A dynamical coherency gate for state recovery: Statistical requiem for the long arc of cislunar orbital mis-prediction

TL;DR

This paper introduces a statistically grounded method for reconstructing accurate long-arc trajectories of distant Earth satellites from TLE data, enabling precise orbit prediction even with sparse and noisy observations.

Contribution

The paper presents a novel approach combining orbital averaging and GMM filtering to recover physically consistent initial conditions from TLEs for long-term trajectory reconstruction.

Findings

Successfully reconstructed the orbit of OGO-1 over five decades.

Achieved accurate reentry prediction within one day of the true decay.

Demonstrated robustness in long-arc trajectory recovery with limited data.

Abstract

We present a statistically grounded methodology for recovering physically consistent initial conditions from historical two-line element sets (TLEs), enabling accurate long-arc trajectory reconstruction for distant and highly eccentric Earth satellites. The approach combines numerical averaging of osculating orbital elements with Gaussian-mixture-model (GMM) filtering with robust fallback strategies to isolate a dynamically coherent subset of mean elements at a common reference epoch. From this filtered ensemble, a representative osculating element is reconstructed, yielding a recovered Cartesian state vector with predictive capability far exceeding that of raw TLE-based propagations and existing approaches. We apply this method to the case of OGO-1 (1964-054A), a spacecraft launched into a cislunar orbit and tracked intermittently over five decades. Despite large observational gaps and significant secular evolution, our recovered state, used within an unscented Kalman filter (UKF), accurately reproduces the full trajectory, including its atmospheric reentry in August 2020, to within one day of the true decay time. This result demonstrates the viability of filtered TLE statistics as a proxy for precise orbit determination, particularly in dynamical regimes where resonances and long-period perturbations dominate. The techniques presented here provide a framework for trajectory reconstruction and prediction using only publicly available data and are broadly applicable to the study of high-altitude debris objects and legacy space missions whose original tracking and covariance data are unavailable.