Estimating the Speed of Nearby Vehicles with a Single Onboard Camera by Smooth Kernel Regression

Estimating the speed of nearby vehicles is essential for driver assistance. A real-time, camera-only pipeline is presented that uses an onboard monocular camera: vehicles are detected and tracked with an off-the-shelf one-stage CNN (YOLOv8); distance is approximated from bounding-box angular width using class-dependent priors (2.0m cars; 2.5m larger vehicles) and camera intrinsics; a Nadaraya-Watson kernel smooths the distance sequence, and its analytic derivative yields relative speed. The approach supports multiple targets without dedicated ranging hardware. Evaluation on CARLA synthetic video with ground truth analyzes estimated vs. ground-truth distance, estimate/ground-truth ratio vs. image-center displacement, and kernel-based speed vs. a polynomial trend. Results show a positional bias away from the image center and a stability-lag trade-off due to smoothing. The contribution is a detector-agnostic distance-speed head that couples angular geometry with analytic Nadaraya-Watson smoothing and differentiation for real-time operation, positioned as a low-cost alternative or complement to active sensors, with limitations and paths to real-world validation outlined.