Unknown input filtering under full accessibility attacks

This study initially addresses the state estimation problem for discrete-time linear time-invariant systems under the influence of both exogenous attacks and random noises. As the filtering side, we make no prior assumptions or have any prior knowledge about the nature of attacks. We employ a specific unknown input filtering approach, which has been examined in prior research, to simultaneously estimate both the system states and attacks. Differing from existing works, our emphasis on full accessibility attacks, a particular class of unknown inputs, reveals that the dynamic estimation gains of the adopted filtering reduce directly to static ones. The second contribution of this study is to mitigate the influence of attacks by utilizing the estimated attack signals. Under this strategy, the deviation between nominal states and attacked states is characterized by evaluating the upper bound of the covariance matrix of the errors.