Two-Line Element Uncertainty for GOCE Statistical Re-entry Predictions

TLEs are important for many Space Situational Awareness (SSA) studies, because of their widespread availability. For many objects such as rocket bodies, stages, and defunct satellites TLEs present the only source of orbital states. Despite their importance, TLEs suffer from some major drawbacks: they are of limited accuracy (especially compared to GPS/TIRA), are often mistagged, miss manoeuvres, and lack covariance information. Although the TLEs are openly available, their observations and corresponding covariance are not. The proper understanding and subsequent modeling and estimation of these uncertainties is paramount for previously mentioned SSA activities. The aim of the paper is to present uncertainty models and estimation techniques, focusing on improving re-entry predictions using TLEs of low-earth orbit (LEO) satellites. Only the uncertainties in the initial translational state and deficiencies in atmospheric density and spacecraft aerodynamic modeling are considered. GOCE, during its re-entry phase, is used as the reference object for this study. Probability distributions are presented for modeling uncertainties in the translational and rotational state, and atmospheric density. A new robust weighted differencing method for estimating the uncertainty of TLEs is introduced. For GOCE during the period of investigation, two types of TLEs are present, namely of the classic and enhanced type. The latter TLEs are obtained from pseudo observations derived from a numerical higher-order fit and propagation. The proposed method is validated using GPS orbit solutions. Moreover, the estimation of the ballistic coefficient through retrofitting is discussed and executed for both TLE types. The obtained estimates of the uncertainty in the initial translational state and atmospheric density are applied to re-entry time predictions of GOCE. Specifically, decay time distributions are obtained using six degree-of-freedom statistical re-entry simulations. The effects of the different environment and spacecraft models is investigated, especially the proper modeling of the attitude control that was present almost entirely throughout re-entry. Moreover, GPS and TLE-derived translational-state inputs are compared. The developed methods and findings are then applied to re-entry predictions of several Delta-K rocket bodies. Enhanced TLEs are shown to have a reduced uncertainty and improved forward propagation stability compared to the older classic type. In fact, enhanced TLEs states are found to be most accurate after their associated epoch, due to the inclusion of propagated pseudo measurements. The ballistic coefficient of enhanced TLEs is found to differ from classic TLEs and is shown to be consistent with retrofit estimates of the ballistic coefficient. This suggests that the coefficient is obtained directly from the numerical fitting process, rather than co-estimated with the mean elements of the TLE themselves, as is the case for classic TLEs. This finding positively affects re-entry predictions. The attitude control and atmospheric density bias are the two major factors on the mean decay epoch. While the atmospheric density uncertainty is by far the most important factor in the decay-time uncertainty. The uncertainty in initial state is shown to have only minor influence on the final decay-time distributions, despite GPS being up to four orders of magnitude more accurate than TLEs. This illustrates the importance of improving atmospheric density modeling for re-entry predictions.