The Vulnerability Analysis of Remote Estimation with Batch-Data Detectors against Integrity Attacks

The vulnerability analysis of remote state estimation with batch-data detectors is investigated in this paper. The considered scenario is that sensors measure the process state and transmit measurements to the remote end via wireless networks, where the yielded innovation may be altered by an adversary in an affine form. At the remote end, a detector utilizing batch statistics is deployed to detect anomalies. In this setup, finding the worst-case estimation performance degradation during a detection interval is formulated as a non-convex optimization problem on the Stiefel manifold with linear equation constraints, which is generally hard to tackle. Such a problem is addressed by introducing new optimization variables, and structural expressions of attack strategies in worst-case are proposed. Then, by means of Riemannian optimization tools, we provide additional properties for such attack strategies in a scalar sensor by solving a Boundary Trust Region Subproblem. Furthermore, analytical attack strategies in worst-case are derived under the case where a sequence of contaminated innovation covariances has been determined. A necessary condition of the existence of attack strategies in worst-case for the attacker with symmetric attack parameter matrices is also presented. Finally, two numerical examples in multi-sensor and a scalar sensor are conducted to demonstrate the validity of results developed.