Pose estimation using linearized rotations and quaternion algebra

In this paper we revisit the topic of how to formulate error terms for estimation problems that involve rotational state variables. We present a first-principles linearization approach that yields multiplicative error terms for unit-length quaternion representations of rotations, as well as for canonical rotation matrices. Quaternion algebra is employed throughout our derivations. We show the utility of our approach through two examples: (i) linearizing a sun sensor measurement error term, and (ii) weighted-least-squares point-cloud alignment.