Online Spatiotemporal Filtering and Bayesian Topology for Tracking in Dynamically Designed Sensor Networks

本课题主要研究实时设计的传感器网络中威胁轨迹的预测问题。传感器网络便于在不同环境中收集信息。这些信息的质量取决于网络的设计，而网络的设计又与网络的覆盖和在线可预测性有关。事实上，传感器网络容易受到时空上不可预测的威胁，如果不及时检测和监控，可能会产生毁灭性的社会经济影响。该项目将同源技术与数据同化相结合，建立了一种在线设计传感器网络的新方法，其覆盖范围可以被实时查询，以及(Ii)使用创新的序贯经验贝叶斯方案来预测网络中时空动态对象的运动轨迹。通过计算持久性图空间的分布，在新的概率设置下验证网络的覆盖率。在吸收收集的数据并估计与网络中时空不确定性相关的参数后，实时设计作为潜在的后验滤波分布的函数，与威胁的潜在运动相关。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project focuses on the problem of predicting threats' trajectories in realtime designed sensor networks. Sensor networks facilitate the collection of information in different environments. The quality of this information relies on the design of the network, which in turn is associated with the network's coverage and online predictability. Indeed, sensor networks are prone to threats, which are quite spatiotemporally unpredictable, and if they are not detected and monitored promptly, they may have a devastating socioeconomic impact.This project engages homological techniques with data assimilation to (i) establish a novel method for online designing a sensor network whose coverage is queried in real time, and (ii) predict trajectories of spatiotemporally dynamic objects moving in the network using an innovative sequential empirical Bayes scheme. The coverage of the network is verified within a new probabilistic setting in the space of persistence diagrams by computing their distribution. Assimilating the collected data and estimating the parameters associated with spatiotemporal uncertainty in the network, the real-time design is derived as a function of the underlying posterior filtering distribution, related to the threats' underlying motion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.