This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second-order Taylor expansions and polynomial bounding techniques is first introduced to estimate the Jacobian variation of a nonlinear transformation. This index is then embedded into a low-order automatic domain splitting algorithm that accurately describes the mapping of an initial uncertainty set through a generic nonlinear transformation by splitting the domain whenever nonlinearities grow above a predefined threshold. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging process that limits the growth of the domains in time by recombining them when nonlinearities decrease. The low-order automatic domain splitting algorithm is then combined with Gaussian mixture models to accurately describe the propagation of a probability density function.
Low-Order Automatic Domain Splitting Approach for Nonlinear Uncertainty Mapping
Journal of Guidance, Control, and Dynamics ; 47 , 2 ; 291-310
2024-01-10
20 pages
Article (Journal)
Electronic Resource
English
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