  In mobile robotics, scan matching of point clouds using Iterative Closest
Point (ICP) allows estimating sensor displacements. It may prove important to
assess the associated uncertainty about the obtained rigid transformation,
especially for sensor fusion purposes. In this paper we propose a novel
approach to 3D uncertainty of ICP that accounts for all the sources of error as
listed in Censi's pioneering work [1], namely wrong convergence,
underconstrained situations, and sensor noise. Our approach builds on two
facts. First, the uncertainty about the ICP's output fully depends on the
initialization accuracy. Thus speaking of the covariance of ICP makes sense
only in relation to the initialization uncertainty, which generally stems from
odometry errors. We capture this using the unscented transform, which also
reflects correlations between initial and final uncertainties. Then, assuming
white sensor noise leads to overoptimism as ICP is biased owing to e.g.
calibration biases, which we account for. Our solution is tested on publicly
available real data ranging from structured to unstructured environments, where
our algorithm predicts consistent results with actual uncertainty, and compares
favorably to previous methods.
