For the problem of relative navigation for space debris, cubature Kalman filter have been introduced based on the angle measurements and range measurements of on-orbit servicing spacecraft which is a numerical approximation algorithm using cubature law, resolving the problem of target missing with the larger error of initial measurement. In order to improve the field of application, a universal variable state transition equation was adopted to extrapolate the state, avoiding the limitation of near-circle orbit type. The simulation results show that the cubature Kalman filter has higher filtering accuracy and faster convergence speed than traditional extended Kalman filter in the situation of the larger error of initial estimation, which provides a theoretical basis for the implementation of the project in future.