Optimal stealthy integrity attacks on remote state estimation: The maximum utilization of historical data

Abstract This paper considers the problem of optimal stealthy integrity attacks on remote state estimation. Smart sensors transmit innovations to a remote estimator through a wireless communication network, where transmitted data can be intercepted and manipulated by attackers. To bypass the false data detector, the attack sequence should satisfy the stealthiness constraint. Instead of utilizing only the current innovation, the historical data are also used for designing the attack policy at each sampling instant. With a finite horizon of historical data used, the evolution of the estimation error covariance at the remote estimator is obtained, and the optimal attack that yields the largest estimation error is derived analytically. To reduce the online computational burden, the optimal attack using sparse combinations of historical innovations is also designed. In addition, the optimal attacks on protected systems with encryption-based countermeasures are analyzed. If encryption resources are sufficient, there always exists such a countermeasure that can completely prevent the stealthy attacks based on historical data. Numerical comparisons illustrate the theoretical results.