New FM-UKF filter beats MEKF for spacecraft attitude-orbit estimation

The paper introduces a geometry-consistent fully multiplicative unscented Kalman filter (FM-UKF) for deep-space navigation, addressing joint attitude and orbit estimation with simultaneous dual star-tracker misalignment calibration. The estimator operates on a mixed quaternion-Euclidean manifold with a 21-dimensional local error state that includes attitude, angular velocity, gyroscope bias, inertial position and velocity, and two tracker-misalignment vectors. It fuses data from gyroscopes, star trackers, and planet line-of-sight measurements, retaining celestial aberration to capture velocity-dependent optical coupling. The multiplicative extended Kalman filter (MEKF) is implemented as a first-order baseline using the same nominal state and measurement geometry.

Monte Carlo simulations reveal that both filters perform similarly at short propagation steps. However, at coarse propagation intervals, the proposed FM-UKF maintains consistency while the MEKF diverges. This robustness makes the FM-UKF particularly suitable for deep-space missions where measurement updates are infrequent and propagation intervals are long. The paper provides 21 pages of detailed results and 13 figures, demonstrating the practical advantages of a fully nonlinear, geometry-respecting approach over first-order linearization.