Trade-off analysis in replay attack detection with safe and suspicious sensor measurements

This paper considers the replay attack detection with safe and suspicious sensor measurements. The safe and suspicious sensors indicate that their measurements cannot and may be modified by malicious attackers, respectively. We firstly discuss the stealthiness of replay attacks against the detector constructed based on safe and suspicious sensor measurements. Then, we propose an attack detection strategy that directly utilizes the measurements with watermarking signals, which can improve the detection performance even without removing the watermarking signals in the measurements. Since the watermarking signals may affect the estimation performance, the trade-off between the detection performance and the estimation performance is analyzed, and the corresponding optimization problem is formulated to obtain the optimal covariance of the watermarking signals that maximizes the detection performance. Finally, a numerical example is provided to verify the effectiveness of theoretical results.