A Hybrid Particle Gaussian Mixture Filtering Method for Cislunar Orbit Determination Under Extreme Uncertainty

2026-03-01

AI Summary

This study addresses the limitations of traditional Gaussian orbit determination methods, which rely on the two-body assumption and fail under the strong three-body perturbations and extreme uncertainties characteristic of cislunar space. To overcome this challenge, the authors propose a hybrid particle Gaussian mixture filtering framework—termed PGM-I and PGM-II—that is, to the best of the authors’ knowledge, the first application of such an architecture to cislunar orbit determination. The approach constructs a purely recursive probabilistic model that effectively integrates ground-based angle-only observations, thereby handling the pronounced nonlinearity and non-Gaussian uncertainty inherent in the problem. Experimental results demonstrate that the proposed method significantly enhances both accuracy and robustness in representative cislunar orbit scenarios, achieving reliable probabilistic orbit tracking using only angular measurements.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Gauss's method of orbit determination (OD) and its variants are among the most popular initial state estimation techniques for astronomers and engineers alike. However, owing to its assumptions regarding the two-body problem, Gauss's method is inapplicable in the cislunar domain, where three body effects dominate. We introduce a hybrid Particle Gaussian Mixture filtering method, a purely recursive probabilistic orbit determination framework based on a combination of the Markov Chain Monte Carlo based Particle Gaussian Mixture-II (PGM-II) and Particle Gaussian Mixture-I (PGM-I) filters. This method enables us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short and long-term cislunar target tracking. We demonstrate this technique on an important cislunar orbit regime.

Problem

• cislunar orbit determination
• extreme uncertainty
• three-body effects
• angles-only observations
• initial state estimation

Innovation

• Hybrid Particle Gaussian Mixture Filtering
• Cislunar Orbit Determination
• Angles-only Observations
• Probabilistic Orbit Determination
• Three-body Dynamics