ATD: Collaborative Research: Mathematical Challenges in Distributed Quickest Detection

所提出的研究的目的是通过开发数学和统计工具，包括大量的传感器与异构的变化时间跨传感器的系统，以推进最快的检测的艺术状态。将考虑三个相关的但日益复杂和实用的模型。首先，将放宽所有传感器的变化时间相同的假设。我们的目标是设计最快的检测算法的情况下，传感器和融合中心之间的直接链接，但不同的变化时间。接下来，接入点可以同时观察来自所有传感器的信号的假设将被放宽。我们的目标是开发最快的攻击检测和定位算法的情况下，融合中心只能访问一个子集的传感器在任何给定的时间。最后，假设每个传感器和融合中心之间有一个直接的链接将放宽。利用传感器观测数据的异质性和稀疏性，提出了一种快速的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，所提出的研究有可能大大提高化学和生物威胁检测算法的效率和鲁棒性。它的目的是开发低复杂度的算法，这将是有用的实施。在理论层面上，拟议的项目将推进顺序分析的艺术状态，并为最佳停止和最快检测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检测化学和生物威胁方面，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，通常有一种以上的症状与疾病有关，这些症状不一定同时发生。这项研究的结果可以用来提高医疗诊断技术的性能。拟议研究的应用范围也使其成为吸引从应用数学到工程的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.