ESA/ESOC - Orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. This study had the purpose of developing and testing algorithms and prototype soft- ware to solve the correlation problem for objects in GEO orbit, including the accurate orbit determination by full least squares solutions with all six orbital elements. In the course of the study it was realized that, because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by non-gravitational pertur- bations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. We have tested two algorithms, both with the property of using fewer observations as a minimum to achieve a correlation confirmed by a least squares orbit. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for objects in Earth orbit (as opposed to both interplanetary orbits and sub-orbital ones). The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. The validation of the innovative algorithms and prototype software was based upon a set of real data, acquired from the Optical Ground Station (OGS) by ESA at the Teide observatory (Canary Islands). We used all the data collected in different programs (in- cluding both survey and follow up, of both GEO and GTO orbits) in the year 2007. These data were processed without the correlation information (which was available for some of them, from the work already performed by the AIUB group), and still it was possible to reconstruct from scratch correlation information essentially equivalent to the one obtained by using information coming either from the Two Line Elements or from the observation scheduling (in particular for follow up programs). In conclusion we have proven that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination. As a byproduct of this project, we tested a Data Exchange Standard (DES), slightly modified from one already in use for asteroid optical data, to transmit data between the two groups in Bern and Pisa and with ESOC. A proposal for a formal DES document is given in the appendix to this report.