Initial Orbit Determination Based on Propagation of Orbit Sets with Differential Algebra

The object of this paper is the initial orbit determination of an orbit set compatible with an observational arc by means of differential algebra. The initial estimate is retrieved as a truncated power series expanded with respect to the uncertainties in the measurements. The analysis of the region is performed with the automatic domain splitting, that splits the orbit set into two or more regions defined by just as many Taylor expansions when the estimated truncation error introduced by the truncated power series exceeds a certain tolerance. A comparison between the proposed initial orbit determination approach and alternative methods from the literature is included to show the improvements achieved by exploiting accuracy information using differential algebra. The goal of the description of the initial orbit determination solution as orbit set is to propagate several independent orbit set to a common epoch and analyze them to decide whether they’re correlated or not. Initial results for the linkage of two independent observations are also included.