Secure Dynamic State Estimation by Decomposing Kalman Filter

Abstract

Abstract We consider the problem of estimating the state of a linear time-invariant Gaussian system in the presence of sparse integrity attacks. The attacker can control p out of m sensors and arbitrarily change the measurements. Under mild assumptions, we can decompose the optimal Kalman estimate as a weighted sum of local state estimates, each of which is derived using only the measurements from a single sensor. Furthermore, we propose a convex optimization based approach, instead of the weighted sum approach, to combine the local estimate into a more secure state estimate. It is shown that our proposed estimator coincides with the Kalman estimator with certain probability when all sensors are benign, and we provide a sufficient condition under which the estimator is stable against the (p, m)-sparse attack when p sensors are compromised. A numerical example is provided to illustrate the performance of the proposed state estimation scheme.