Trajectory optimization for rendezvous with bearing-only tracking

In this paper a bearing-only tracking system for spacecraft rendezvous is proposed. The observability of the system is analyzed and the trajectory optimization algorithms to enhance the observability of the spacecraft rendezvous are presented. Firstly, the relative dynamic model and measurement model are established, and the necessary and sufficient condition for the observability when maneuvering is quantitatively determined using the pseudo linear method. Then, a Kalman filter is used to obtain the optimal estimation of the states according to the observation data. The relevant parameters in the filtering process are optimized to generate the trajectory with maximum observability. Two optimization algorithms are presented, including minimizing the filter covariance matrix trace and maximizing the Fisher information matrix determinant. Numerical results show that the combination optimization of the observability and fuel consumption can generate an optimal control trajectory with high tracking precision.