Unbiased Bearing-Only Localization and Circumnavigation of a Constant Velocity Target

This paper studies the problem of controlling an autonomous vehicle (the agent) to localize and circumnavigate an unknown target (which can be an Unmanned Ground Vehicle or an Unmanned Surface Vehicle) moving with a constant but also unknown velocity. We suppose that the agent can only measure the bearings to the target. An adaptive estimation algorithm using only bearing measurements (without explicit differentiation) is proposed to simultaneously estimate the position and the velocity of the target. Unlike existing results, unbiased target estimation is attained such that the estimation errors in both target's position and velocity converge to zero. The proposed target estimator also does not explicitly demand persistent excitation, a condition commonly required by most bearing-based localization methods in the literature. Then, a circumnavigation controller is designed to steer the agent to approach and encircle the target at a prescribed distance. Asymptotic stability of the overall system including the target estimator and circumnavigation controller is rigorously analyzed. Numerical simulations verify the performance of the proposed algorithms.