Robust UAV Search for Environments with Imprecise Probability Maps

This paper introduces a new framework for UAV search operations and proposes a new approach to calculate the minimum number of looks needed to achieve a given level of confidence of target existence in an uncertain gridded environment. Typical search theory formulations describe the uncertainty in the environment in a probabilistic fashion, by assigning probabilities of target existence to the individual cells of the grid. While assumed to be precisely known in the search theory literature, these probabilities are often the result of prior information and intelligence, and will likely be poorly known. The approach taken in this paper models this imprecise knowledge of the prior probabilities in the individual cells using the Beta distribution and generates search actions that are robust to the uncertainty. Use of the Beta distribution leads to an analytical prediction of the number of looks in a particular cell that would be needed to achieve a specified threshold in the confidence of target existence. The analytical results are demonstrated in both an expected value setting and a framework that takes into account the variance of the posterior distribution. The effectiveness of the proposed framework is demonstrated in several numerical simulations.