High-Definition Map-Based Autonomous Vehicle Localization Using LiDAR Point Cloud Similarity Metrics: A Comparative Experimental Study

Accurate localization is a critical requirement for autonomous vehicle (AV) navigation, particularly in environments where GPS signals are unreliable or unavailable. A wide range of LiDAR-based point cloud similarity metrics have been proposed for high-definition (HD) map localization, but systematic comparisons of distinct metric families on the same real-world dataset, under identical conditions, remain scarce. In this paper, we present an offline comparative study of three point cloud similarity metrics within a unified HD map-based localization framework, under the assumption of largely static environments and planar, yaw-dominant vehicle motion typical of on-road driving. The HD map is constructed as a directed graph of GPS coordinates, each linked to a corresponding LiDAR scan, collected over a 30-min drive on a university campus using a Velodyne VLP-16 sensor and a ublox ZED-F9P RTK-GPS receiver, yielding 19,500 time-synchronized point clouds. Within this framework, we develop and compare three similarity metrics drawn from distinct families: Fast Point Feature Histograms (FPFH) with KDTree-based matching, Procrustes-based alignment via singular value decomposition, and a planar projection method based on 2D angular histogram cross-correlation. Each metric is evaluated on the same dataset in terms of similarity score profile (localizability) and per-pair computational cost. FPFH provides rich local geometric matching but at an average per-pair cost of approximately 1018 s, making it suitable only for offline analysis. Procrustes alignment yields the smoothest score profiles, with an exact self-similarity baseline of zero, at an average of 2.63 s per pair. The planar projection method produces the most location-invariant profiles at an average of 11.6 s per pair. We also discuss the recursive localization architecture into which any of these metrics could be embedded, and analyze the gap between current per-pair costs and what would be required for online deployment, which we identify as a direction for future work. The study contributes a controlled, reproducible benchmark of three metric families on a single real-world dataset, and provides guidance for selecting similarity metrics under stated operating assumptions.