State estimation for linear systems with unknown input and random false data injection attack

This study focuses on the state estimation problem for a linear system with unknown input and random false data injection attack. The unknown input is treated as a process with a non-informative prior. A residue-based χ² detector is used to improve security of the linear system due to the randomness of the attack. Based on different detection information scenarios provided by the detector, a novel state estimator against the false data injection attack is proposed. Convergence and stability on the state estimation are investigated, and sufficient conditions are established to ensure boundedness of mean error covariance. Finally, the effectiveness of the proposed method is demonstrated by a numerical example.