Optimal Attack Schedule for Two Sensors State Estimation Under Jamming Attack

In this paper, we investigate stable state estimation and optimal attack schedule problems of the wireless Cyber-Physical Systems (CPS) with two sensors under Denial-of-Service (DoS) attack. At each sampling time, a DoS attacker can conduct jamming attack in a certain frequency band to jam the two wireless packet dropping channels and cause packet dropouts. Due to the different frequency bandwidths of the two channels, one and only one channel is jammed by the jamming attack at each time step. A sufficient condition is presented to ensure the stability of the state estimation based on the Kalman filter. And the optimal attack schedule, which maximizes the expected average estimation error at the remote estimator, is proposed in the viewpoint of the attacker. Moreover, when there is a special intrusion detection system (IDS) at the estimator, the optimal attack schedule is also provided. A numerical simulation is given out to illustrate the effectiveness of the obtained results.