Semi-analytical Orbital Error Propagation Considering Impulsive Maneuver Uncertainties

Addressing the challenge of unified modeling for impulsive maneuver time-vector coupled deviations in traditional orbital uncertainty propagation, a differential algebra (DA)-based semi-analytical orbital uncertainty evolution method is developed. A time-scale variable is introduced to explicitly characterize impulsive timing deviations, enabling derivation of unified high-order state error polynomials for multi-impulse scenarios through segmented DA connections. An automatic domain splitting (ADS) strategy is implemented to adaptively partition the maneuver time domain, significantly improving prediction accuracy in strongly nonlinear regions. The method is applied to impulsive guidance optimization. achieving joint optimization of impulsive timing and magnitude within each ADS subdomain for high-precision robust guidance. Numerical validation using Earth-Moon three-body periodic orbits demonstrates up to three orders of magnitude reduction in prediction error compared to conventional methods, with optimized guidance showing reduced control effort and enhanced robustness.