  This paper considers the design of a distributed state-observer for
discrete-time Linear Time-Invariant (LTI) systems in the presence of sensor
attacks. We assume there is a network of observer nodes, communicating with
each other over an undirected graph, each with partial measurements of the
output corrupted by some adversarial attack. We address the case of sparse
attacks where the attacker targets a small subset of sensors. An algorithm
based on Alternating Direction Method of Multipliers (ADMM) is developed which
provides an update law for each observer which ensures convergence of each
observer node to the actual state asymptotically.
