This paper studies static state estimation in multi-sensor settings, with a caveat that an unknown subset of the sensors are compromised by an adversary, whose measurements can be manipulated arbitrarily. The attacker is able to compromise $q$ out of $m$ sensors. A new performance metric, which quantifies the asymptotic decay rate for the probability of having an estimation error larger than $\delta$, is proposed. We develop an optimal estimator for the new performance metric with a fixed $\delta$, which is the Chebyshev center of a union of ellipsoids. We further provide an estimator that is optimal for every $\delta$, for the special case where the sensors are homogeneous. Numerical examples are given to elaborate the results.

中文翻译：

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使用拜占庭传感器进行安全状态估计：一种概率方法

本文研究了多传感器设置中的静态估计，但需要注意的是，传感器的未知子集会被对手破坏，其测量值可以被任意操纵。攻击者能够从 $m$ 个传感器中破坏 $q$。提出了一种新的性能指标，该指标量化了估计误差大于 $\delta$ 的概率的渐近衰减率。我们为具有固定 $\delta$ 的新性能指标开发了一个最佳估计器，这是椭球并集的切比雪夫中心。我们进一步提供了一个对于每个 $\delta$ 都是最优的估计器，对于传感器是同质的特殊情况。给出了数值例子来阐述结果。