Consensus-based quaternion estimation for aggregated spacecraft system with multiple sensors

In this paper, we consider the consensus-based quaternion estimation problem of aggregated spacecraft with multiple sensors. It is known that the quaternion has an inherent unit-norm constraint and a subtle ambiguity since the mapping from the rotation matrix to the quaternion is two-to-one. These facts imply that the updates for the quaternion should be multiplicative instead of additive and make it nontrivial to extend the classical Kalman consensus filter (based on the additive update) for quaternion estimation problem. In order to solve this problem, we propose a novel multiplicative quaternion Kalman consensus filter (MQK-CF) in this paper. We compare the proposed MQK-CF with an additive consensus-based quaternion filter. It turns out that the additive consensus-based quaternion filter suffers from erroneous fusion of datum due to its sensitivity to numerical errors. The validity of the proposed multiplicative quaternion Kalman consensus filter is verified by numerical simulations for a static attitude estimation scenario.