Detection and Localization of Material Releases with Sparse Sensor Configurations

We consider the problem of detecting and localizing a material release utilizing sparse sensor measurements. We formulate the problem as one of abrupt change detection. The problem is challenging because of the sparse sensor deployment and complex system dynamics. We restrict ourselves to propagation models consisting of diffusion plus transport according to a Gaussian puff model. We derive optimal inference algorithms, provided the model parametrization is known precisely, within a hybrid detection-localization hypothesis testing framework with linear growth in the hypothesis space. The primary assumptions are that the mean wind field is deterministically known and that the Gaussian puff model is valid. Under these assumptions, we characterize the change in performance of detection, time-to-detection and localization as a function of the number of sensors. We then examine some performance impacts when the underlying dynamical model deviates from the assumed model