Non-Gaussian error propagation in orbital mechanics
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The problem of propagating orbital uncertainty is examined. The dominant earth oblateness (J2) and atmospheric drag perturbations are included in the equations of motion. The covariance due to uncertainty in position and velocity is propagated forward in time in the conventional rectangular and polar coordinates. The initial covariance matrix is propagated through Linear Error Theory in both the coordinate systems. After linearization in polar coordinates, the nonlinear transformation from the polar coordinates to the rectangular coordinates is successful in approximating the highly non-Gaussian nature of the full orbit evolution of the actual distribution. These results are in close qualitative agreement with the conventional Monte-Carlo Simulations.
author list (cited authors)
Junkins, J. L., Akella, M. R., & Alfriend, K. T.