Networked Filtering with Feedback for Discrete-Time Observations

Filtering is an essential operation in a variety of applications, such as Internet-of-Things and network localization and navigation. Distributed filtering in networked systems is a challenging problem due to the constraints on both the sensing and the communication capabilities of the system. In this paper, we investigate distributed filtering for a two-node system in discrete-time scenarios. In particular, each node is associated with an unknown state and obtains an observation of the two states at each time. One of the two nodes transmits encoded messages to the other node via a Gaussian channel with feedback. The receiver node infers its unknown state in real-time based on its observations and the received messages. We design an encoding strategy for generating transmitted messages and show that it optimizes the distributed filtering performance when certain conditions on the observation model are satisfied. Numerical results quantify the advantage of the designed encoding strategy compared to reference techniques.