Observability analysis and optimal beacon selection for angles-only orbit determination

The optical angle measurement is widely used in autonomous orbit determination for deep-space probes. The orbit determination accuracy depends on the geometric configuration of observation beacons. Considering the observability metrics, this paper proposes an optimal observation beacon selection method based on the Fisher information matrix. First, the Fisher information matrix regarding probe position in two forms is provided, and the observability and observability degree of the system are analyzed. Second, to rapidly and reliably assess the amount of observation information, optimal beacon selection criteria are proposed based on the trace of the Fisher information matrix, and combinatorial optimization problems are solved under various scenarios. Third, the bounds and their influencing factors of state estimation error are further evaluated, and the parameter sensitivity in the unobservable case is investigated. Finally, the proposed method is applied to multiple scenarios. Numerical simulations verify its feasibility and stability. In triangulation, the positioning error based on optimal beacon pairs is at least 35% lower than that using other planetary pairs. The optimization efficiency of beacon selection can be increased by 20% compared to the covariance matrix-based method. For filtering estimation, the candidate beacon combinations that can ensure high filtering accuracy can be screened more efficiently. The proposed method can effectively enhance the performance of deep-space autonomous optical orbit determination and holds promising application prospects for future deep-space exploration missions.