Observability analysis of cooperative orbit determination using inertial inter-spacecraft angle measurements

The cooperative orbit determination (OD) using inertial inter-spacecraft measurements is of great value for the constellation. Previous studies concluded that the cooperative OD system in the two-body dynamics is observable using the inertial angle measurement. This paper performs an observability analysis for the inertial angle-only cooperative OD system based on the observability matrix (OM), and finds that the previous conclusions do not hold for some special configurations. Eight special configurations are proposed, and for each configuration, the unobservable orbit elements are analytically revealed by analyzing the linear relationship among different columns of the OM. Moreover, a method of improving the observability of the two-spacecraft system is proposed by adding another spacecraft. An extended Kalman filter is employed to numerically illustrate the observability of the proposed special configurations and to show the relationship between the observability and the convergence ratio of estimations. Monte Carlo simulations show that the convergence ratios of the observable orbit elements and state combinations are higher than 97%, while convergence ratios of the unobservable states are lower than 70%. With one non-planar elliptic orbit added, all the elements of the three-spacecraft system are observable, and the estimated errors converge within 6 h. The results found in this paper can provide a reference for the design and management of the constellation.