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

本计画主要研究在即时设计感测网路中，如何预测威胁的移动轨迹。传感器网络有助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范围和在线可预测性有关。事实上，传感器网络很容易受到威胁，这是相当时空不可预测的，如果他们没有及时检测和监测，他们可能会有一个毁灭性的社会经济影响。本项目采用同源技术与数据同化（i）建立一个新的方法，在线设计一个传感器网络，其覆盖范围是查询在真实的时间，以及（ii）使用创新的顺序经验贝叶斯方案来预测在网络中移动的时空动态对象的轨迹。通过计算持久性图的分布，在持久性图空间中的新概率设置内验证网络的覆盖范围。同化收集的数据和估计的参数与时空的不确定性在网络中，实时设计是作为一个功能的潜在的后验滤波分布，有关的威胁'潜在的motion.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.