In this article, we consider the security problem for the consensus-based distributed state estimation. To resist the malicious attacker who can falsify the data transmitted through the wireless channel, each node equips with an attack defender, which is based on the measurement of its built-in sensor. Under the stealthy attack, which can deceive the defender, we investigate the resilience and convergence of the distributed estimation in two different attack scenarios. For the attack with enough communication resources, we provide a sufficient condition of the optimal attack to quantify the maximum estimation performance degradation. We also analyze the resilience of the worst case distributed estimation caused by the attacker. For the attack with limited resources, the optimal Kalman gain for each node is derived to maximize its estimation performance under the attack. We also give a sufficient condition to guarantee the convergence of the distributed estimation in this case. Finally, numerical simulations are provided to illustrate the effect of the defender on guaranteeing the resilience of sensor networks against attacks.

中文翻译：

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基于弹性共识的分布式过滤：隐形攻击下的收敛分析


在本文中，我们考虑基于共识的分布式状态估计的安全问题。为了抵御可以伪造通过无线通道传输的数据的恶意攻击者，每个节点都配备了一个基于其内置传感器测量的攻击防御器。在可以欺骗防御者的隐形攻击下，我们研究了两种不同攻击场景下分布式估计的弹性和收敛性。对于具有足够通信资源的攻击，我们提供了最优攻击的充分条件来量化最大估计性能下降。我们还分析了攻击者造成的最坏情况分布式估计的弹性。对于资源有限的攻击，导出每个节点的最优卡尔曼增益，以最大化其在攻击下的估计性能。我们还给出了保证这种情况下分布式估计收敛的充分条件。最后，提供数值模拟来说明防御者在保证传感器网络抵御攻击的弹性方面的作用。