Revisiting the orbital tracking problem

TL;DR

This paper introduces a new local coordinate system and improved Kalman filtering methods for more accurate orbit tracking of space objects, especially under high eccentricity, addressing non-Gaussian uncertainties in traditional Cartesian coordinates.

Contribution

It develops the Adapted Structural (AST) coordinate system and proposes closed-form iterated Kalman filters (OCEKF and OCUKF) for enhanced orbit estimation accuracy.

Findings

AST coordinates better handle non-Gaussian uncertainties.

Iterated Kalman filters outperform non-iterated versions in high eccentricity scenarios.

Closed-form filters provide computationally efficient alternatives.

Abstract

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.