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Estimating the relative pose and angular velocity of an uncooperative space object is a critical component for many applications such as on-orbit assembly, inspection, and servicing. This paper presents new mathematical insights that permit a kinematic batch filter formulation for angular velocity estimation using quaternion measurements for relative orientation, thereby eliminating the need to know the moment of inertia of the target. In particular, a novel batch approach to computing the associated uncertainties for the angular velocity magnitude, spin-axis direction, and overall angular velocity vector estimates is presented and compared against previous recursive methodologies. Finally, a realistic use-case scenario is demonstrated in real-time on flightlike hardware.
Kaki et al. (Mon,) studied this question.