Secure Distributed State Estimation of an LTI System over Time-Varying Networks and Analog Erasure Channels

TL;DR

This paper develops distributed algorithms for secure state estimation of linear systems over networks with time-varying connectivity and unreliable communication channels, ensuring robustness against adversarial attacks and packet losses.

Contribution

It introduces novel distributed estimation methods that handle adversarial sensor compromises and stochastic communication failures in dynamic network environments.

Findings

Algorithms achieve correct state estimation under adversarial conditions.

Guarantees mean-square stability despite packet drops.

Applicable to networks with bounded delays and intermittent connectivity.

Abstract

We study the problem of collaboratively estimating the state of an LTI system monitored by a network of sensors, subject to the following important practical considerations: (i) certain sensors might be arbitrarily compromised by an adversary and (ii) the underlying communication graph governing the flow of information across sensors might be time-varying. We first analyze a scenario involving intermittent communication losses that preserve certain information flow patterns over bounded intervals of time. By equipping the sensors with adequate memory, we show that one can obtain a fully distributed, provably correct state estimation algorithm that accounts for arbitrary adversarial behavior, provided certain conditions are met by the network topology. We then argue that our approach can handle bounded communication delays as well. Next, we explore a case where each communication link stochastically drops packets based on an analog erasure channel model. For this setup, we propose state estimate update and information exchange rules, along with conditions on the network topology and packet drop probabilities, that guarantee mean-square stability despite arbitrary adversarial attacks.