Resilient Distributed Estimation Through Adversary Detection

This paper studies resilient multi-agent distributed estimation of an unknown vector parameter when a subset of the agents is adversarial. We present and analyze a Flag Raising Distributed Estimator ($\mathcal{FRDE}$) that allows the agents under attack to perform accurate parameter estimation and detect the adversarial agents. The $\mathcal{FRDE}$ algorithm is a consensus+innovations estimator in which agents combine estimates of neighboring agents (consensus) with local sensing information (innovations). We establish that, under $\mathcal{FRDE}$, either the uncompromised agents' estimates are almost surely consistent or the uncompromised agents detect compromised agents if and only if the network of uncompromised agents is connected and globally observable. Numerical examples illustrate the performance of $\mathcal{FRDE}$.