Estimation theory has been the prevailing paradigm for studying passive SONAR. The position of the contact is an unknown parameter estimated from pressure observations at a hydrophone array and an acoustic propagation model. The performance limit most often cited in this approach is the Cramer-Rao lower bound (CRLB) on the variance of any unbiased estimator, which was evaluated for the passive SONAR problem in [Baggeroer, Kuperman, Schmidt, JASA, 1988]. There are three main reasons that the CRLB is suspect in calculating the limits of passive SONAR performance. First, the CRLB is based on the local curvature of the main lobe of the probability density function. However, in many passive SONAR scenarios, the sharpness of the main lobe is not the primary factor limiting performance, but rather the existence of sidelobes in range-depth space. Second, the CRLB is known to be a high SNR bound, but the current passive SONAR challenges fall in low SNR regimes at longer tactical ranges. Third, the sidelobes in range-depth space introduce ambiguities which imply that the classical estimators used for passive SONAR are biased, and thus the CRLB does not predict their performance. An alternative perspective is to look at the amount of information the array observations contain about the source location, averaged over a large number of contacts. The Gaussian channel model from information theory gives an upper bound on the amount of information the array data will hold given an ensemble of possible source locations. This upper bound on the information, in turn, dictates the maximum number of cells in any grid imposed on the search space. For any gridded search, the relevant performance metric is the probability of error in assigning the source to a grid cell. Any grid whose information entropy exceeds the mutual information available at the array is guaranteed to have its probability of error bounded away from zero. The bound on the information available is a function of SNR as well as the array geometry and acoustic environment. For a given SNR, it is possible to solve for the minimum range cell size allowing for arbitrarily small error probability. Conversely, for a desired range resolution, it is possible to find the minimum per hydrophone SNR necessary to achieve arbitrarily small probability of error.

This material is based upon work supported by the Office of Naval Research under Grant No. N00014-00-1-0379.