Abstract Gaussian Mixture Models and State Transition Tensors are combined to propagate state uncertainty to demonstrate an analytical and accurate future uncertainty and conjunction assessment. The initial uncertainty distribution is split into a Gaussian Mixture Model to reduce the size of covariance associated with each mixture component. This reduction in size allows for a significantly more accurate nonlinear mapping of each individual component. For higher accuracy in the mixture component propagation, State Transition Tensors are used to capture the nonlinear effects due to higher-order dynamics, as shown already in work by Fujimoto and Scheeres. In this paper, this GMM-STT method is used to analyze collisions using different dynamical models. The first case study demonstrates the application of this method in two-body problem dynamics; the second also adds J 2 secular effects; and the third brings in full J 2 and Solar Radiation Pressure dynamics through a Simplified Dynamical System. This paper also includes a two-body problem repeating conjunction example to establish a relationship between the propagation time and the number of mixture components needed for an accurate probability of collision computation. In each example, as the number of mixture components increases, the probability of collision converges with the Monte Carlo truth, proving the feasibility of this method.

    Highlights Orbit Determination models make accurate uncertainty propagation essential. Propagation with nonlinear dynamics leads to non-Gaussian future uncertainty. Conjunction models require accurately propagated future state and uncertainty. Gaussian Mixture Model - State Transition Tensor model gives accurate uncertainty. Model accuracy is confirmed with comparison to Monte Carlo Probability of Collision.


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    Title :

    Nonlinear semi-analytical uncertainty propagation for conjunction analysis


    Contributors:

    Published in:

    Acta Astronautica ; 203 ; 568-576


    Publication date :

    2022-12-08


    Size :

    9 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English