Unknown Input Observers Design For Real-Time Mitigation of the False Data Injection Attacks

This paper is devoted to studying the effect of false data injection attacks on the state estimation of discrete linear time-invariant systems in the presence of unknown disturbance. The proposed scheme firstly decouples the disturbance signal from the estimation error by exploiting the concepts of unknown input observers. Then, the observer gain has been designed based on the Kalman filter algorithm while a saturation term has been assigned to the output error in the update rule of the estimated states. Thanks to the saturation-limit dynamics introduced into the error dynamics of the Kalman filter-based estimation, the proposed method is applicable for the real-time applications. The effectiveness of the proposed scheme has been validated through a numerical example by taking two different scenarios into considerations. First, the comparative results show the superiority of the proposed scheme in state estimation under the presence of high-frequency measurement noise. Next, further to the high-frequency measurement noise, it is assumed that the sensed measurements are also manipulated by an adversary, leading to outliers in the measurements. As for this scenario, the attained results show how successfully the proposed scheme can mitigate the effect of the outliers in the presence of unknown disturbances.