This activity aims to provide improved mathematical and algorithmic approaches to propagate orbital uncertainties and to provide ways to map those uncertainties from the phase space, i.e. orbital elements or state vectors to other quantities without assuming simple linear relations between those quantities and phase space. The approaches shall be suitable for at least the propagation of orbital uncertainty for Low-Earth-Orbit (LEO) objects and re-entries of space objects.

Collision avoidance is part of routine operations today. Detailed re-entry predictions and assessment of on-ground risks are regularly performed for high interest objects such as payloads of ESA or its member states. Both activities rely on uncertainty information, which has to be propagated along the trajectory and mapped to quantities which are not state vectors, e.g. collision plane and on-ground location. Current approaches rely on either Monte Carlo methods (with few runs) or propagation of covariance assuming a simple model of the dynamics, in particular of the air drag perturbation. The propagated covariance is then projected linearly on the quantities of interest. Besides the simple modelling of the dynamics, this approach assumes Gaussian uncertainty distribution and propagation and that the uncertainty can be mapped by linear transformation of the covariance matrix. This approach is clearly not appropriate for re-entry predictions but also limits the reliability of collision risk estimates. The study shall provide ways to overcome these shortcomings and therefore it shall encompass the following tasks: 1) Review and analysis task: Mathematical and algorithmic approaches to propagate orbital uncertainties which may initially not be Gaussian and whose evolution depends on dynamical models which are described by parameters and time series of parameters whose uncertainties are not Gaussian either shall be analysed and investigated. Methods to map those uncertainties to other quantities of interest shall also be investigated. 2)Evaluation and test via software prototype: For at least two applications the suitability of the identified approaches shall be analysed and the most promising approach tested in a prototype implementation. The two applications are re-entry predictions with mapping of orbit uncertainty to on ground location and orbit propagation involving time series for collision avoidance with mapping to time of closest approach and collision risk.