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

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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.