This work has been submitted to the IEEE for possible publication. Abstract -- In this paper we reexamine the process through which a Neural Radiance Field (NeRF) can be trained to produce novel LiDAR views of a scene. Unlike image applications where camera pixels integrate light over time, LiDAR pulses arrive at specific times. As such, multiple LiDAR returns are possible for any given detector and the classification of these returns is inherently probabilistic. Applying a traditional NeRF training routine can result in the network learning "phantom surfaces" in free space between conflicting range measurements, similar to how "floater" aberrations may be produced by an image model. Code is available at https://github.com/mcdermatt/PLINK Neural Radience Fields (NeRFs) provide continuous representations of scenes by storing information about the surrounding world inside the weights of a neural network [1]. Recent works have extended NeRFs from camera images to LiDAR point clouds for use in localization [2], odometry [3], path planning [4], and data augmentation [5, 6]. To date, LiDAR applications of NeRFs have assumed a deterministic model of the scene.

This paper quantifies an error source that limits the accuracy of lidar scan matching, particularly for voxel-based methods. Lidar scan matching, which is used in dead reckoning (also known as lidar odometry) and mapping, computes the rotation and translation that best align a pair of point clouds. Perspective errors occur when a scene is viewed from different angles, with different surfaces becoming visible or occluded from each viewpoint. To explain perspective anomalies observed in data, this paper models perspective errors for two objects representative of urban landscapes: a cylindrical column and a dual-wall corner. For each object, we provide an analytical model of the perspective error for voxel-based lidar scan matching. We then analyze how perspective errors accumulate as a lidar-equipped vehicle moves past these objects.

Because scanning-LIDAR sensors require finite time to create a point cloud, sensor motion during a scan warps the resulting image, a phenomenon known as motion distortion or rolling shutter. Motion-distortion correction methods exist, but they rely on external measurements or Bayesian filtering over multiple LIDAR scans. In this paper we propose a novel algorithm that performs snapshot processing to obtain a motion-distortion correction. Snapshot processing, which registers a current LIDAR scan to a reference image without using external sensors or Bayesian filtering, is particularly relevant for localization to a high-definition (HD) map. Our approach, which we call Velocity-corrected Iterative Compact Ellipsoidal Transformation (VICET), extends the well-known Normal Distributions Transform (NDT) algorithm to solve jointly for both a 6 Degree-of-Freedom (DOF) rigid transform between two LIDAR scans and a set of 6DOF motion states that describe distortion within the current LIDAR scan. Using experiments, we show that VICET achieves significantly higher accuracy than NDT or Iterative Closest Point (ICP) algorithms when localizing a distorted raw LIDAR scan against an undistorted HD Map. We recommend the reader explore our open-source code and visualizations at https://github.com/mcdermatt/VICET, which supplements this manuscript.

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