Tracking an Object with Unknown Accelerations using a Shadowing Filter

TL;DR

This paper introduces a shadowing filter for tracking objects with unknown and changing accelerations, offering a robust and efficient alternative to traditional stochastic filters like Kalman filters, especially with limited or inaccurate sensor data.

Contribution

The paper presents a novel shadowing filter approach that is computationally simple and more robust than Bayesian filters for tracking maneuvering objects with unknown accelerations.

Findings

Shadowing filter reduces to linear equations, increasing efficiency.

The filter is robust against missing data and correlation issues.

It outperforms Kalman filters in certain tracking scenarios.

Abstract

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.