ATD: Collaborative Research: Mathematical Challenges in Distributed Quickest Detection

拟议研究的目的是通过为由大量传感器组成的系统开发数学和统计工具来提高最快检测的技术水平，这些系统在传感器之间具有不同的变化时间。将考虑三个相关但日益复杂和实用的模型。首先，所有传感器的改变时间相同的假设将被放宽。目标是为传感器和融合中心之间有直接链接但变化时间不同的场景设计最快的检测算法。下一步，将放宽接入点可以同时观察来自所有传感器的信号的假设。目标是为融合中心在任何给定时间只能访问传感器子集的场景开发最快的攻击检测和定位算法。最后，将放宽每个传感器和融合中心之间存在直接联系的假设。利用传感器观测数据的异构性和稀疏性，开发针对该场景的最快攻击检测和定位算法，具有重要的理论和应用价值。在应用层面上，拟议的研究有可能大幅提高化学和生物威胁检测算法的效率和稳健性。它的目的是开发对实现有用的低复杂性算法。在理论层面上，该项目将推动序列分析技术的发展，并为最优停车和最快检测的控制问题的一般方法学基础提供新的途径。拟议的工作不仅在检测化学和生物威胁方面具有广泛的潜在应用，而且在其他领域也具有广泛的潜在应用。例如，在医学诊断中，与一种疾病相关的症状往往不止一个，这些症状不一定同时发生。这项研究的结果可以用于提高医疗诊断技术的性能。拟议研究的广泛应用也使这一主题成为吸引从应用数学到工程等不同学科和背景的学生的理想话题。

The aim of the proposed research is to advance the state of the art of quickest detection by developing mathematical and statistical tools for systems consisting of large numbers of sensors with heterogeneous change times across sensors. Three related yet increasingly complicated and practical models will be considered. First, the assumption that the change times are the same at all sensors will be relaxed. The goal is to design quickest detection algorithms for the scenario with direct links between the sensors and the fusion center but with different change times. Next, the assumption that the access point can observe signals from all the sensors simultaneously will be relaxed. The goal is to develop quickest attack detection and localization algorithms for the scenario in which the fusion center can access only a subset of sensors at any given time. Finally, the assumption that there is a direct link between each sensor and the fusion center will be relaxed. The heterogeneity and sparsity of sensor observations will be exploited to develop quickest attack detection and localization algorithms for this scenario.The proposed research is expected to make substantial contributions to both applications and theory. On the application level, the proposed research has the potential to substantially improve the efficiency and robustness of chemical and biological threat detection algorithms. It is meant to develop lowcomplexity algorithms that will be useful for implementation. On the theoretical level, the proposed project will advance the state of the art of sequential analysis and contribute new approaches to the general methodological base for optimal stopping and control problems for quickest detection. The proposed work has widespread potential applications not only in the detection of chemical and biological threats but also other areas as well. For example, in medical diagnosis, there are often more than one symptom related to a disease and these symptoms do not necessarily occur at the same time. The results of this research can be used to improve the performance of medical diagnostic techniques. The breadth of applications of the proposed research also makes this an ideal topic for attracting students from diverse disciplines and backgrounds from applied mathematics to engineering.