Distributed sequential algorithms for regional source localization

We study the problem of source localization as a multiple hypothesis testing, where each hypothesis corresponds to the event that the source belongs to a particular region. We use sequential hypothesis tests based on posterior computations to solve for the correct hypothesis. Measurements corrupted with noise are used to calculate conditional posteriors. We prove that the regional localization problem has geometric properties that allow correct detection almost surely in the limit of infinite measurements. We present the Sense, Transmit & Test algorithm that allows sequential sensing, communication and testing and we analyze the accuracy of this distributed algorithm and show that the test ends in a finite time. We also present numerical results illustrating properties of the suggested algorithm.