Research on observability analysis-based autonomous navigation method for deep space

In this paper, the autonomous navigation approaches for different observation models are studied based on observability analysis. Based on the observability analysis of the nonlinear system, the observability matrix is derived from the theory of differential geometry. Then, a method for measuring the observability index of the system is derived, and the analytical method of the observability index for state variable is given. The principle is applied in the autonomous navigation system for deep space. The observability indexes of navigation system corresponding to different observation models are studied, and the observability indexes of the orbital elements are investigated. The result of the observability analysis is used as a selection criterion of the observation model used in the navigation system. And then, the navigation approaches under different observation models are established by utilizing the extended Kalman filter. Finally, the autonomous navigation approach presented in the paper is validated by the practical data of a deep impact mission. The relation between the observability index of the navigation system and the estimation accuracy of orbit elements is verified, and the method of observability analysis is demonstrated to be feasible.