Debiasing of two-line element sets for batch least squares pseudo-orbit determination in MEO and GEO

• Deterministic biases exist in Two-Line Element Sets (TLEs) due to mismodelling of the Lunar perturbation in SGP4. • The bias period is commensurate to the orbital period of the Moon and degrades accuracy of Pseudo-Orbit Determination (P-OD). • Debiasing can be performed by either using long fit windows, of the order of months, or through a simple sinusoidal model. • P-OD with biased TLEs is discouraged as debiasing leads to up to 80% reduction in post-fit position error. The availability of accurate and timely state predictions for objects in near-Earth orbits is becoming increasingly important due to the growing congestion in key orbital regimes. The Two-Line Element Set (TLE) catalogue remains, to this day, one of the few publicly-available, comprehensive sources of near-Earth object ephemerides. At the same time, TLEs are affected by measurement noise and are limited by the low accuracy of the SGP4 theory, introducing significant uncertainty into state predictions. Previous literature has shown that filtering TLEs with batch least squares methods can yield significant improvements in long-term state prediction accuracy. However, this process can be highly sensitive to TLE quality which can vary throughout the year. In this study, it is shown that either extended-duration fit windows of the order of months, or the removal of systematic biases in along-track position prior to state estimation can produce significant reductions in post-fit position errors. Simple models for estimating these systematic biases are shown to be effective without introducing the need for high-complexity Machine Learning (ML) models. Furthermore, by establishing a TLE-based error metric, the need for high accuracy ephemerides is removed when creating these models. For selected satellites in the Medium Earth Orbit (MEO) regime, post-fit position errors are reduced by up to 80%, from approximately 5 km to 1 km; meanwhile, for selected satellites in the Geostationary Earth Orbit (GEO)/Geosynchronous Earth Orbit (GSO) regime, large oscillations in post-fit position error can be suppressed.