Implicit Runge-kutta Methods for Uncertainty Propagation

Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. Existing sigma pointor particle-based methods for uncertainty propagation use explicit numerical integrators for propagating the closely spaced orbital states as part of the prediction step of the nonlinear filter (e.g. the unscented Kalman filter, Gaussian sum filter, or particle filter). As such, these methods cannot exploit the proximity of the orbital states, and each orbit is propagated independently. To remove this limitation and enable the orbital states to be propagated together, we have developed an implicit Runge-Kutta-based method for uncertainty propagation, and consider the propagation of the 13 sigma points needed to represent uncertainty (of a six-dimensional Gaussian state) in the unscented Kalman filter. In some cases, we can propagate uncertainty using the new propagator at about the same computational cost compared to that of propagating a single orbital state, even before the algorithm is potentially parallelized. The new propagator is applicable to all regimes of space, and additional features include its ability to estimate and control the truncation error, exploit analytic and semi-analytic methods, and provide accurate ephemeris data via built-in interpolation.