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.

本文研究了在存在稀疏传感器攻击和未知扰动的情况下线性系统的扰动解耦安全状态估计问题，其中扰动解耦状态估计意味着由此产生的估计误差不依赖于扰动的值。首先，引入冗余强可观测性和冗余强检测性的概念，分析扰动解耦安全状态估计问题的可解性。事实证明，当且仅当系统是冗余强可观察的（冗余强可检测的）时，尽管存在攻击和干扰，但状态可以重建（渐近估计）。第二，基于正交投影技术提供了用于重建（渐近估计）状态的设计程序。具体来说，通过计算传感器测量的一系列正交投影，构造残差信号来识别可靠的状态重建集（渐近状态估计），然后基于最小二乘法（基于观察者的方法）是建议重建（渐近估计）状态。第三，讨论了数值误差对残差信号的影响。最后给出了两个例子来验证所提方法的有效性。然后提出了一种基于最小二乘法（基于观察者的方法）来重建（渐近估计）状态。第三，讨论了数值误差对残差信号的影响。最后给出了两个例子来验证所提方法的有效性。然后提出了一种基于最小二乘法（基于观察者的方法）来重建（渐近估计）状态。第三，讨论了数值误差对残差信号的影响。最后给出了两个例子来验证所提方法的有效性。