Tracking an Object with Unknown Accelerations using a Shadowing Filter
This addresses a challenging tracking problem for maneuvering objects like ships or aircraft, offering a robust alternative to stochastic methods, though it appears incremental as it builds on variational approaches.
The paper tackles the problem of tracking objects with unknown and arbitrarily changing accelerations using limited and inaccurate sensor data, proposing a shadowing filter that is efficient, robust to missing data and singular correlations, and in some cases outperforms Kalman filters by ignoring error correlations.
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.