A Security Protection Scheme for Distributed State Estimation Based on Double-Watermarks

Distributed sensor networks face security challenges since the state estimates between adjacent sensors may be tampered or monitored by attackers. Once the attack bypasses the detection mechanism and is integrated into the distributed state estimation, the performance of the system will be compromised. In this paper, the securities of distributed state estimation under confidentiality and integrity attacks are studied. A loophole in single watermarking protection strategy is revealed, thus the existing solution cannot balance the false alarm rate and missed alarm rate by the aid of the equipped Kullback-Leibler (K-L) divergence detector. To solve this problem, an improved scheme based on double-watermarks protection strategy is proposed. Under the condition that the designed watermarks are secure, it is infeasible for an attacker to launch such a covert injection attack which can evade K-L divergence detector. Therefore, a suitable detection threshold can be determined, to achieve both low false alarm rate and missed alarm rate. Furthermore, considering that the manner in which the tampered data is discarded weakens the performances of distributed state estimation, the feasibilities of extracting the original signals from the polluted ones under sparse attack and uniformity attack are investigated. A method for recovering the real estimates by indirectly reconstructing attack signals is provided, which is realized by solving an optimization problem. The advantage of distributed state estimation is thus preserved. Finally, the simulation experiments verify the effectiveness of the proposed scheme. Note to Practitioners—The motivation for this paper stems from the security challenges faced by distributed sensor networks. In order to identify the forged data shared by different nodes in the distributed network, the existing method is to add a protective watermark into the transmitted signal. This paper reveals a loophole of the single watermarking strategy, and gives a new solution based on double-watermarks framework. In this case, the attack detection performance is significantly improved, and an alarm will be more likely to be triggered by a real attack rather than noise. For the received polluted signals, this paper provides a method for recovering the real data by indirectly reconstructing the attack signals. Therefore, the performance of distributed sensor networks will not be compromised. Preliminary simulation experiments suggest that the proposed solution is feasible but it has not yet been tested in production. In future research, we will further explore the design of batch producing watermarks by chaotic control, to improve the efficiency of implementation.