ATD: Collaborative Research: Mathematical Challenges in Distributed Quickest Detection

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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.