Revisiting the filtering problem

Paper number

IAC-19,A6,7,6,x50344

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.

Year

2019

Abstract

Consider a space object in orbit about the earth and suppose a
sequence of angles only measurements is available at known times. The
objective of the filtering problem is to successively update the
predicted distribution of the state of the orbiting object.  Each
overall step of the filtering algorithm includes two parts: a
propagation step and an update step.  These tasks are simplest if the
distribution of the propagated state vector and the measurement can be
described in terms of Gaussian distributions, so that a variant of the
classic Kalman filter can be used.  It is well-known that ECI
coordinates are unsuited for this purpose since the distribution of
propagated position vector can have a pronounced banana shape (and
hence is non-Gaussian) for large propagation times.  A better
coordinate system is given by equinoctial coordinates, which perform
well in many (but not all) circumstances.  Equinoctial coordinates
depend on a ``reference plane'', typically taken to be the equatorial
plane.

In this paper, we explore the use of a recently developed new set of
coordinates called ``Adapted STtructural (AST)'' coordinates.  They are
essentially a ``local'' or adapted version of equinoctical coordinates.
The main difference from equinoctial coordinates is that the 
reference plane is now taken to be the orbital plane of the
current best estimate of the state.  There are also a few other
differences between AST and equinoctial coordinates.

One of the benefits of AST coordinates is that a version of an
extended Kalman filter (EKF) can be developed to simplify the update
step, in contrast to the more typically used update based on the
unscented Kalman filter (UKF).  In this paper, we give a detailed
investigation of the AST-EKF algorithm.  In particular, we show that
in certain circumstances under high ellipticity and using AST
coordinates, the EKF update step can outperform the more conventional
UKF update step.

Abstract document

IAC-19,A6,7,6,x50344.brief.pdf

Manuscript document

IAC-19,A6,7,6,x50344.pdf (🔒 authorized access only).

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