Continuous-Time Distributed Filtering via a Gaussian Feedback Channel

Filtering refers to the methods for inferring time-varying parameters and is a crucial task in cyber-physical systems. An important category of filtering is distributed filtering, where sensor nodes transmit observations via communication links to inference nodes that estimate the unknown states. Distributed filtering is challenging in the sense that the communication constraint of the sensor nodes limits the amount of information available to the inference node, calling for the co-design of communication and computing. This paper establishes a theoretical framework for the co-design of communication and computing in distributed filtering, building on an information-theoretic view of the Kalman-Bucy filtering. In particular, this paper considers a networked system consisting of two nodes, where each node aims to infer its own time-varying state in continuous-time scenarios. The two nodes are connected by a Gaussian feedback channel. Via the feedback link, one of the nodes can obtain the sensor observations and received signals of the other node. This paper develops an optimal linear strategy, namely the information difference encoding strategy, for generating signals transmitted via the Gaussian feedback channel. This paper also presents an inequality that relates Shannon information with Fisher information in distributed filtering. The inference accuracy and power efficiency of the information difference encoding strategy are quantified via simulations.