Colloquium | Joshua Horwood, Sausages, Pancakes, and Bananas: The Diet of Uncertainty Quantification in Space Surveillance

MC 5417

Speaker

Joshua Horwood
NUMERICA CORPORATION

Title

Sausages, Pancakes, and Bananas: The Diet of Uncertainty Quantification in Space Surveillance

Abstract

What do the problems of (a) maintaining a catalog of Earth-orbiting space objects, (b) computing a probability of collision between two space objects, and (c) determining where to point a sensor to maximize information gain, all have in common? Answer: They are require a faithful representation of the uncertainty in the orbital state of a space object. Traditionally, such uncertainties or probability density functions (PDFs) are represented as multivariate Gaussian distributions. In many cases, the covariance matrix of the Gaussian is not well-conditioned leading to "sausage" or "pancake" shaped ellipsoids (level sets). In some extreme cases, these ellipsoids can deform into banana-shaped level sets.

In this talk, I will review a recently developed PDF called the Gauss von Mises distribution [1] that more faithfully characterizes these orbital uncertainties. I will then describe how a GVM distribution is propagated in time under the perturbed two-body problem of orbital mechanics, in support of the aforementioned problems (a)-(c). Finally, I will demonstrate how one can verify if a propagated GVM distribution is indeed realistic using the framework of empirical distribution function testing.

[1] J. T. Horwood and A. B. Poore, "Gauss von Mises distribution for improved uncertainty realism in space situational awareness," SIAM Journal of Uncertainty Quantification, vol. 2, pp. 276–304, 2014.