Remote secure fusion estimation of cyber–physical systems under false data injection attacks

This paper discusses the secure fusion estimation issue for cyber–physical systems subject to malicious attacks. Smart sensors equipped with computing modules transmit local posteriori estimations to remote fusion center through wireless communication channels. The transmission process is considered to be vulnerable to false data injection attacks. Therefore, to enhance the resilient of the estimator, protection and fusion strategies are collaboratively designed under cases where the attack information is unavailable or partially available. Noteworthy, instead of using innovation information from smart sensors, a set of auxiliary data transmitted along with local estimations is utilized for attack detection at the remote side. Then, according to the detection signal, the protector at each instant decides whether to drop the received estimations directly, and whether to take compensation measures. Further, the evolution and convergence results of fusion estimation covariance under different cases are analytically derived, and the comparisons of the convergence results are also theoretically deduced. Besides, most of existing achievements on fusion estimation are derived by utilizing local optimal Kalman filter, which implies that the fusion estimation may not be globally optimal and can be further improved. Thus, based on the analysis of steady-state and convergence of error covariance for Kalman filter, a novel iterative procedure for updating the local filter gains is proposed as the first attempt to further reduce fusion estimation error. Several examples including practical application in radar tracking and microgrids are finally provided to verify the derived results.