Abstract
The determination of the state of resident space objects (RSOs) is fundamental to maintain a collision-free environment in space, predict space events and perform space activities. Due to the development of new sensor technologies and the ever-growing number of RSOs, the number of observations available is increasing by the day. In addition, the nature of the observations makes it very difficult to obtain a precise state of the object with only one passage of the object over the observing station. For this reason, the problem of data association becomes relevant: one has to find multiple observations of the same RSO to precisely determine its orbit. Depending on the length and precision of observations, dedicated solutions need to be developed. In this research uncertainty regions associated to the states of RSOs are semi-analytically defined through Taylor expansions, thus making not necessary point-wise sampling or dynamics simplification. This is enabled by differential algebra (DA). For very short and/or uncertain observations, a DA version of the Admissible Region (AR) from literature is defined and an efficient filter is developed for the automatic recognition of chains of observations. This filter includes a new figure of merit (FoM) for the association problem based on range intersection. When observations are long enough to allow for an initial orbit determination (IOD) solution, a new algorithm which defines the uncertainty region without a-priori constraints is developed. The main result within this framework is the definition of a clear working boundary between AR and IOD approaches depending on the optical observing strategy adopted. An advanced Monte Carlo simulation (MCS) is then employed to perform data association as intersection of the uncertainty regions defined. For longer observations where orbit determination (OD) can be performed, an optimisation routine which decouples the principal directions of the uncertainty is developed for efficient propagation and uncertainty update. Results show that the decoupling alleviates the necessity of tuning the FoM for association. Finally, the influence of different coordinate systems on uncertainty propagation is studied. It is found that not only the computation time is affected, but the absorbtion of nonlinearities in the dynamics is highly dependent on the integration variable chosen.