Decentralized Inference and its Application to Network Localization and Navigation

Abstract

Decentralized inference is important for complex networked systems and enables numerous applications such as network localization and navigation (NLN), Internet-ofThings (IoT), and smart cities. This thesis establishes a theoretical foundation of decentralized inference for networks with limited sensing and communication capabilities. In the considered network, each node aims to infer in real-time an evolving state based on local observations and on messages exchanged with its neighbors. The objectives of the thesis include: (i) designing message encoding strategies that maximize inference accuracy; (ii) establishing connections between information- and estimation-theoretical quantities; and (iii) characterizing the impact of the sensing and communication capabilities of the network on the inference accuracy.

First, we investigate a system of two nodes connected via a Gaussian channel. For such a system, we design a real-time strategy for generating the encoded messages exchanged between the nodes and derive conditions under which such a strategy provides optimal inference accuracy. Building on an information-theoretic perspective of Kalman–Bucy filtering in centralized settings, we derive a relationship between Shannon information and Fisher information for decentralized inference. Then, based on results for two-node systems, we characterize the behavior of decentralized inference error in multi-node networks with general channel models. We establish both necessary and sufficient conditions on the sensing and communication capabilities of the network for the boundedness of the mean-square error over time. We show that, in addition to Shannon capacity, anytime capacity plays a critical role in characterizing the impact of the network’s communication capability on the inference accuracy.

This thesis deepens the understanding of decentralized inference in complex networked systems; uncovers connections among estimation, information, and control theories; and provides guidelines for designing decentralized inference algorithms and network operation strategies in applications such as NLN and IoT.