Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
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Joshua Horwood
NUMERICA CORPORATION
Sausages, Pancakes, and Bananas: The Diet of Uncertainty Quantification in Space Surveillance
What do the problems of (a) maintaining a catalog of Earthorbiting 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 wellconditioned leading to "sausage" or "pancake" shaped ellipsoids (level sets). In some extreme cases, these ellipsoids can deform into bananashaped 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 twobody 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.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader