A 4D Radar Camera Extrinsic Calibration Tool Based on 3D Uncertainty Perspective N Points

4D imaging radar is a type of low-cost millimeter-wave radar(costing merely 10-20% of lidar systems) capable of providing range, azimuth, elevation, and Doppler velocity information. Accurate extrinsic calibration between millimeter-wave radar and camera systems is critical for robust multimodal perception in robotics, yet remains challenging due to inherent sensor noise characteristics and complex error propagation. This paper presents a systematic calibration framework to address critical challenges through a spatial 3d uncertainty-aware PnP algorithm (3DUPnP) that explicitly models spherical coordinate noise propagation in radar measurements, then compensating for non-zero error expectations during coordinate transformations. Finally, experimental validation demonstrates significant performance improvements over state-of-the-art CPnP baseline, including improved consistency in simulations and enhanced precision in physical experiments. This study provides a robust calibration solution for robotic systems equipped with millimeter-wave radar and cameras, tailored specifically for autonomous driving and robotic perception applications.