Fully Multiplicative Attitude and Orbit Determination for Deep space Navigation

Abstract

This paper develops a geometry-consistent fully multiplicative unscented Kalman filter (FM-UKF) for joint spacecraft attitude--orbit estimation with simultaneous dual star-tracker misalignment calibration. The estimator uses a 21-dimensional local error state combining attitude, angular velocity, gyroscope bias, inertial position and velocity, and two tracker-misalignment vectors on a mixed quaternion--Euclidean manifold. Gyroscope, star-tracker, and planet line-of-sight measurements are fused, with celestial aberration retained to capture velocity-dependent optical coupling. A multiplicative extended Kalman filter (MEKF) is implemented as a first-order baseline using the same nominal state, attitude retraction, and unit-vector measurement geometry. Monte Carlo results show similar short-step performance, while at coarse propagation intervals the proposed FM-UKF remains consistent and the MEKF exhibits divergence.