Multifidelity Orbit Uncertainty Propagation using Taylor Polynomials

TL;DR

This paper introduces a multifidelity method for nonlinear orbit uncertainty propagation that combines Taylor polynomial expansions with adaptive Gaussian mixture modeling to improve computational efficiency while maintaining accuracy.

Contribution

The paper presents a novel multifidelity approach that integrates Taylor expansions, Gaussian mixture models, and differential algebraic techniques for efficient orbit uncertainty propagation.

Findings

Method achieves higher efficiency than high-fidelity models

Limited accuracy loss demonstrated across regimes

Effective combination of low- and high-fidelity models

Abstract

A new multifidelity method is developed for nonlinear orbit uncertainty propagation. This approach guarantees improved computational efficiency and limited accuracy losses compared to fully high-fidelity counterparts. The initial uncertainty is modeled as a weighted sum of Gaussian distributions whose number is adapted online to satisfy the required accuracy. As needed, univariate splitting libraries are used to split the mixture components along the direction of maximum nonlinearity. Differential Algebraic techniques are used to propagate these Gaussian kernels and compute a measure of nonlinearity required for the split decision and direction identification. Taylor expansions of the flow of the dynamics are computed using a low-fidelity dynamical model to maximize computational efficiency and corrected with selected high-fidelity samples to minimize accuracy losses. The effectiveness of the proposed method is demonstrated for different dynamical regimes combining SGP4 theory and numerical propagation as low- and high-fidelity models respectively.