Resilient Distributed Estimation Through Adversary Detection

This paper studies resilient multiagent distributed estimation of an unknown vector parameter when a subset of the agents is adversarial. We present and analyze a flag raising distributed estimator (<inline-formula> <tex-math notation="LaTeX">$\mathcal {FRDE}$</tex-math></inline-formula>) that allows the agents under attack to perform accurate parameter estimation and detect the adversarial agents. The <inline-formula> <tex-math notation="LaTeX">$\mathcal {FRDE}$</tex-math></inline-formula> algorithm is a consensus+innovations estimator in which agents combine estimates of neighboring agents (consensus) with local sensing information (innovations). We establish that, under <inline-formula><tex-math notation="LaTeX">$\mathcal {FRDE}$</tex-math></inline-formula>, either the uncompromised agents' estimates are almost surely consistent, or the uncompromised agents detect compromised agents (with arbitrarily small false alarm probability) if and only if the network of uncompromised agents is connected and globally observable. Numerical examples illustrate the performance of <inline-formula> <tex-math notation="LaTeX">$\mathcal {FRDE}$</tex-math></inline-formula>.