Uncertainty propagation and conjunction assessment for resident space objects

Presently, the catalog of Resident Space Objects (RSOs) in Earth orbit tracked by the U.S. Space Surveillance Network (SSN) is greater than 21,000 objects. The size of the catalog continues to grow due to an increasing number of launches, improved tracking capabilities, and in some cases, collisions. Simply propagating the states of these RSOs is a computational burden, while additionally propagating the uncertainty distributions of the RSOs and computing collision probabilities increases the computational burden by at least an order of magnitude.

Tools are developed that propagate the uncertainty of RSOs with Gaussian initial uncertainty from epoch until a close approach. The number of possible elements in the form of a precomputed library, in a Gaussian Mixture Model (GMM) has been increased and the strategy for multivariate problems has been formalized. The accuracy of a GMM is increased by propagating each element by a Polynomial Chaos Expansion (PCE). Both techniques reduce the number of function evaluations required for uncertainty propagation and result in a sliding scale where accuracy can be improved at the cost of increased computation time. A parallel implementation of the accurate benchmark Monte Carlo (MC) technique has been developed on the Graphics Processing Unit (GPU) that is capable of using samples from any uncertainty propagation technique to compute the collision probability. The GPU MC tool delivers up to two orders of magnitude speedups compared to a serial CPU implementation. Finally, a CPU implementation of the collision probability computations using Cartesian coordinates requires orders of magnitude fewer function evaluations compared to a MC run.

Fast computation of the inherent nonlinear growth of the uncertainty distribution in orbital mechanics and accurately computing the collision probability is essential for maintaining a future space catalog and for preventing an uncontrolled growth in the debris population. The uncertainty propagation and collision probability computation methods and algorithms developed here are capable of running on personal workstations and stand to benefit users ranging from national space surveillance agencies to private satellite operators. The developed techniques are also applicable for many general uncertainty quantification and nonlinear estimation problems.