Information theoretic bounds on source localization performance

This paper examines the underwater acoustic source localization problem as an unorthodox communication problem. This perspective produces novel bounds on the performance of any source localization algorithm. The search space is divided into a grid whose cell size is determined by operational constraints. The message transmitted by the source is the cell it is located within. The receiver uses pressure observations from a sensor array to receive this message with a minimum probability of error. A necessary condition to choose the correct grid cell with arbitrarily small positive probability of error is that the mutual information between the source location and the estimate of it must equal or exceed the entropy of the grid. This mutual information can be bounded from above using the Gaussian channel approximation. The source channel coding theorem then determines the minimum necessary SNR to achieve a desired range resolution, or equivalently the best possible range resolution for a given SNR, assuming arbitrarily small probability of error. The resulting resolution bound is discussed in comparison to the Cramer-Rao Bound. The resolution bound is computed for typical underwater environments, and Monte-Carlo experiments are presented for these same environments.