We consider remote state estimation in the presence of an active eavesdropper. A sensor forward local state estimates to a remote estimator over a network, which may be eavesdropped by an intelligent adversary. Aiming at improving the eavesdropping performance efficiently, the adversary may adaptively alternate between an eavesdropping and an active mode. In contrast to eavesdropping, the active attack enables the adversary to sabotage the data transfer to the estimator, and improve the data reception to itself at the same time. However, launching active attacks may increase the risk of being detected. As a result, a tradeoff between eavesdropping performance and stealthiness arises. We present a generalized framework for active eavesdropping and propose a criterion based on the packet reception rate at the estimator to evaluate the stealthiness of the eavesdropper. Moreover, the tradeoff is formulated as a constrained Markov decision process. After deriving a sufficient condition under which at least one stationary policy satisfies the stealthiness constraint and also bounds the eavesdropping performance, we develop an optimal attack policy for the eavesdropper and focus on the structural analysis of the optimal policy. Furthermore, numerical examples are provided to illustrate the developed results.

中文翻译：

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存在主动窃听者的远程状态估计

我们考虑在存在主动窃听者的情况下进行远程状态估计。传感器通过网络将本地状态估计转发到远程估计器，这可能会被智能对手窃听。为了有效提高窃听性能，攻击者可以自适应地在窃听和主动模式之间交替。与窃听相反，主动攻击使对手能够破坏到估计器的数据传输，同时改善对自身的数据接收。但是，发起主动攻击可能会增加被检测到的风险。结果，出现了窃听性能和隐蔽性之间的权衡。我们提出了一个用于主动窃听的通用框架，并提出了一个基于估计器的数据包接收率的标准来评估窃听者的隐身性。此外，权衡被表述为受约束的马尔可夫决策过程。在推导出至少一个固定策略满足隐蔽性约束并限制窃听性能的充分条件后，我们为窃听者开发了一种最优攻击策略，并专注于最优策略的结构分析。此外，还提供了数值例子来说明开发的结果。在推导出至少一个固定策略满足隐蔽性约束并限制窃听性能的充分条件后，我们为窃听者开发了一种最优攻击策略，并专注于最优策略的结构分析。此外，还提供了数值例子来说明开发的结果。在推导出至少一个固定策略满足隐蔽性约束并限制窃听性能的充分条件后，我们为窃听者开发了一种最优攻击策略，并专注于最优策略的结构分析。此外，还提供了数值例子来说明开发的结果。