Hill's guidance for pursuing a target on elliptical orbit and analysis of its error

Hill's guidance in elliptical orbit is studied for short range rendezvous of spacecraft. Hill's guidance for pursing a target on arbitrary elliptical orbit is proposed based on the state transition matrix. The analytic expression of the system state with continuous constant thrust is derived. According to this mathematical expression, we analyze the error of Hill's guidance, including the linearization error and J2 perturbation error. Then an improved method of Hill's guidance is designed by error compensation. Simulation results show that the Hill's guidance on elliptical orbit is feasible, and the improved method can further enhance the guidance accuracy.