Simultaneous Distributed Estimation and Attack Detection/Isolation in Social Networks: Structural Observability, Kronecker-Product Network, and Chi-Square Detector

TL;DR

This paper introduces a distributed method for simultaneous state estimation and attack detection in social networks, using local chi-square detectors and LMI-based gain design, without assuming local observability or bounded noise support.

Contribution

It presents a fully distributed attack detection and estimation scheme that handles Gaussian noise without support bounds, and does not require local observability, suitable for large-scale social networks.

Findings

Outperforms centralized chi-square detection methods.

Handles unbounded Gaussian noise without simplifying assumptions.

Enables attack detection without local observability constraints.

Abstract

This paper considers distributed estimation of linear systems when the state observations are corrupted with Gaussian noise of unbounded support and under possible random adversarial attacks. We consider sensors equipped with single time-scale estimators and local chi-square ($\chi^2$) detectors to simultaneously opserve the states, share information, fuse the noise/attack-corrupted data locally, and detect possible anomalies in their own observations. While this scheme is applicable to a wide variety of systems associated with full-rank (invertible) matrices, we discuss it within the context of distributed inference in social networks. The proposed technique outperforms existing results in the sense that: (i) we consider Gaussian noise with no simplifying upper-bound assumption on the support; (ii) all existing $\chi^2$-based techniques are centralized while our proposed technique is distributed, where the sensors \textit{locally} detect attacks, with no central coordinator, using specific probabilistic thresholds; and (iii) no local-observability assumption at a sensor is made, which makes our method feasible for large-scale social networks. Moreover, we consider a Linear Matrix Inequalities (LMI) approach to design block-diagonal gain (estimator) matrices under appropriate constraints for isolating the attacks.