Dr. Jeff Aristoff,  Numerica Corp.

Mathematical Challenges in Space Situational Awareness

Space Situational Awareness (SSA) is the comprehensive knowledge
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.