A closed-form solution for nonlinear covariance prediction is formulated for two-body orbits and the solution is generalized for perturbed orbits. Nonlinear terms arise from errors in the nonlinear state transition matrix caused by errors in the state. With nonlinear terms included, the predicted covariance cannot become unrealistically small after long prediction intervals. Simulations demonstrate that the second moments of Monte Carlo error distributions are accurately characterized by nonlinear covariance prediction, whereas linear covariance prediction grossly under-estimates these moments. For perturbed orbits, a linear matrix-Riccati equation with gravitational and other disturbance accelerations can be solved numerically to determine a linear covariance prediction, and the nonlinear two-body prediction solution is an additive correction to this solution.
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