  Consider a space object in an orbit about the earth. An uncertain initial
state can be represented as a point cloud which can be propagated to later
times by the laws of Newtonian motion. If the state of the object is
represented in Cartesian earth centered inertial (Cartesian-ECI) coordinates,
then even if initial uncertainty is Gaussian in this coordinate system, the
distribution quickly becomes non-Gaussian as the propagation time increases.
Similar problems arise in other standard fixed coordinate systems in
astrodynamics, e.g. Keplerian and to some extent equinoctial. To address these
problems, a local "Adapted STructural (AST)'' coordinate system has been
developed in which uncertainty is represented in terms of deviations from a
"central state".
  Given a sequence of angles-only measurements, the iterated nonlinear extended
(IEKF) and unscented (IUKF) Kalman filters are often the most appropriate
variants to use. In particular, they can be much more accurate than the more
commonly used non-iterated versions, the extended (EKF) and unscented (UKF)
Kalman filters, especially under high eccentricity. In addition, iterated
Kalman filters can often be well-approximated by two new closed form filters,
the observation-centered extended (OCEKF) and unscented (OCUKF) Kalman filters.
