Relative orbit determination for unconnected spacecraft within a constellation

A study proposes an indirect relative orbit determination (OD) method based on spherical geometry to realize relative OD for whole constellations. A link between unconnected spacecraft is first established via an intermediate spacecraft. The relative orbit between the target and intermediate spacecraft is obtained using intersatellite ranging measurements developed earlier. The indirect relative OD method is developed based on spherical trigonometry to obtain the relative orbit of the target spacecraft. The obtainable orbit elements using this proposed method are analyzed in various geometric configurations, and for a different number of intermediated spacecraft. The extension of the proposed method to orbits in perturbed dynamics is discussed.