Resilient State Estimation for Control Systems Using Multiple Observers and Median Operation

This paper addresses the problem of state estimation for linear dynamic systems that is resilient against malicious attacks on sensors. By "resiliency" we mean the capability of correctly estimating the state despite external attacks. We propose a state estimation with a bank of observers combined through median operations and show that the proposed method is resilient in the sense that estimated states asymptotically converge to the true state despite attacks on sensors. In addition, the effect of sensor noise and process disturbance is also considered. For bounded sensor noise and process disturbance, the proposed method eliminates the effect of attack and achieves state estimation error within a bound proportional to those of sensor noise and disturbance. While existing methods are computationally heavy because online solution of nonconvex optimization is needed, the proposed approach is computationally efficient by using median operation in the place of the optimization. It should be pointed out that the proposed method requires the system states being observable with every sensor, which is not a necessary condition for the existing methods. From resilient system design point of view, however, this fact may not be critical because sensors can be chosen for resiliency in the design stage. The gained computational efficiency helps real-time implementation in practice.