Hybrid Kalman–Nonlinear Excitation–Regulation Framework for Improved Orbital Prediction under Drag and Perturbation Uncertainty

This paper presents a hybrid orbital prediction framework that integrates classical Kalman filtering with a nonlinear excitation–regulation (K–R) instability model to improve prediction accuracy in Low Earth Orbit (LEO). Orbit propagation in LEO is significantly affected by thermospheric drag variability, perturbation coupling, and uncertainty in ballistic parameters, which often lead to nonlinear divergence in trajectory prediction when using conventional analytical or estimation-based methods. The proposed approach addresses this limitation by embedding a bounded nonlinear regulation mechanism within a physics-consistent Kalman propagation architecture, allowing the system to stabilize instability-driven deviations during propagation rather than correcting them only after residual errors appear. The framework models orbital evolution as a dynamic balance between excitation forces arising from drag–energy coupling and perturbation variability, and regulation mechanisms that constrain divergence in the state space. The nonlinear K–R component operates as a micro-stabilization layer that preserves deterministic orbital dynamics while mitigating instability growth. This structure maintains computational efficiency and compatibility with standard Two-Line Element (TLE) propagation workflows. The methodology is validated using real orbital datasets representing three distinct regimes: the International Space Station as an actively maintained spacecraft, Envisat as a large uncontrolled debris object, and the Hubble Space Telescope as a semi-stable scientific satellite. Prediction performance is evaluated across operational horizons ranging from 30 minutes to 6 hours using forward propagation and comparison with subsequent observed states. Results demonstrate consistent reduction in positional error relative to classical SGP4 propagation, with improved stability observed across all orbital environments. The study establishes that instability regulation plays a central role in improving short- and medium-horizon orbit prediction and provides a generalizable framework applicable to active spacecraft, debris tracking, and scientific missions. The hybrid Kalman–K–R model offers a physically interpretable and operationally feasible approach for enhancing orbit determination, conjunction assessment, and space situational awareness systems in increasingly congested LEO environments.