Collision Probability through Orbital Uncertainty Propagation

Collision Probability through Orbital Uncertainty Propagation: The Hybrid Differential Algebra and Gaussian Mixture Model Approach

Leon Dasi, Mireia (TU Delft Aerospace Engineering; TU Delft Astrodynamics & Space Missions)

Mooij, E. (mentor)
van der Wal, W. (graduation committee)
van Kampen, E. (graduation committee)

Delft University of Technology

Aerospace Engineering

2022-01-28

The number of space objects has largely increased in the recent years, becoming a considerable threat to the present and future of satellite operations and human spaceflight. This introduces a need to accurately compute the risk of collision between satellites and space debris. Current methodologies are limited by the type of encounter and the vehicle shape, usually simplified by a sphere. These assumptions rely mainly on linearization of the dynamics and simplification of the uncertainty distribution as a Gaussian function. Developing a collision probability calculation method that overcomes these limitations and provides high-accuracy results is the topic of this work. The methodology developed follows the hybrid Differential Algebra (DA) and Gaussian Mixture Model (GMM) method for uncertainty propagation. The DA technique allows to propagate the covariance of the satellite position and velocity without applying linearisation. Moreover, the Gaussian assumption for the satellite uncertainty is dropped by using a weighted sum of Gaussian distributions that can approximate any probability density function. Finally, the method is adapted to any satellite geometry by developing a numerical quadrature technique based on a combination of spheres to model the real body shape. The combination of these methodologies to compute the collision probability is labelled as the multi-sphere DA-GMM method. This technique has been verified with a set of test cases by means of a Monte Carlo simulation and compared to alternative algorithms. It is found that the method improves the accuracy in calculating the collision probability by more than 70% with respect to conventional alternatives. Regarding real-life scenarios, the Cosmos-2251/Iridium-33 and the Chang Zheng-4C/Cosmos-2004 encounters are simulated. In both cases, the time of encounter and collision risk have been correctly estimated with the DA-GMM method. Finally, in view of the recent destruction of satellite Cosmos-1408 as a result of an anti-satellite missile test, a screening of its resulting debris threatening the International Space Station (ISS) is performed. During a two-week period, ten close encounters were detected, one of which posed a significant risk to the ISS. When applying the method considering the real shape of the ISS, the collision probability decreases by two orders of magnitude, proving the significance of this approach to correctly estimate the risk and guide space operations.

Space debris
Collision avoidance
International Space Station
Gaussian Mixture Model
Differential Algebra

http://resolver.tudelft.nl/uuid:c92519fe-c3db-49d6-8cf0-c56ba81ffc11

2025-01-28

Student theses

master thesis

© 2022 Mireia Leon Dasi