Orbit Determination for Impulsively Maneuvering Spacecraft Using Gaussian-Embedded Augmented State Transition Tensors

Accurate estimation of impulsive maneuvers is critical for orbit determination of maneuvering space objects, which plays a vital role in space situational awareness. This paper presents a batch estimation algorithm that enables joint estimation of orbital states and impulsive maneuver parameters through a smooth dynamical framework based on Gaussian impulse approximation. By embedding the Gaussian-modeled maneuvers into the dynamical system, high-order state transition tensors (STTs) are derived to model maneuver uncertainty propagation, leading to a second-order optimal least squares solution. The proposed method avoids the complexity of traditional piecewise STTs formulations and naturally extends to multi-impulse scenarios without additional modeling effort. Extensive Monte Carlo simulations demonstrate that the proposed algorithm achieves estimation accuracy, convergence, and robustness comparable to state-of-the-art methods under varying observation conditions, maneuver intensities, and initialization errors, while requiring significantly less modeling effort. Moreover, the algorithm exhibits minimal sensitivity to Gaussian shaping parameters and maintains stable estimation variance across a wide parameter range. Overall, the proposed algorithm provides a practically scalable and robust solution for impulsive maneuver estimation, offering significant potential for autonomous orbit determination and operational space surveillance applications.