  Distribution-to-Distribution (D2D) point cloud registration algorithms are
fast, interpretable, and perform well in unstructured environments.
Unfortunately, existing strategies for predicting solution error for these
methods are overly optimistic, particularly in regions containing large or
extended physical objects. In this paper we introduce the Iterative Closest
Ellipsoidal Transform (ICET), a novel 3D LIDAR scan-matching algorithm that
re-envisions NDT in order to provide robust accuracy prediction from first
principles. Like NDT, ICET subdivides a LIDAR scan into voxels in order to
analyze complex scenes by considering many smaller local point distributions,
however, ICET assesses the voxel distribution to distinguish random noise from
deterministic structure. ICET then uses a weighted least-squares formulation to
incorporate this noise/structure distinction into computing a localization
solution and predicting the solution-error covariance. In order to demonstrate
the reasonableness of our accuracy predictions, we verify 3D ICET in three
LIDAR tests involving real-world automotive data, high-fidelity simulated
trajectories, and simulated corner-case scenes. For each test, ICET
consistently performs scan matching with sub-centimeter accuracy. This level of
accuracy, combined with the fact that the algorithm is fully interpretable,
make it well suited for safety-critical transportation applications. Code is
available at https://github.com/mcdermatt/ICET
