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arxiv: 2606.04334 · v1 · pith:LU6PAWHVnew · submitted 2026-06-03 · 🌌 astro-ph.EP · astro-ph.IM· stat.AP

Hybrid Particle Gaussian Mixture (H-PGM) Solution for Cislunar Target Tracking

Ishan Paranjape , Tarun Hejmadi , Utkarsh Ranjan Mishra , Suman Chakravorty This is my paper

Pith reviewed 2026-06-28 04:44 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IMstat.AP
keywords cislunar target trackingangles-only observationshybrid particle Gaussian mixtureMCMC Kalman filteringorbit determinationnon-Keplerian dynamicsprobabilistic estimation
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The pith

The H-PGM hybrid filter enables angles-only orbit determination for cislunar targets by sequentially combining MCMC and Kalman particle Gaussian mixture updates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a recursive probabilistic orbit determination approach for the cislunar region, where three-body effects invalidate standard Keplerian assumptions used in Gauss's method. It demonstrates that a hybrid particle Gaussian mixture filter can incorporate angles-only observations from terrestrial telescopes to produce state estimates for both short- and long-term tracking. The technique also allows fusion of prior target information to shrink uncertainty. Demonstrations across multiple cislunar orbit regimes show the hybrid outperforming homogeneous and alternative hybrid filters.

Core claim

A purely recursive probabilistic orbit determination framework called H-PGM fuses probabilistic information with angles-only observations through a sequential combination of the MCMC-based Particle Gaussian Mixture-II filter and the Kalman-update-based Particle Gaussian Mixture-I filter, enabling short- and long-term cislunar target tracking that outperforms several homogeneous and hybrid alternatives.

What carries the argument

The H-PGM hybrid filtering technique, a sequential MCMC-then-Kalman combination of PGM-II and PGM-I that fuses angles-only telescope data and optional prior information into updated state estimates.

Load-bearing premise

That the sequential MCMC-then-Kalman combination of PGM-II and PGM-I accurately represents the non-Keplerian dynamics and measurement likelihoods without substantial model mismatch or filter divergence in the tested regimes.

What would settle it

Demonstration of filter divergence or statistically worse performance than the compared methods in any of the tested cislunar regimes under angles-only observations would falsify the outperformance claim.

read the original abstract

Gauss's method of orbit determination (OD) is one of the most popular, minimal assumption target tracking techniques in astrodynamics, especially for generating an initial state estimate. However, due to Gauss's method's assumption of Keplerian motion (part of the larger two-body problem), this method cannot be applied in a cislunar environment, where three body, non-planar effects dominate. In this work, we showcase a hybrid Particle Gaussian Mixture (H-PGM) filtering method, a purely recursive probabilistic OD framework that relies upon a sequential combination of the Markov Chain Monte Carlo (MCMC) based Particle Gaussian Mixture-II (PGM-II) and Kalman update based Particle Gaussian Mixture-I (PGM-I) filters. This method allows us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short- and long-term cislunar target tracking. This method also allows us to fuse other target \textit{a priori} information in an effort to reduce target uncertainty in the short term. This hybrid filtering technique is demonstrated for several popular and important cislunar orbit regimes and compared with several homogeneous and hybrid filtering frameworks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a Hybrid Particle Gaussian Mixture (H-PGM) filtering method for cislunar target tracking. It sequentially combines the MCMC-based Particle Gaussian Mixture-II (PGM-II) filter with the Kalman-update-based Particle Gaussian Mixture-I (PGM-I) filter to process angles-only observations from terrestrial telescopes. The approach is described as a recursive probabilistic orbit determination framework that can incorporate a priori information and is demonstrated across several cislunar orbit regimes with comparisons to homogeneous and other hybrid filters.

Significance. If the performance claims hold under quantitative scrutiny, the hybrid method could provide a practical tool for handling non-Keplerian dynamics in cislunar space situational awareness where traditional Gauss methods fail. The fusion of probabilistic information with angles-only data addresses a timely need, though the absence of supporting metrics limits assessment of its contribution relative to existing filters.

major comments (2)
  1. [Abstract] Abstract: The abstract asserts demonstration and comparison across regimes yet supplies no quantitative metrics, error statistics, or validation details; central performance claims therefore rest on unshown evidence.
  2. [Methods] The sequential MCMC-then-Kalman combination of PGM-II and PGM-I is presented as accurately representing non-Keplerian dynamics and measurement likelihoods, but no analysis of potential model mismatch or filter divergence is provided for the tested regimes.
minor comments (2)
  1. The distinction between PGM-I and PGM-II should be introduced with explicit references to their original formulations upon first use.
  2. Figure captions and table headings should include units and error measures to allow direct interpretation of any performance plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The abstract asserts demonstration and comparison across regimes yet supplies no quantitative metrics, error statistics, or validation details; central performance claims therefore rest on unshown evidence.

    Authors: We agree that the abstract would benefit from explicit quantitative support. In the revised manuscript we will update the abstract to include representative error statistics (e.g., median position and velocity RMSE values) and a brief statement of the validation approach used across the tested cislunar regimes. revision: yes

  2. Referee: [Methods] The sequential MCMC-then-Kalman combination of PGM-II and PGM-I is presented as accurately representing non-Keplerian dynamics and measurement likelihoods, but no analysis of potential model mismatch or filter divergence is provided for the tested regimes.

    Authors: The referee correctly notes the absence of an explicit discussion of model mismatch and divergence risk. While the comparative simulations in the manuscript provide indirect evidence of stability, we will add a dedicated paragraph in the Methods section that examines potential mismatch sources, reports any observed divergence events in the tested regimes, and describes the safeguards inherent in the hybrid switching logic. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes H-PGM as a sequential procedural combination of the previously published PGM-II (MCMC) and PGM-I (Kalman) filters applied to angles-only observations. No equations, derivations, or fitted parameters are presented that reduce the claimed tracking performance or outperformance to quantities defined by the authors' own inputs, self-citations, or ansatzes. The central results rest on empirical demonstration across cislunar regimes against external benchmarks rather than self-referential constructions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the method implicitly assumes standard dynamical and measurement models for cislunar motion.

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discussion (0)

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Reference graph

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