Closed-Loop Rendezvous Guidance for Enhancing Observability in Bearings-Only Navigation

Abstract

A simple closed-loop guidance law for spacecraft rendezvous is proposed to enhance observability in bearings-only navigation. A general observability metric that is Fisher information matrix is utilized in quantifying the observability. In this paper, the optimal delta-v is obtained at each maneuvering time step to maximize the objective function. The objective function consists of three sub-goals; maximizing observability, satisfying the final boundary condition, and avoiding a collision to the chief spacecraft. The proposed guidance law can provide a simpler and more intuitive delta-v command, compared to previous all-time or receding horizon optimal solutions. In addition, the proposed guidance law can be easily synthesized as a guidance and navigation coupled algorithm because the optimal delta-v can be readily updated according to the change of current position and velocity estimates. Numerical simulations demonstrate that the proposed law can enhance observability compared to the traditional two-impulse rendezvous and exhibits a model-error robust behavior compared to the open-loop guidance law. A contour of FIM and a reachable space are newly defined and used to visually analyze the obtained results.