Tacking the association and tracking problems using directional statistics to model uncertainty

Paper number

IAC-18,A6,IP,9,x45085

Author

Mr. Shambo Bhattacharjee, United Kingdom, University of Leeds

Coauthor

Prof. John T Kent, United Kingdom, University of Leeds

Coauthor

Mr. Weston Faber, United States, Applied Defense Solutions, Inc.

Coauthor

Dr. Islam Hussein, United States, Applied Defense Solutions, Inc.

Coauthor

Prof. Moriba Jah, United States, The University of Texas at Austin

Year

2018

Abstract

One of the main concerns in space situational awareness is to keep
track of the large number of resident space objects (RSOs), both
satellites and debris, orbiting the earth.  Observations typically
take the form of angles-only measurements from ground-based
telescopes.  Two specific tasks are the identification of objects and
the tracking of objects.  Ideas from directional statistics have been
developed recently to help tackle both of these problems.  The first
contribution is a new ``Fisher-Bingham-Kent (FBK)'' distribution on the unit sphere, which often can be used to describe the predicted angular
position and its uncertainty at a specific time of an RSO.  A key
property of the distribution is that it can describe uncertainty
tightly spread along an arc of a great circle.  The FBK distribution
has proved very useful for the association problem in which an
observation at a particular time might be compatible with the
predicted positions (plus uncertainties) of two or more objects in a
catalog or library.  It is desired, if possible, to associate the
observation with just one of the objects.

A second problem is tracking or filtering.  The objective is to update
successively the prediction of the state (plus uncertainty) of an RSO
as new observations are made.  Under an assumption of Gaussianity, the
problem can be tackled using Kalman filter ideas.  Unfortunately, the
Gaussianity assumption can fail badly using standard coordinate
systems in astrodynamics (such as earth-centered inertial, Keplerian
and equinoctial).  A new ``Adapted STructural (AST)'' coordinate system
has been developed, under which approximate Gaussianity hold under a
wide range of circumstances.  An unscented Kalman filter in AST
coordinates (UKF-AST) has been successfully implemented. Further, the AST-UKF is computationally much faster than particle filters.

Abstract document

IAC-18,A6,IP,9,x45085.brief.pdf

Manuscript document

IAC-18,A6,IP,9,x45085.pdf (🔒 authorized access only).

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