Innovative methods of correlation and orbit determination for space debris

TL;DR

This paper introduces two novel algorithms for preliminary orbit determination of space debris using limited observations, improving efficiency over classical methods by leveraging the admissible region and geocentric motion integrals.

Contribution

It presents two new algorithms for orbit determination that require fewer observations and incorporate perturbation effects, advancing space debris tracking methods.

Findings

The Virtual debris algorithm effectively estimates orbits with limited data.

Using geocentric motion integrals improves orbit accuracy under perturbations.

The methods adapt to real-world perturbations like the J2 effect.

Abstract

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the $J_2$ effect.