On the Design of Resilient Distributed Single Time-Scale Estimators: A Graph-Theoretic Approach

2025-05-03

AI Summary

To address the insufficient robustness of distributed state estimation in sensor networks under communication/sensor failures and cyber-attacks, this paper proposes a single-timescale distributed estimation algorithm. The method innovatively incorporates *q*-node and *q*-link connectivity—concepts from graph theory—into estimator design, thereby relaxing the conventional strong-connectivity assumption and eliminating the need for inner-layer consensus iterations inherent in dual-timescale approaches. By integrating fault-tolerant consensus protocols, distributed observer construction, and Schur stability analysis, the proposed algorithm guarantees Schur stability of the estimation error system even when up to *q* sensors or *q* communication links fail. Compared with existing methods, it significantly reduces communication overhead while enhancing topological adaptability and preserving observability under partial network degradation.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements

Abstract

Distributed estimation in interconnected systems has gained increasing attention due to its relevance in diverse applications such as sensor networks, autonomous vehicles, and cloud computing. In real practice, the sensor network may suffer from communication and/or sensor failures. This might be due to cyber-attacks, faults, or environmental conditions. Distributed estimation resilient to such conditions is the topic of this paper. By representing the sensor network as a graph and exploiting its inherent structural properties, we introduce novel techniques that enhance the robustness of distributed estimators. As compared to the literature, the proposed estimator (i) relaxes the network connectivity of most existing single time-scale estimators and (ii) reduces the communication load of the existing double time-scale estimators by avoiding the inner consensus loop. On the other hand, the sensors might be subject to faults or attacks, resulting in biased measurements. Removing these sensor data may result in observability loss. Therefore, we propose resilient design on the definitions of $q$-node-connectivity and $q$-link-connectivity, which capture robust strong-connectivity under link or sensor node failure. By proper design of the sensor network, we prove Schur stability of the proposed distributed estimation protocol under failure of up to $q$ sensors or $q$ communication links.

Problem

• Design resilient distributed estimators for sensor networks
• Enhance robustness using graph-theoretic structural properties
• Ensure stability under sensor or link failures

Innovation

• Graph-theoretic approach enhances estimator robustness
• Relaxes connectivity and reduces communication load
• Resilient design ensures stability under failures