Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods

TL;DR

This paper compares the density evolution equation and Gaussian mixture model for long-term satellite density propagation in phase space, highlighting their efficiency and accuracy against Monte Carlo methods under nonlinear dynamics.

Contribution

It introduces a semi-analytical formulation for the density evolution equation and compares it with Gaussian mixture models for long-term propagation in high-altitude satellite scenarios.

Findings

Density evolution equation is efficient for long-term propagation.

Gaussian mixture model provides analytical density calculation from moments.

Both methods outperform Monte Carlo in efficiency and validity.

Abstract

This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propagation, is formulated under the influence of solar radiation pressure and Earth's oblateness using semi-analytical methods. Different from the density evolution equation and Monte Carlo techniques, for the Gaussian mixture model, the analytical calculation of the density is accessible from the first two statistical moments (i.e., the mean and the covariance matrix) corresponding to each sub-Gaussian distribution for an initial Gaussian density distribution. An insight is given into the phase space long-term density propagation problem subject to nonlinear dynamics. The efficiency and validity of the density propagation are demonstrated and compared between the density evolution equation and the Gaussian mixture model with respect to standard Monte Carlo techniques.