Networked Filtering with Feedback for Continuous-Time Observations

This paper investigates distributed filtering in continuous-time scenarios building on an information-theoretic view of Kalman–Bucy filtering. We consider a two-node system where each node is associated with a time-varying state and obtains noisy observations of both nodal states at each time. In addition, one of the two nodes receives encoded messages from the other node via a Gaussian channel with feedback and infers its current state based on available observations and received messages. We design a real-time encoding strategy for generating the transmitted messages and show under which conditions this strategy is optimal. Moreover, we present a relation between information dissipation rate and Fisher information for distributed filtering. Our finding is an extension of the connection established by Mitter and Newton between Shannon and Fisher information for Kalman–Bucy filtering.