Trajectory Optimization for Unknown Maneuvering Target Tracking with Bearing-only Measurements

This paper studies trajectory optimization of an autonomous underwater vehicle (AUV) to track an unknown maneuvering target both in the 2D and 3D space. Due to the restrictions on sensing capabilities in the underwater scenario, the AUV is limited to collecting only bearing measurements to the target. A framework called {\it GP-based Bearing-only Tracking (GBT)} is proposed with integration of online learning and planning. First, a Gaussian process learning method is proposed for the AUV to handle unknown target motion, wherein pseudo linear transformation of bearing measurements is introduced to address nonlinearity of bearings. A probabilistic bearing-data-dependent bound on tracking error is then rigorously established. Based on it, optimal desired bearings that can reduce tracking uncertainty are obtained analytically. Finally, the trajectory optimization problem is formulated and transformed into an easily solved one with parametric transformation. Numerical examples and comparison with existing methods verify the feasibility and superior performance of our proposed framework.