A model framework for high-accuracy orbit determination and propagation of cislunar space debris

Abstract

Cislunar space is getting increasingly important. Countries like the US and China are directing their attention towards the Moon with the Artemis and Chang’e missions. Simultaneously, space debris pollution of our orbits is escalating, increasing the risk of the Kessler syndrome occurring. Space Situational Awareness (SSA) aims to prevent this. The sheer amount of space debris makes continuous tracking unfeasible. This creates the need for accurate orbit determination and propagation between observations. Model frameworks have been developed extensively for space debris in near-Earth orbits, but there is little experience with cislunar space. This region is more challenging because of its unstable nature, increasing the risk of losing track of objects.

In this research, a model framework is developed, using the open-source Python package Tudat, that can estimate and propagate long-term cislunar space debris orbits accurately from optical data, whilst quantifying the uncertainties realistically over time using Monte Carlo simulation. Orbit determination has been performed using Weighted Least-Squares. The algorithm can estimate (amongst other parameters) initial states of the objects, model parameters like radiation pressure properties, and observation bias. We apply our framework to the Chang’e 2 and 3 upper stages. A selection of 13 estimation windows has allowed for analysis on a diverse range of orbital and observation characteristics. Moreover, the effect of close Moon approaches on orbit determination quality and propagation accuracy has been investigated.

A generic model framework has been found that achieves sufficient accuracy with reasonable computational load for all 13 use cases and can be used as a foundation for other cislunar space debris studies. The generic framework only estimates initial state, and uses a relatively simple dynamical model and integrator configuration. This allows sufficiently accurate propagation up to 2 years out-of-sample, depending strongly on the stability of the orbit. Afterwards, the generic model framework is tailored on individual use cases to improve its performance. Parameters like the radiation pressure coefficient and observation bias are estimated in this process. The tailored model framework improved performance for 8 out of 13 use cases (compared to the generic model framework), decreasing out-of-sample RMSE between 20-95% and increasing period of sufficient accuracy with up to 250 days. Estimating on 7-10 months of observations results in the best orbit determination quality and propagation accuracy for the cislunar use cases. The tailored model framework performs robustly for various non-linear orbits, except for out-of-sample close Moon approaches. Several solutions are proposed to solve this issue. Finally, it is found that the effect of uncertainty for cislunar space debris orbits over time is significant in the current framework. Uncertainty over time is especially large when estimating on short estimation windows (<4 months) and for orbits experiencing non-linear behaviour.