Dr. Joshua Horwood, Numerica Corporation

Uncertainty Quantification in Space Situational Awareness

The space situational awareness (SSA) mission encompasses intelligence, reconnaissance of all space objects, and the prediction of space events, possible collisions, threats, and activities. A common requirement for many SSA functions such as tracking, conjunction analysis (probability of collision), and resource management is that of uncertainty quantification (UQ). This talk will provide an overview of some of the key issues and challenges surrounding the problem of UQ including that of properly characterizing the uncertainty in the orbital state of a space object. In particular, a new class of multivariate probability density functions will be introduced called the Gauss von Mises (GVM) family of distributions. The distinguishing feature of the GVM distribution is its definition on a cylindrical manifold, the underlying state space in which systems of orbital element coordinates are more accurately defined. Such coordinates, when used in conjunction with the new GVM distribution, can provide a statistically rigorous treatment of uncertainty needed for uncertainty propagation and non-linear filtering, orbit determination, and tracking. Results will be shown that demonstrate that the uncertainty propagation algorithm implicit in the new GVM filter has the same computational cost as the traditional unscented Kalman filter, with the former capable of maintaining a proper characterization of the uncertainty for up to eight times as long as the latter.

Dr. Horwood graduated from the University of Waterloo (Canada) with a Bachelor's of Mathematics degree in applied math in 2003. He received the Certificate of Advanced Studies in Mathematics in 2004 and the Ph.D. degree in 2008 from the University of Cambridge (UK). His technical background and interests include classical mechanics, astrodynamics, non-linear estimation, and multi-target tracking. In 2009, Dr. Horwood joined Numerica Corporation and is currently engaged in leading and managing the company's program in space situational awareness.