Coding-based distributed filtering for cyber–physical systems under denial of service attacks

This article investigates the distributed recursive filtering problem for discrete-time stochastic cyber–physical systems. A particular feature of our work is that we consider systems in which the state is constrained by saturation. Measurements are transmitted to nodes of a sensor network over unreliable wireless channels. We propose a linear coding mechanism, together with a distributed method for obtaining a state estimate at each node. These designs aim to minimize the state estimation error covariance. In addition, we derive a bound on this covariance, and accommodate the design parameters to minimize this bound. The resulting design depends on the packet loss probabilities of the wireless channels. This permits applying the proposed scheme to systems in which communications suffer from denial-of-service attacks, as such attacks typically affect those probabilities. Finally, we present a numerical example illustrating this application.