ATD: Collaborative Research: Mathematical Challenges in Distributed Quickest Detection

所提出的研究的目的是通过开发由大量传感器组成的系统的数学和统计工具来提高最快检测的技术水平，这些传感器具有不同的变化时间。本文将考虑三个相关但日益复杂和实用的模型。首先，所有传感器的变化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直接连接但具有不同变化时间的场景设计最快的检测算法。其次，放宽接入点可以同时观察到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，假设在每个传感器和融合中心之间有一个直接的连接将被放松。传感器观测的异质性和稀疏性将被用来开发针对这种情况的最快的攻击检测和定位算法。本研究可望在应用和理论两方面作出重大贡献。在应用层面上，本研究有可能大幅提高化学和生物威胁检测算法的效率和鲁棒性。它旨在开发对实现有用的低复杂度算法。在理论层面上，提议的项目将推进顺序分析的最新技术，并为快速检测最佳停止和控制问题的一般方法基础提供新的方法。所提出的工作不仅在化学和生物威胁的检测方面，而且在其他领域也有广泛的潜在应用。例如，在医学诊断中，与疾病相关的症状往往不止一种，而且这些症状不一定同时发生。本研究结果可用于提高医学诊断技术的性能。拟议研究的应用广度也使其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主题。

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.