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

• Published in: Celestial mechanics and dynamical astronomy Vol. 134; no. 3
• Main Authors: Sun, Pan, Colombo, Camilla, Trisolini, Mirko, Li, Shuang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2022; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Analytical methods; Astrophysics and Astroparticles; Classical Mechanics; Continuity equation; Covariance matrix; Density distribution; Dynamical Systems and Ergodic Theory; Dynamics of Space Debris and NEO; Evolution; Geophysics/Geodesy; High altitude; Mathematical analysis; Modelling; Nonlinear dynamics; Normal distribution; Original Article; Physics; Physics and Astronomy; Probabilistic models; Propagation; Radiation pressure; Solar oblateness; Solar radiation; Statistical analysis; Two dimensional models; Density propagation; Density evolution equation; Planetary oblateness; Semi-analytical equation; Solar radiation pressure; Gaussian mixture model
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-022-10066-8

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.