Worst-Case Stealthy Linear Attacks on Distributed Kalman Filter Under Kullback-Leibler Divergence

This paper investigates the worst-case attack problem of cyber physical systems under false data injection (FDI) attacks. The scenario considered contains nodes exchanging local estimation data generated by distributed Kalman filters with their neighbors through wireless network and malicious attackers injecting false data into the transmitted information. To optimize the effects of FDI attacks with stochastic linked transmission between nodes and Kullback-Leibler divergence detectors, an upper bound of expected estimation error covariance is developed, based on which, a numerical solution of the one-step worst-case attack is obtained. The attack effects of the worst-case attack compared with random attacks are evaluated via some numerical examples.