In this article, we study resilient distributed diffusion for multi-task estimation in the presence of adversaries where networked agents must estimate distinct but correlated states of interest by processing streaming data. We show that in general diffusion strategies are not resilient to malicious agents that do not adhere to the diffusion-based information processing rules. In particular, by exploiting the adaptive weights used for diffusing information, we develop time-dependent attack models that drive normal agents to converge to states selected by the attacker. We show that an attacker that has complete knowledge of the system can always drive its targeted agents to its desired estimates. Moreover, an attacker that does not have complete knowledge of the system including streaming data of targeted agents or the parameters they use in diffusion algorithms, can still be successful in deploying an attack by approximating the needed information. The attack models can be used for both stationary and non-stationary state estimation. In addition, we present and analyze a resilient distributed diffusion algorithm that is resilient to any data falsification attack in which the number of compromised agents in the local neighborhood of a normal agent is bounded. The proposed algorithm guarantees that all normal agents converge to their true target states if appropriate parameters are selected. We also analyze trade-off between the resilience of distributed diffusion and its performance in terms of steady-state mean-square-deviation (MSD) from the correct estimates. Finally, we evaluate the proposed attack models and resilient distributed diffusion algorithm using stationary and non-stationary multi-target localization.

中文翻译：

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具有对手的网络中的弹性分布式扩散

在本文中，我们研究了在存在对手的情况下多任务估计的弹性分布式扩散，其中，网络代理必须通过处理流数据来估计不同但相关的关注状态。我们表明，一般而言，传播策略对不遵守基于传播的信息处理规则的恶意代理没有弹性。特别是，通过利用用于扩散信息的自适应权重，我们开发了与时间有关的攻击模型，该模型驱动正常的代理收敛到攻击者选择的状态。我们表明，对系统有全面了解的攻击者可以始终将其目标代理变为预期的估计值。此外，攻击者不完全了解系统（包括目标代理的流数据或它们在扩散算法中使用的参数），仍然可以通过近似所需的信息来成功部署攻击。攻击模型可用于稳态和非稳态状态估计。此外，我们提出并分析了一种弹性分布式扩散算法，该算法可抵抗任何数据篡改攻击，在这种攻击中，正常代理人本地邻域中受损代理程序的数量受到限制。如果选择了适当的参数，则所提出的算法可确保所有正常代理均收敛至其真实目标状态。我们还根据正确的估计值，根据稳态均方差（MSD）分析了分布扩散的弹性与其性能之间的权衡。最后，我们使用固定和非固定多目标定位来评估所提出的攻击模型和弹性分布式扩散算法。