Orbit Determination for Spacecraft with Dual Maneuver Modes via Tanh-Smoothed Parameterization

A novel orbit determination method for unknown-maneuvering spacecraft is proposed, enabling the simultaneous estimation of orbital states and maneuver parameters using angle-only observations. A hyperbolic-tangent function is introduced to smoothly parameterize both impulsive and constant-thrust maneuvers, providing accurate maneuver-profile representation and enforcing continuous differentiability of the orbital state across maneuvers. On this basis, the smoothed extended state transition tensors are derived to construct the parameter-to-observation mapping and formulate a second-order correction equation that captures key nonlinear effects. Furthermore, the influence of the smoothing factor on the mapping precision is analyzed, leading to an adaptive smoothing-factor selection strategy that minimizes mapping errors and enhances the accuracy of computed corrections. Finally, a three-layer iterative correction framework is developed, where the inner layer iteratively solves the second-order correction equation to compute accurate corrections; the middle layer adaptively selects the smoothing factor to preserve mapping fidelity under maneuver-epoch uncertainty and find the optimal corrections; the outer layer updates the estimated parameters based on the selected results. Numerical simulations covering impulsive and constant-thrust maneuvers in both Low‐Earth Orbit and Medium‐Earth Orbit scenarios validate the approach, demonstrating rapid convergence, high estimation accuracy, insensitivity to large initial errors and scenario adaptability and showing more reliable convergence performance over existing maneuver-reconstruction techniques.