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

Ishan Paranjape, Tarun Hejmadi, Utkarsh Ranjan Mishra, Suman Chakravorty

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.

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

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.
Paper Structure (11 sections, 14 equations, 7 figures, 1 table, 3 algorithms)

This paper contains 11 sections, 14 equations, 7 figures, 1 table, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Cislunar Dynamics and Observation Model
  3. Particle Gaussian Mixture Filters
  4. Bayesian Filtering Preliminaries
  5. Particle Gaussian Mixture-I Filter
  6. Particle Gaussian Mixture-II Filter
  7. Hybrid Particle Gaussian Mixture Filtering Method
  8. Results and Discussion
  9. Hybrid Filtering Approach
  10. Comparison to PGM-I Based Filtering Techniques
  11. Conclusions and Future Work

Figures (7)

  • Figure 1: State estimate propagation and clustering, MCMC sampling, and ensemble update steps for the PGM-II filter.
  • Figure 2: A large multivariate uniform PDF representing $p_0^{-}(\mathbf{x})$ for all examples in Section \ref{['sec:Results']}
  • Figure 3: Posterior state estimates after two measurements and at the end of the simulation/first pass using our hybrid PGM-based filter.
  • Figure 4: Single pass filtering results for a target within the 9:2 NRHO orbit
  • Figure 5: Limitations of utilizing KF-PGM with a linear fit between the first two measurements
  • ...and 2 more figures