Disturbance decoupled secure state estimation: An orthogonal projection-based method

Abstract

This paper investigates the disturbance decoupled secure state estimation problem of a linear system in the presence of sparse sensor attacks and unknown disturbances, where disturbance decoupled state estimation means that the resulting estimate errors do not depend on the value of disturbances. First, the solvability of the disturbance decoupled secure state estimation problems is analyzed by introducing the concepts of redundantly strong observability and redundantly strong detectability. It is proved that the states can be reconstructed (estimated asymptotically) despite the existence of attacks and disturbances if and only if the system is redundantly strongly observable (redundantly strongly detectable). Second, the design procedure for reconstructing (asymptotically estimating) the states is provided based on the orthogonal projection technique. Specifically, by calculating a sequence of orthogonal projections of the sensors’ measurements, a residual signal is constructed to identify a reliable set for state reconstruction (asymptotic state estimation), and then a least square-based method (an observer-based method) is proposed to reconstruct (asymptotically estimate) the states. Third, the effects of numerical errors on the residual signals are discussed. Finally, two examples are given to validate the effectiveness of the proposed methods.