Integrity attacks on remote estimation with spatial–temporal information sources

This paper considers the design issue of optimal integrity attacks on remote estimation with multiple information sources in cyber–physical systems. The specific scenario is that the smart sensors transmit innovations via a wireless network to the remote estimator. There are two types of sensors—safe and suspicious ones, where the innovations of safe sensors have no possibility of being modified by a malicious attacker, but the innovations from suspicious sensors may be intercepted and modified. The typical integrity attacks focus on utilizing the innovations of suspicious sensors and current innovations, which underutilize the available information that limits the impact on remote estimation and may be exposed under mutual verification between safe and suspicious sensors. Consequently, we propose a stealthy integrity attack with a finite horizon of historical data from both types of sensors, i.e., the so-called integrity attack with spatial–temporal information sources, which further enhances the effectiveness of integrity attacks. The stealthiness constraints and the corresponding estimation error covariances under the proposed attacks are obtained. The analytical expressions of optimal integrity attack strategies are derived by maximizing the estimation error under stealthiness constraints. In addition, we investigate the properties of the optimal integrity attack strategies when the attacks occur consecutively. Finally, some numerical simulations are presented to demonstrate the effectiveness of the obtained results.