Autonomous Hybrid State Estimation in the Perturbed Two-Body System

HANSON B. 1, BEWLEY T. 1, ROSENGREN A. 1

1 University of California San Diego, La Jolla, United States; 2 Jet Propulsion Laboratory, Pasadena, United States

The Cartesian state uncertainty of heliocentric objects governed primarily by central-body gravity with perturbations tends to oscillate between near-Gaussian and strongly non-Gaussian regimes over the orbit. Hybrid estimators leverage this behavior by employing moment-based filters during the former and ensemble-based filters during the latter. Moment-based estimation filters (e.g., the Kalman filter, extended Kalman filter, the unscented Kalman filter, etc.) are those that march the first and second central moments of the state, while ensemble-based estimation filters (e.g., the particle filter, the Gaussian mixture filter, grid-based Bayesian estimation exploiting sparsity, etc.) are those that march an ensemble of members that represent the uncertainty of the state. The latter are more accurate than the former when uncertainty becomes highly non-Gaussian but are computationally unwarranted otherwise. To date, ensemble filters have been underutilized for spacecraft state estimation due to their computational expense, especially when the state of the spacecraft is high-dimensional. Moment filters have sufficed thus far due to frequent measurement corrections from ground stations, but there exist trajectories where state uncertainty may become highly non-Gaussian between measurement updates, such as in highly perturbed environments. Implementation of a hybrid filter hinges on the mechanisms that control the transitions between the two frameworks. Previous work has demonstrated a correlation between a moment-based metric and a measure of higher-order information in the uncertainty that can be exploited for hybrid estimation for geocentric orbits. Here, we confirm that this correlation also holds across a range of heliocentric orbits through tandem propagation. We then demonstrate a hybrid estimation filter, the unscented Kalman filter/particle filter (UKF/PF), that uses the normalized Euclidean distance to switch from the UKF (moment-based) to the PF (ensemble-based), and the Henze-Zirkler statistic to switch back. The hybrid UKF/PF effectively balances and integrates the complementary strengths of both filtering frameworks, demonstrating considerable potential for use in autonomous spacecraft navigation. The efficacy of the proposed filter is demonstrated on two high fidelity trajectories: first, the state uncertainty propagation of the asteroid 2024 YR4 from its last reported orbit solution in November 2025 to its close approach of the Moon in December 2032. Second, we demonstrate the hybrid filter’s applicability to an autonomous navigation strategy for a theorized solar probe. By tuning the switching mechanism, we show that the approach can be biased toward efficiency or accuracy as desired.