  A commonly encountered problem is the tracking of a physical object, like a
maneuvering ship, aircraft, land vehicle, spacecraft or animate creature
carrying a wireless device. The sensor data is often limited and inaccurate
observations of range or bearing. This problem is more difficult than tracking
a ballistic trajectory, because an operative affects unknown and arbitrarily
changing accelerations. Although stochastic methods of filtering or state
estimation (Kalman filters and particle filters) are widely used, out of vogue
variational methods are more appropriate in this tracking context, because the
objects do not typically display any significant random motions at the length
and time scales of interest. This leads us to propose a rather elegant approach
based on a \emph{shadowing filter}. The resulting filter is efficient (reduces
to the solution of linear equations) and robust (uneffected by missing data and
singular correlations that would cause catastrophic failure of Bayesian
filters.) The tracking is so robust, that in some common situations it actually
performs better by ignoring error correlations that are so vital to Kalman
filters.
