The statistical accuracy of an arctangent bearing estimator

One of the most widely used underwater acoustic sensors in the world is the DIFAR sonobuoy, which consists of an omni-directional hydrophone and two dipole sensors oriented orthogonally. The directional information provided by the dipoles makes it possible to estimate the bearing to an underwater acoustic source. In this paper, the performance of an arctangent bearing estimator is examined for both sinusoidal and Gaussian signals in isotropic Gaussian noise. It is shown that the estimator is unbiased, and exact formulas for the bearing error (variance) are presented. These formulas allow for the case in which multiple data blocks are averaged before forming the bearing estimate. Several examples based on the numerical evaluation of the bearing variance are presented, and the performance is compared with the Cramer-Rao lower bound.