Addressing Stochastic Consistency for Fusing Absolute and Relative Orbit Determination for Satellite Swarms

Swarms of Earth-orbiting satellites are crucial for a manyfold of applications that serve our society. Those missions rely on precise knowledge of the absolute position of each satellite of the swarm and their relative positions. The state-of-the-art algorithms that obtain independent absolute positioning and relative positioning between two satellites are called the Precise Orbit Determination (POD) and the Precise Baseline Determination (PBD), respectively. Instead of computing multiple PODs and PBDs separately, one could also combine both estimation processes in one large single fusion algorithm, which is an approach that has not been studied in greater detail. We call this fusion the Precise Orbit Determination of Satellite Swarms (PODSS). This paper serves as a proof of concept to demonstrate the feasibility of this approach. We investigate the potential for fusing the solutions of POD and PBD algorithms. Furthermore, relatively straightforward implementation approaches are proposed. Three methods are compared to perform such a fusion at the results level, where existing precise orbit and baseline results are fused. Subsequently, two approaches are discussed to embed the fusion into the framework of existing sequential filters. In addition to demonstrating that the accuracy of the POD of a swarm of satellites can be significantly enhanced, our findings also reveal a more favorable convergence behavior of the filter when operating on the fused states. We would anticipate even better results with a more sophisticated fusion at the observation level.