Vehicle Speed Estimation Using Infrastructure-Mounted LiDAR via Rectangle Edge Matching

Smart transportation infrastructure is increasingly deployed, and cooperative perception using stationary Light Detection and Ranging (LiDAR) sensors installed at intersections and along roadsides is becoming more important. However, infrastructure LiDAR often suffers from sparse point-cloud data (PCD) at long ranges and frequent occlusions, which can degrade the stability of inter-frame displacement and speed estimation. This paper proposes a real-time vehicle speed estimation method that operates robustly under sparse and partially observed conditions. The proposed approach extracts boundary points from clustered vehicle PCD and removes outliers, and then fits a 2D rectangle to the vehicle contour via Gauss–Newton optimization by minimizing distance-based residuals between boundary points and rectangle edges. To further improve robustness, we incorporate Hessian augmentation terms that account for boundary states and size variations, thereby alleviating excessive boundary violations and abnormal deformation of the width and height parameters during iterations. Next, from the fitted rectangles in consecutive frames, we construct a nearest corner with respect to the LiDAR origin and an auxiliary point, and perform 2D SVD-based alignment using only these two representative points. This enables efficient computation of inter-frame displacement and speed without full point-cloud registration (e.g., iterative closest point (ICP)). Experiments conducted at an intersection in K-City (Hwaseong, Republic of Korea) using a 40-channel LiDAR, a test vehicle (Genesis G70), and a real-time kinematic (RTK) system (MRP-2000) show that the proposed method stably preserves representative points and fits rectangles, even in sparse regions where only about two LiDAR rings are observed. Using CAN-based vehicle speed as the reference, the proposed method achieves an MAE of 0.76–1.37 kph and an RMSE of 0.90–1.58 kph over the tested speed settings (30, 50, and 70 kph, as well as high speed (~90 kph)) and trajectory scenarios. Furthermore, per-object processing-time measurements confirm the real-time feasibility of the proposed algorithm.