Ground-based orbit determination for spacecraft formations

Spacecraft formations offer interesting challenges to orbit determination, especially for ground-based tracking. In fact, the limited distances between spacecraft and the possible ambiguity of the observables gathered from the ground have an impact on the solution process. The paper aims to apply the filtering techniques on a refined dynamical model, which can include the main perturbation effects - due to the oblateness of the Earth and, at the lower altitudes, the air drag - on spacecraft trajectories, representing them in series with a remarkably limited number of terms even in eccentric case. The idea is to focus on theoretically expected behavior rather than dealing with an enriched but heavier state including parameters directly related to the perturbing effects. In such a way, it could be possible to obtain a good estimate even with limited spacecraft tracking information. This is an important asset in navigating a formation from the Earth, due to the needed partition of ground station resources among different platforms belonging to the formation, and to the possible ambiguity among the measurements, which further reduce the available data. The specific nature of the dynamic model calls for an estimator with a flexible and ?open? architecture, easily allowing for changes and additions in the model itself. Therefore, the estimator selected for testing the approach has been the Unscented Kalman Filter, versatile enough to allow for increasing model accuracy without the need for tedious computation of the Jacobian. This approach is also intended to offer a different way to investigate special perturbed configurations, via the semi-analytical and almost exact representation of the trajectories. In such a perspective, one of the first application, which is shortly outlined in the paper, will be the analysis of spacecraft formations under the J2 effect. In fact, recent studies identified a set of almost periodic relative configurations among the spacecraft. This set (sometimes referred as the special or magical inclination's one) has been recently identified by means of numeric search, and has also received some (partial) explanation. Due to the interest in control effort reduction, it is deemed that a better understanding of this special dynamics, possibly provided by means of a selected modeling approach, can be of some interest.