IEEE Workshop on Underwater Acoustic Signal Processing, Fall 2001
Title: Information Theory for Source Localization
Author: John R. Buck

Source localization has traditionally been considered as an estimation problem in which the goal is to use the observed pressure field and an acoustic propagation model to estimate an unknown source location with the smallest possible variance [Baggeroer, et al., JASA, 1988]. In many environments, reducing the variance of the estimate is less important than sidelobe suppression. This motivates an alternative perspective in which the search region is divided into a grid whose cell size is dictated by logistical constraints, and the localization algorithm attempts to assign the source to the correct cell with the minimum probability of error. In this approach, the source localization problem can be considered as a communication problem. Specifically, the source is (perhaps unwillingly) transmitting a message whose content is the grid cell it is located in, and the receiver wishes to use the pressure data observed at the array to decode this message with minimal probability of error.

In order to achieve an arbitrarily small probability of error in the grid cell assignment of the source, the Channel Coding Theorem indicates that the mutual information between the pressure observations and the source location must be equal to or greater than the entropy of the source location. The Gaussian channel model provides an upper bound on this mutual information as a function of SNR, which we evaluate in a typical shallow water scenario for both the spatially isotropic and Kuperman-Ingenito noise models. These results provide necessary, but not sufficient conditions, on the average per hydrophone SNR required to achieve a desired range resolution with arbitrarily small probability of choosing a sidelobe of the ambiguity surface. Alternatively, the results may also be formulated to provide a lower bound on the range resolution that may be achieved with arbitrarily small probability of error in choosing the correct source location.

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