Secure and robust state estimation under sensor attacks, measurement noises, and process disturbances: Observer-based combinatorial approach

This paper presents a secure and robust state estimation scheme for continuous-time linear dynamical systems. The method is secure in that it correctly estimates the states under sensor attacks by exploiting sensing redundancy, and it is robust in that it guarantees a bounded estimation error despite measurement noises and process disturbances. In this method, an individual Luenberger observer (of possibly smaller size) is designed from each sensor. Then, the state estimates from each of the observers are combined through a scheme motivated by error correction techniques, which results in estimation resiliency against sensor attacks under a mild condition on the system observability. Moreover, in the state estimates combining stage, our method reduces the search space of a minimization problem to a finite set, which substantially reduces the required computational effort.