ M]. We also recover the results in the literature when using Pr[Pk ¿ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper.

I. Introduction

In the past decade, networked control systems have gained attention from both the control community and the network and communication community. When compared with classical feedback control systems, networked control systems have several advantages. For example, they can reduce the system wiring, make the system easy to operate, maintain and diagnose, and increase system agility. Although networked control systems have advantages, inserting a network in between the plant and the controller can introduce many problems as well. For example, in communication networks, data packets that carry the information can be dropped, delayed or even reordered due to the network traffic conditions. When closing the control loop over such communication networks, the overall system might have poor performance or even become unstable when the aforementioned issues exist. Thus the effect that those issues have on the closed loop system performance must be fully analyzed before networked control systems become commonplace.