Orbit determination and prediction for uncooperative spacecrafts with continuous low-thrust maneuver via piecewise estimation

The exponential growth of mega-constellation satellites, typified by SpaceX’s Starlink, poses unprecedented challenges for existing space surveillance, particularly when tracking uncooperative spacecrafts executing continuous orbit-raising/deorbiting maneuvers. This situation makes the conventional orbit determination (OD) and prediction (OP) struggle with three critical issues: insufficient observational data, unknown maneuvering parameters, and the cumulative effects of unmodeled thrust. To address these issues, this study proposes a piecewise estimation-based OD method by developing a semi-analytical thrust acceleration (TA) model. The TA model employs time-explicit polynomial expansions with state-dependent coefficients to characterize the continuous low-thrust effect. The OD system integrates a piecewise least-squares estimation algorithm with dynamic compensation, enabling accurate TA resolution within one-day observation windows. Specifically, the OP system incorporates the latest TA estimate to account for the future continuous low-thrust effect. Experiments with sparse radar observations of Starlink satellites demonstrate the effectiveness of the proposed method. The TA estimation errors remain below 0.5% relative to the reference obtained from precise ephemerides. The OP capabilities maintain one-day and two-day position accuracy below 2 and 4 km, respectively, improving by more than 60% compared to the unified OD method. More importantly, the approach exhibits operational robustness, achieving OD convergence with initial TA errors up to 35%. These advantages make the proposed approach a practicable solution for autonomous catalog maintenance of maneuvering spacecraft. • A piecewise estimation-based orbit determination (OD) framework is developed for uncooperative spacecrafts with continuous low-thrust maneuver. • The continuous low-thrust effect is modeled by a semi-analytical expansion comprised of constant, linear, and nonlinear terms related to the spacecraft’s state, with the relative estimation errors of thrust acceleration (TA) below 0.5% under sparse tracking data condition, compared to those from the precise ephemerides. • Accurate orbit prediction (OP) is achievable by incorporating the latest TA estimate into the orbit dynamics system, with the one-/two-day position prediction error better than 2 km/4 km, respectively, for the maneuvering Starlink satellites. • The developed piecewise estimation-based OD framework demonstrates high robustness, achieving convergence with the initial TA errors up to 35%.