  The fusion of Iterative Closest Point (ICP) reg- istrations in existing state
estimation frameworks relies on an accurate estimation of their uncertainty. In
this paper, we study the estimation of this uncertainty in the form of a
covariance. First, we scrutinize the limitations of existing closed-form
covariance estimation algorithms over 3D datasets. Then, we set out to estimate
the covariance of ICP registrations through a data-driven approach, with over 5
100 000 registrations on 1020 pairs from real 3D point clouds. We assess our
solution upon a wide spectrum of environments, ranging from structured to
unstructured and indoor to outdoor. The capacity of our algorithm to predict
covariances is accurately assessed, as well as the usefulness of these
estimations for uncertainty estimation over trajectories. The proposed method
estimates covariances better than existing closed-form solutions, and makes
predictions that are consistent with observed trajectories.
