Optimal observer trajectories for passive target localization using bearing-only measurements

Bearing-only target localization is a classical nonlinear estimation problem, which has continued to be of theoretical and practical interest over the last five decades. The problem is to estimate the location of a fixed target, based on a sequence of noisy, passive bearing measurements, acquired by a sensor mounted onboard a moving observer. Although this process is, in theory, observable even without an observer maneuver, estimation performance (i.e., accuracy, stability and convergence rate) can be greatly enhanced by properly exploiting observer motion to increase observability. This paper addresses the problem of determining optimal observer trajectories for bearings-only fixed-target localization. The approach presented herein is based on maximizing the determinant of the Fisher information matrix (FIM), while taking into account various constraints imposed on the observer trajectory (e.g., by the target defense system). Gradient based numericl schemes, as well as a recently introduced method based on differential inclusion, are used to solve the resulting optimal control problem. Computer simulations, utilizing the familiar maximum likelihood (ML) and Stansfield estimators, are presented, which demonstrate the enhancement to target position estimability using the optimal observer trajectories.