We study the state estimation for c

We study the state estimation for cyber-physical systems (CPSs) whose communicationchannels are subject to mixed denial-of-service (DoS) and false data injection (FDI) attacks.Cyber-attacks compromise the security and privacy of sensor and communication information. Unlike systems subject to only one single type of attacks (either DoS or FDI attacks),systems under mixed attacks will make the implementation of the optimal state estimation infeasible. We first obtain the optimal estimator for CPSs under mixed cyberattacks. The optimal estimator consists of an exponentially growing number of components, and thus its computation effort exponentially grows in time. To efficiently computethe optimal estimate, we propose an approximate estimator by using the generalizedpseudo-Bayesian algorithm. We prove that for a stable system, both the optimal estimatorand the proposed approximate estimator are secure; and theoretically characterize theboundedness of the distance between the optimal and the approximate estimates.