Resident Space Object Tracking and Classification Using Methods in Geometric Statistics and Computational Topology
Abstract
An important first step in the classification of space objects is mathematically formalizing the space in which these objects reside. For ease of implementation, most tracking algorithms used by the space situational awareness community employ linear Gaussian approximations to nonlinear perturbations and uncertainties in Euclidean space. While such approximations have been found to perform sufficiently well over short time periods, satellites can often go weeks in orbit between observations and measurement updates. It is during this time period that nonlinearities in uncertainty propagate to non negligible proportions, especially due to its representation in Cartesian coordinates. Further to this last point, the constantly changing nature of the time dependent state makes direct comparison of states on two separate objects meaningless. Therefore, to perform classification, object trajectories with stable, slow moving parameters must be compared via a metric on trajectory space. Since the space of Keplerian1 trajectories is not homeomorphic to R6, there is no single set of 6 elements that uniquely describe all trajectories without singularities. The space must therefore be either embedded in higher dimensions, or several coordinate charts must be used with topology taken into consideration during coordinate transformations. The objective of this research is to determine rigorous methods to quantifiably compare two or more resident space objects on the global space of trajectories for use in tracking and classification.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 14, 2022
- Source ID
- FA95501910262
Entities
People
- Moriba Jah
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Texas at Austin