Fully Multiplicative Attitude and Orbit Determination for Deep space Navigation

What the math gives to ML

The paper provides a transferable mechanism for filtering and propagating uncertainty on mixed state spaces: quaternion attitude and spherical optical measurements are handled multiplicatively, while Euclidean variables use additive errors. Its key practical result is that a fully multiplicative unscented filter remains statistically consistent under coarse propagation intervals where a first-order multiplicative EKF diverges. The strongest neural-network transfer is a manifold-aware recurrent or state-space layer that uses learned dynamics but performs sigma-point propagation and retraction in local tangent coordinates. This should be tested through normalized estimation error and divergence thresholds as propagation steps become coarse, rather than only through task accuracy.