Byzantine-Resilient Distributed State Estimation: A Distance-Based Multivariable Filtering Mechanism

Abstract

This paper studies the problem of resilient distributed state estimation for a linear system using a network of agents, some of which are subject to the Byzantine attacks. First, by introducing the distance function to quantify the difference between the estimates of the neighboring agents, a multivariable filtering mechanism is designed such that the regular agents can extract the reliable information from the vectors sent by their in-neighbors. Then, using the properties of the distance-based multivariable filtering mechanism and the detectability decomposition, resilient distributed observers are designed for the regular agents to asymptotically estimate the state vector of the system despite the adversarial influence of the Byzantine attacks. Furthermore, a graph-dependent Lyapunov function is proposed to analyze the convergence of the proposed method. In contrast to the existing scalar filtering mechanism-based methods, the proposed method can reduce the complexity of the reliable information extraction, and does not require the existence of multiple individual agents to detect each unstable eigenvalue of the system matrix. Finally, an example is given to demonstrate the effectiveness of the proposed method. Note to Practitioners—This paper is motivated by the problem of collaboratively estimating the state vector of a dynamical system using a network of agents in an attack-prone environment. Existing methods for regular agents to extract the reliable information from the received vectors generally rely on the scalar filtering mechanism, which increase in complexity as the dimension of the system increases and require relatively conservative observability assumption. In contrast, we propose a multivariable filtering mechanism-based resilient distributed state estimation method that has lower complexity and works under milder observability assumption. In future research, we will consider the applications of the proposed method to address the related problems such as target tracking, environmental monitoring, surveillance and patrolling.