New analytical method speeds spacecraft uncertainty modeling 100x
A sample-free framework computes banana-shaped confidence boundaries in minutes, not hours.
A fully analytical, sample-free framework for nonlinear uncertainty propagation in perturbed astrodynamics is introduced. Using Differential Algebra and Isserlis' theorem, skewness and kurtosis moments are extracted without repeated numerical integration. The method models three-dimensional "banana-shaped" confidence boundaries and is validated on a cislunar Near-Rectilinear Halo Orbit and close-proximity trajectories around Apophis during Earth's flyby. It matches Monte Carlo accuracy while cutting computational runtime by orders of magnitude.
- Uses Differential Algebra to propagate polynomial dynamics, avoiding repeated numerical integration for moment extraction.
- Validated on cislunar Near-Rectilinear Halo Orbits and Apophis flyby trajectories, matching Monte Carlo accuracy.
- Reduces computational runtime from hours to minutes—orders of magnitude faster than traditional Monte Carlo methods.
Why It Matters
Real-time uncertainty quantification for spacecraft operations, enabling faster mission design and safer autonomous navigation in complex gravity fields.