Probabilistic analysis of a passive acoustic diver detection system for optimal sensor placement and extensions to localization and tracking

Our previous work describes a simple algorithm for automated detection of diver presence using a single passive hydrophone. This technique is based on extracting a single feature, the "Swimmer Number", from the hydrophone signal, which correlates with diver presence. At any point in time, diver presence can be automatically determined by thresholding the incoming Swimmer Number at an appropriate level. For this system (and other threshold based detection systems) this paper explains how to calculate the probability of detecting a diver at various ranges from the hydrophone. This function is then used to evaluate the probability of detecting a diver at any point in a region, given an arbitrary number of hydrophones which are scattered in arbitrary positions over the region. We next show how non-linear optimization techniques can be used to find the optimal set of sensor positions, which maximize the detection probability over a region of interest, for a given number of sensors. Lastly, we show how this theory can be incorporated into tracking systems, which estimate the location of a moving diver at any point in time, given the outputs of an arbitrarily positioned set of hydrophones.