Uncertainty Evaluation Tool for Medium-Term Low-Earth Orbit Propagation

The Earth orbit is becoming a risky environment and is getting increasingly crowded, mainly because of on-orbit breakup events and launches of mega-constellations of satellites. Space Surveillance and Tracking (SST) is in charge of monitoring Earth orbiting objects and related fragmentation events, as well as providing collision avoidance and re-entry services. Within the SST framework, orbital propagation is crucial in many activities, especially those related to collision risk assessment, in which high accuracy predictions of the objects' orbital states are required. However, propagation accuracy is affected by several sources of errors, arising from uncertainties depending on object-related and environmental factors, especially in Low-Earth Orbit (LEO) scenarios. First, orbital perturbation modelling represents a major issue, especially concerning the estimation of the Earth's atmospheric density. Indeed, under the same orbital conditions, different atmospheric models output different density values, which can undergo additional significant variations due to the solar activity. Another critical source of uncertainty is related to the accuracy in the knowledge of the physical parameters of space objects, such as the area-to-mass ratio (A/M), typically unknown for debris, also due to the limits of ground-based sensors on the minimum detectable size. Overall, even small errors in the atmospheric density modelling or in the A/M estimation can produce an accumulation of the position error, which is mostly in the along-track direction for LEO propagations. In this context, the uncertainty evaluation process consists in assessing how the input uncertainties on the environment and the objects' characteristics affect the propagation error in output as a function of propagation time. Despite being a nontrivial operation (due to the large number of functional parameters), the ability to quantify the effects of the uncertainties on medium-term propagations is important not only to determine which effects are less significant than others, but also to define confidence intervals allowing to support SST functions, such as conjunction analysis and sensor tasking. This paper tackles the problem of uncertainty evaluation by reviewing analytical and semi-analytical approaches, with the aim to develop a computationally light tool useful to define propagation error boundaries. The performance of the tool is tested for medium-term propagation scenarios in LEO, comparing the estimated errors with those computed by propagating the objects with different A/M or perturbation settings.