Tracking a moving vessel from bearing measurements

This paper presents a method for tracking a distant moving target using only bearing measurements obtained from a tracking platform. The method is an improvement of the Hinich-Bloom passive tracking approach presented in [1]. The target is assumed to be moving at constant speed on a fixed heading, whereas the platform maneuvers during the measurement period. The direction cosines of the bearings are computed with respect to a rotation of the coordinate system that places 0° at the mean estimated target bearing. This is done to minimize the approximation bias due to the linearization of sine bearing as a function of inverse range and time. The coordinate system is rotated back to estimate the target coordinates. When the noise is Gaussian, the estimates of target range and heading are approximately maximum likelihood when the target´s relative range is slowly varying during the observation period. In this case the mean square errors of the target parameter estimates are the smallest achievable within the order of the approximation.