Nonlinear Uncertainty Transformation for Geometry-Aware Spacecraft Optical Navigation

Autonomous optical navigation requires a spacecraft to determine where it is and how it is oriented using onboard measurements. Small optical-tracker mounting errors couple the attitude and orbit estimates and can bias both if not estimated. This work treats spacecraft attitude, orbit, and the three-axis alignment of two optical trackers as a single estimation problem using stellar and celestial-body direction measurements. The formulation preserves the multiplicative geometry of attitude and unit-vector measurements and extends the nonlinear uncertainty treatment from unscented sampling to sparse Gauss–Hermite quadrature (SGHQ) at Levels 2 and 3. A multiplicative extended Kalman filter (MEKF), a fully multiplicative unscented Kalman filter (FM-UKF), and fully multiplicative sparse Gauss–Hermite quadrature filters (FM-SGHQFs) at Levels 2 and 3 are evaluated under identical dynamics, measurements, calibration states, and noise realizations. Monte Carlo results show little separation at the fine estimator-cycle interval, but clear differences at the coarse estimator-cycle interval. The FM-UKF and Level 3 FM-SGHQF retain close agreement between predicted covariance and empirical Monte Carlo dispersion, whereas the implemented MEKF loses consistency and the Level 2 FM-SGHQF becomes overconfident. Among the methods considered, the FM-UKF provides the best balance between statistical consistency and computational cost across the investigated regimes.