Trajectory optimization using Cramér-Rao lower bound for bearings-only target tracking

Abstract

The paper presents the optimal trajectory with minimum Cramér-Rao Lower Bound (CRLB) for 2D bearings-only target tracking problem. In the bearings-only target tracking problem, the position and velocity of the target is estimated only from the bearing angle information. The CRLB of the given estimation problem is derived. The optimal path is defined as a path that minimizes the weighted sum of CRLB diagonal entries. It is equivalent to the weighted sum of minimum estimation covariances. The optimal control problem is defined by employing UAV dynamic equations of motion. The UAV is assumed to perform subsequent coordinated turns for angle measurements. The optimal lateral acceleration of the UAV is calculated. The advantage of the optimal trajectory is demonstrated and compared through simulated examples. Maximum likelihood estimator is applied in the simulation.