Geometrical interpretation of the localization performance of a sonobuoy system

This is an explorative paper which focuses on the accuracy of locating an underwater acoustic source using the broadband information collected at arbitrarily positioned, submerged, omnidirectional hydrophones. The paper presents expressions for the localization-error covariance of an optimally weighted least-square-error estimator for two sources of error: ocean acoustic noise and sensor perturbations. The performance measure used for comparisons is the mean square euclidean localization error, which is the trace of the localization-error covariance matrix. Comparisons of performance are made between two specific systems: one based on two sensors and the other based on three sensors. The main contribution of the paper is the explanation of the improved performance obtained by using a geometric approach to visualize the localization error. This geometric interpretation method is demonstrated by an explanation of the principles involved in the dramatic improvement in the mean square euclidean error obtained by adding a third sensor to a two-sensor system. The geometric interpretation is an approach based on the eigen structure of the sensor-system covariance matrices. This is a very useful tool for visualizing the localization error for any arbitrary source-sensor configuration.