Characterizing Lidar Range-Measurement Ambiguity due to Multiple Returns

This paper introduces Dr-LiSA, a first-of-its-kind direct method for localizing 2D spinning radar intensity measurements in $SE(3)$ against 3D lidar maps. Radar-lidar localization combines the complementary strengths of the two sensing modalities: radar is robust to adverse weather and precipitation, while lidar provides high-fidelity 3D maps in favourable conditions. However, existing radar-lidar localization methods are restricted to planar $SE(2)$ localization and have generally fallen short of the accuracy achieved by lidar-lidar and even radar-radar systems. A key challenge is the substantial sensing-modality gap between radar and lidar, which observe and represent scene structure in fundamentally different ways. Dr-LiSA bridges this gap using a learned forward model that predicts radar measurements from a lidar submap at a candidate pose, enabling direct photometric alignment of predicted and observed radar scans in $SE(3)$. Dr-LiSA outperforms prior radar-lidar approaches in $SE(2)$ while achieving planar accuracy competitive with state-of-the-art radar-radar localization across more than 90 km of on-road data.

LiDAR configuration selection in roadside sensing remains constrained by limited controlled evidence across sensors. To address this gap, we present MR-LiDAR, a controlled cross-configuration benchmark comparing four LiDAR configurations from 16 to 128 beams on dynamic vehicle and vulnerable road user (VRU) targets. Its cross-configuration main set covers matched daytime, nighttime, and vehicle-occlusion conditions, while three deployment and operating condition subsets examine mounting height, target speed, and curved-road geometry. By reducing confounding from scene and trajectory variation, MR-LiDAR links sensor configuration to target point acquisition and algorithmic detection outcomes. We characterize distance-dependent point loss, define effective beam count as the number of vertical beams intersecting the target's angular extent, and introduce a point-based Occlusion Ratio. The results show that 16- and 32-beam configurations degrade earlier with distance, while VRUs exhibit greater point sparsity than motor vehicles. Nominal beam count alone is insufficient to explain roadside scanning capability. In the cross-configuration main set, the 80- and 128-beam configurations achieve comparable results, consistent with their nearly identical downward beam layouts. A uniform 80-beam counterfactual yields only about one third of the effective beam count of the actual non-uniform configuration. Illumination and the tested speed range have little influence on target-point-count patterns, whereas mounting height and near-field road geometry can substantially alter configuration ordering. Finally, an empirical minimal-sufficient configuration matrix combines frame-level geometric sufficiency with matched-box quality and includes threshold sensitivity analysis, providing bounded configuration guidance for the tested conditions.

LiDAR relocalization has attracted increasing attention as it can deliver accurate 6-DoF pose estimation in complex 3D environments. Recent learning-based regression methods offer efficient solutions by directly predicting global poses without the need for explicit map storage. However, these methods often struggle in challenging scenes due to their equal treatment of all predicted points, which is vulnerable to noise and outliers. In this paper, we propose LEADER, a robust LiDAR-based relocalization framework enhanced by a simple, yet effective geometric encoder. Specifically, a Robust Projection-based Geometric Encoder architecture which captures multi-scale geometric features is first presented to enhance descriptiveness in geometric representation. A Truncated Relative Reliability loss is then formulated to model point-wise ambiguity and mitigate the influence of unreliable predictions. Extensive experiments on the Oxford RobotCar and NCLT datasets demonstrate that LEADER outperforms state-of-the-art methods, achieving 24.1% and 73.9% relative reductions in position error over existing techniques, respectively. The source code is released on https://github.com/JiansW/LEADER.