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This paper considers distributed estimation of linear systems when the stateobservations are corrupted with Gaussian noise of unbounded support and underpossible random adversarial attacks. We consider sensors equipped with singletime-scale estimators and local chi-square ($\chi^2$) detectors tosimultaneously opserve the states, share information, fuse thenoise/attack-corrupted data locally, and detect possible anomalies in their ownobservations. While this scheme is applicable to a wide variety of systemsassociated with full-rank (invertible) matrices, we discuss it within thecontext of distributed inference in social networks. The proposed techniqueoutperforms existing results in the sense that: (i) we consider Gaussian noisewith no simplifying upper-bound assumption on the support; (ii) all existing$\chi^2$-based techniques are centralized while our proposed technique isdistributed, where the sensors \textit{locally} detect attacks, with no centralcoordinator, using specific probabilistic thresholds; and (iii) nolocal-observability assumption at a sensor is made, which makes our methodfeasible for large-scale social networks. Moreover, we consider a Linear MatrixInequalities (LMI) approach to design block-diagonal gain (estimator) matricesunder appropriate constraints for isolating the attacks.

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