This paper studies the problem of distributed resilient state estimation (RSE) for linear measurement models in the presence of locally-bounded Byzantine nodes that may arbitrarily deviate from the prescribed update rule. Necessary and sufficient conditions for the existence of a distributed algorithm to solve the RSE problem in the almost sure sense are characterized in term of the topology-associated robustly collective observability. Under these conditions, a distributed projected stochastic resilient filtering algorithm is proposed. Compared with the existing results where asymptotic or probabilistic finite-time analysis is established, the exponential convergence (in sense of mean square) of the proposed algorithm is proved. To further improve computational performance of the algorithm, an adaptive event-triggered mechanism is constructed without compromising its correctness of the estimate.

中文翻译：

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拜占庭弹性分布式状态估计的均方指数收敛

本文研究了在存在可能任意偏离规定更新规则的局部有界拜占庭节点的情况下线性测量模型的分布式弹性状态估计（RSE）问题。在几乎确定的意义上解决 RSE 问题的分布式算法的存在的必要和充分条件是用拓扑相关的鲁棒集体可观测性来表征的。在此条件下，提出了一种分布式投影随机弹性滤波算法。与已有的渐近或概率有限时间分析的结果相比，证明了该算法的指数收敛性（均方意义上）。为了进一步提高算法的计算性能，在不影响估计正确性的情况下，构建了自适应事件触发机制。