This paper proposes two distributed state estimation protocols for static linear cyber–physical systems under Byzantine links/nodes caused by adversarial attacks. First, a basic version of secure distributed algorithm is proposed where the influence of the Byzantine links/nodes is countered by adopting a local min-switching decision (LMSD) rather than the existing coordinate-wise trimmed means (CWTM). Necessary and sufficient conditions on the network connectivity are provided to guarantee all the regular nodes asymptotically converge to the least square estimate of the system state in the presence of a certain number of Byzantine links/nodes and sensor noises. Further, by adopting event-triggered and minimum subset decision techniques, an improved low-complexity algorithm is proposed that allows the LMSD to be intermittently performed with average linear complexity. A main advantage over the existing CWTM-based algorithms is the use of the LMSD mechanism to significantly reduce the network connectivity requirements and do not assume any observability conditions on the local nodes.

本文提出了由对抗性攻击引起的拜占庭链路/节点下的静态线性网络物理系统的两种分布式状态估计协议。首先，提出了一种安全分布式算法的基本版本，其中通过采用局部最小切换决策（LMSD）而非现有的按坐标调整的方法（CWTM）来抵消拜占庭链路/节点的影响。提供了网络连接的充要条件，以确保在存在一定数量的拜占庭链接/节点和传感器噪声的情况下，所有常规节点都渐近收敛至系统状态的最小二乘估计。此外，通过采用事件触发和最小子集决策技术，提出了一种改进的低复杂度算法，该算法允许以平均线性复杂度间歇地执行LMSD。相对于现有的基于CWTM的算法，主要优点是使用LMSD机制可以显着降低网络连接要求，并且在本地节点上不承担任何可观察性条件。