Three-spacecraft autonomous orbit determination and observability analysis with inertial angles-only measurements

Autonomous orbit determination (OD) for a group of spacecraft using only inter-spacecraft measurements has considerable value in space systems engineering. This paper proposes a novel solution for cooperative autonomous OD for a system comprised of three spacecraft, by employing inertial angles-only measurements. Based on the two-body dynamics of each spacecraft, the observability problem for the two-spacecraft and three-spacecraft systems is analyzed with the Lie-derivative criterion. It is deduced that the two-spacecraft system is third-order locally weakly unobservable, while the three-spacecraft system with three sets of inter-spacecraft observations is third-order locally weakly observable under certain sufficient conditions. To complement the theoretical analysis, we use a numerical method to compute the observability measure to illustrate the degree of observability. Several scenarios are designed to demonstrate the influence of orbital configurations, of J(2) dynamics, and measurement noise on the degree of observability. In addition, the observability of the three-spacecraft system is also compared with the two-spacecraft system. Finally, practical cases of three-spacecraft autonomous OD are simulated which demonstrate the application and feasibility of the proposed method.