Operator Dynamics Approach to Short-Arc Orbital Prediction Based on Wigner Distribution

We propose a novel filtering framework based on phase-space that treats the error distribution as the marginal of a Wigner quasi-probability distribution and defines an effective uncertainty constant quantifying the minimal resolvable phase-space cell. Recognizing that observational updates systematically reduce uncertainty, we adopt a generalized Koopman-von Neumann equation grounded in operator dynamical modeling to propagate the density operator corresponding to the error distribution. The scaling parameter $\kappa$ quantifies the reduction in uncertainty following each filter update. Because the potential is retained only to second order, both propagation and update preserve Gaussian form, permitting direct application of Kalman recursion. Validated on 1215 orbits (LEO-GEO), the method shows that within a 3 min fit / 10 min forecast window observational noise contributes 350 m while unmodelled dynamics adds only 0.6 m. Kruskal-Wallis rank-sum tests and the accompanying scatter-plot trend rank semi-major axis as the dominant sensitive parameter. The proposed model outperforms Chebyshev and high-fidelity propagators in real time, offering a physically interpretable route for short-arc orbit prediction.