Population orbit determination: Algorithms and Simulations

The thesis deals with the problem of population orbit determination for uncollaborative objects, when observations are a scarce resource. In this case we not only have to find an orbit compatible with the observations, but also to solve the identification problem, i.e., finding among independent detections of celestial bodies those belonging to the same physical object. After reviewing classical methods, we describe a full sequence of algorithms allowing build-up and maintenance of a catalog of objects starting from a database of observations. The most difficult step is the linkage, when two or more separate sets of observations are used to assess whether they can belong to the same object and an orbit exists to fit the data. We present two algorithms capable of dealing with the linkage and of keeping the computational load within acceptable limits. The first algorithm is based on the admissible region, which bounds the set of possible orbits by reasonable hypotheses on the dynamics of the object. The second algorithm relies on the conservation of the integrals of motion of the Kepler problem. To test these algorithms we applied them to different classes of objects: 1) we showed that it is possible to build up a catalog of Geosynchronous debris from scratch starting from sparse real data; 2) we performed catalog build-up and maintenance for Low Earth orbit debris starting from simulated data and keeping the orbit accuracy within the collision avoidance requirements; 3) we simulated the discovery and risk assessment process for a population of small impacting Near Earth Objects; 4) we successfully attributed Pan-STARRS PS1 data to numbered and multi-apparition asteroids, and performed a statistical analysis of the postfit residuals. The performed simulations validated not only the algorithms, but also hypothetical optical networks proposed in the Space Situational Awareness framework.