of the near-Earth space environment accomplished through the tracking and

identification of Earth-orbiting space objects (satellites, debris) needed

to protect space assets and maintain awareness of potentially adversarial

space deployments. Fundamental to SSA are the problems of data/track

association (correlation), nonlinear estimation (data fusion), conjunction

analysis (probability of collision), and maneuver detection. Common

amongst these challenges is the need to predict the future location of an

orbiting object (i.e., orbit propagation) while correctly managing and

representing its uncertainty.

Efficiently and accurately modeling trajectories of the vast number of

objects in orbit around the Earth is difficult because the equations of

motion are nonlinear, the infrequency of observations may require modeling

trajectories over long periods of time, and the number of objects to be

modeled is on the order of 10^5 and growing owing to object breakups and

improved sensors. In this talk, I will present a new technique for

propagating orbits in the presence of uncertain initial conditions and

dynamics, and demonstrate how this technique can be applied to problems

that arise in other fields. The broader mathematical challenges in SSA

will also be discussed.