Watermarking-based protection strategy against stealthy integrity attack on distributed state estimation

This article studies the security of distributed state estimation under data integrity attacks. Each sensor is equipped with a Kullback-Leibler (K-L) divergence detector to diagnose the authenticity of the received data. A necessary and sufficient condition for the insecurity of the distributed estimator is derived, in which the stealthy attack can evade the detector and degrade the estimation performance. Furthermore, an algorithm is proposed to generate stealthy attack sequences. To overcome the vulnerability, a data transmission strategy based on watermarking is proposed. The effect of the watermarking parameters on the attack in different scenarios is subsequently analyzed. It is proved that the K-L divergence detector can effectively distinguish the stealthy attack with the help of the proposed strategy, thereby ensuring the security of the distributed state estimator. Compared with traditional encryption mechanisms, the proposed strategy neither increases the computational complexity nor sacrifices the estimation performance in the absence of attacks. A simulation example is presented to demonstrate the effectiveness of the developed approach.