---
title: "Dust Cloud Dispersion | Truman DeWalch"
description: "High-fidelity modeling of orbital dust cloud dynamics and momentum transfer"
url: "https://trumandewalch.dev/research/dust-cloud-dispersion"
route: "/research/dust-cloud-dispersion"
---

Dissertation Component

# Dust Cloud Dispersion Modeling

Sigma-point propagation for targeted orbital dust dynamics

**Timeline:** 2023 – 2024

**Publication:** AAS/AIAA 2024

**Status:** Published

Unscented sigma points capture nonlinear dust-cloud dispersion, including a split cluster off the mean orbit.

## Summary

- Sigma-point propagation for nonlinear dust cloud dynamics.
- Gaussian mixture splitting handles multi-modal dispersion.
- Explores accuracy improvements over linearized methods for just-in-time collision avoidance (JCA) modeling.

## Overview

When dust particles are deployed in orbit, they don't simply drift in a straight line. Each particle experiences **differential perturbations** based on its size, mass, and position: smaller particles feel stronger solar radiation pressure, atmospheric drag varies with altitude, and gravitational harmonics create subtle orbital precession differences. Understanding this dispersion is critical for predicting whether deployed dust will successfully intercept a debris target.

This research developed a **sigma-point (unscented) transformation** approach for propagating dust cloud uncertainty through the nonlinear orbital dynamics. By carefully selecting representative "sigma points" that capture the distribution's moments, we avoid the linearization errors inherent in Extended Kalman Filters while remaining computationally tractable compared to full Monte Carlo simulation.

## The Challenge

Dust cloud state estimation must handle several complicating factors:

- **Nonlinear Dynamics:** Perturbation forces are nonlinear functions of position and velocity—linearization introduces errors that compound over propagation intervals
- **High Dimensionality:** A dust cloud has millions of particles; tracking each individually is computationally prohibitive
- **Multi-modal Distributions:** Differential perturbations can split a compact cloud into distinct clusters, violating Gaussian assumptions
- **Atmospheric Uncertainty:** Density variations at dust altitudes introduce additional state uncertainty that must be captured

## Technical Approach

The solution combines sigma-point propagation with **Gaussian mixture splitting**. When the predicted distribution becomes too non-Gaussian (detected via statistical tests), the distribution is split into multiple components, each propagated separately. This adaptively handles the multi-modal behavior while keeping computational cost bounded.

- **Unscented Transform** 2n+1 sigma points capture mean and covariance; propagated through full nonlinear dynamics without Jacobians
- **Mixture Splitting** Gaussian mixture model adaptively splits when Mahalanobis distance exceeds threshold
- **Perturbation Modeling** Configurable perturbations: gravity harmonics (EGM96/2008), drag, SRP, third-body (Sun/Moon)
- **Native Acceleration** Rust/C++ backends support fast batch evaluation for optimization workloads

## Current Evaluation Focus

01

### Prototype work

Comparing sigma-point propagation with simpler baseline models

02

### Ongoing study

Cloud-state behavior under richer uncertainty propagation

These ongoing comparisons help clarify how different uncertainty-propagation approaches influence collision probability estimates and debris-remediation decision-making.

## Publication

### "Dispersion of Targeted Orbital Dust Clouds: Applications to Just-in-time Collision Avoidance"

DeWalch, T., Fitzgerald, R.

AAS/AIAA Astrodynamics Specialist Conference 2024

Presents the sigma-point propagation methodology for dust cloud uncertainty quantification, explores how it compares with linearized methods, and evaluates the approach against Monte Carlo ground truth.

## Tools & Technologies

Python · NumPy · SciPy · Rust · Unscented Transform · Gaussian Mixtures · Monte Carlo

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