Underwater localization using an omnidirectional sensor system

This paper investigates the accuracy of locating an underwater acoustic source using the broadband information collected at arbitrarily positioned, submerged, omnidirectional hydrophones. An optimally weighted least square error estimator is used for the localization and the Euclidean variance is used as the measure of performance. Performance comparisons are made between two specific systems: one based on two sensors and the other based on three sensors. It is shown that the Euclidean variance of localization error can be reduced by a few orders of magnitude by adding a third sensor to a two-sensor system providing the third sensor is properly positioned. The main contribution of the paper, which is viewed as being pedagogical, is the explanation of the improved performance. A geometric interpretation is presented to explain the principles involved in this dramatic improvement in the Euclidean variance obtained by adding a third sensor to a two-sensor system. This approach also shows that adding more sensors to an optimally positioned three-sensor cluster does not improve the performance as much as adding the third sensor. The geometric interpretation demonstrates why there is such an improvement using an approach based on the eigenstructure of the sensor system covariance matrices