{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:08:42Z","timestamp":1787029722932,"version":"build-2736575974"},"reference-count":35,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T00:00:00Z","timestamp":1765584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate extrinsic calibration between radar and camera sensors is essential for reliable multi-modal perception in robotics and autonomous navigation. Traditional calibration methods often rely on artificial targets such as checkerboards or corner reflectors, which can be impractical in dynamic or large-scale environments. This study presents a fully targetless calibration framework that estimates the rigid spatial transformation between radar and camera coordinate frames by aligning their observed trajectories of a moving object. The proposed method integrates You Only Look Once version 5 (YOLOv5)-based 3D object localization for the camera stream with Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Random Sample Consensus (RANSAC) filtering for sparse and noisy radar measurements. A passive temporal synchronization technique, based on Root Mean Square Error (RMSE) minimization, corrects timestamp offsets without requiring hardware triggers. Rigid transformation parameters are computed using Kabsch and Umeyama algorithms, ensuring robust alignment even under millimeter-wave (mmWave) radar sparsity and measurement bias. The framework is experimentally validated in an indoor OptiTrack-equipped laboratory using a Skydio 2 drone as the dynamic target. Results demonstrate sub-degree rotational accuracy and decimeter-level translational error (approximately 0.12\u20130.27 m depending on the metric), with successful generalization to unseen motion trajectories. The findings highlight the method\u2019s applicability for real-world autonomous systems requiring practical, markerless multi-sensor calibration.<\/jats:p>","DOI":"10.3390\/s25247574","type":"journal-article","created":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T08:46:52Z","timestamp":1765874812000},"page":"7574","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Targetless Radar\u2013Camera Calibration via Trajectory Alignment"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7397-1055","authenticated-orcid":false,"given":"Ozan","family":"Durmaz","sequence":"first","affiliation":[{"name":"Electrical and Electronics Engineering Department, Eskisehir Osmangazi University, Meselik, Eskisehir 26040, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1708-8817","authenticated-orcid":false,"given":"Hakan","family":"Cevikalp","sequence":"additional","affiliation":[{"name":"Electrical and Electronics Engineering Department, Eskisehir Osmangazi University, Meselik, Eskisehir 26040, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1109\/TRO.2021.3075644","article-title":"ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual\u2013Inertial, and Multimap SLAM","volume":"37","author":"Campos","year":"2021","journal-title":"IEEE Trans. Robot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1109\/TRO.2016.2624754","article-title":"Past, Present, and Future of Simultaneous Localization and Mapping: Towards the Robust-Perception Age","volume":"32","author":"Cadena","year":"2016","journal-title":"IEEE Trans. Robot."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Lee, C.L., Hsueh, Y.H., Wang, C.C., and Lin, W.C. (2020\u201324, January 24). Extrinsic and Temporal Calibration of Automotive Radar and 3D LiDAR. Proceedings of the IEEE\/RSJ IROS, Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9341715"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"97147","DOI":"10.1109\/ACCESS.2023.3312382","article-title":"Radars for Autonomous Driving: A Review of Deep Learning Methods and Challenges","volume":"11","author":"Srivastav","year":"2023","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pearce, A., Zhang, J.A., Xu, R., and Wu, K. (2023). Multi-Object Tracking with mmWave Radar: A Review. Electronics, 12.","DOI":"10.3390\/electronics12020308"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Domhof, J., Kooij, J.F., and Gavrila, D.M. (2019, January 20\u201324). An Extrinsic Calibration Tool for Radar, Camera and Lidar. Proceedings of the IEEE ICRA, Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8794186"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6082","DOI":"10.1109\/TITS.2023.3251183","article-title":"Globally Optimal Robust Radar Calibration in Intelligent Transportation Systems","volume":"24","author":"Li","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_8","unstructured":"Bochkovskiy, A., Wang, C.Y., and Liao, H.Y.M. (2020). YOLOv4: Optimal Speed and Accuracy of Object Detection. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15435","DOI":"10.1109\/JSEN.2022.3167251","article-title":"MS-YOLO: Object Detection Based on YOLOv5 Optimized Fusion of mm-Wave Radar and Vision","volume":"22","author":"Song","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Cheng, L., Sengupta, A., and Cao, S. (2023). 3D Radar and Camera Co-Calibration: A Flexible and Accurate Method for Target-Based Extrinsic Calibration, University of Arizona. Technical Report.","DOI":"10.1109\/RadarConf2351548.2023.10149669"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Heng, L. (2020\u201324, January 24). Automatic Targetless Extrinsic Calibration of Multiple 3D Lidars and Radars. Proceedings of the IEEE\/RSJ IROS, Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9340866"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sch\u00f6ller, C., Schnettler, M., Kr\u00e4mmer, A., Hinz, G., Bakovic, M., G\u00fczet, M., and Knoll, A.C. (2019). Targetless Rotational Auto-Calibration of Radar and Camera for Intelligent Transportation Systems. arXiv.","DOI":"10.1109\/ITSC.2019.8917135"},{"key":"ref_13","unstructured":"Wise, E., Per\u0161i\u0107, J., Grebe, C., Petrovi\u0107, I., and Kelly, J. (June, January 30). A Continuous-Time Approach for 3D Radar-to-Camera Extrinsic Calibration. Proceedings of the IEEE ICRA, Xi\u2019an, China."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1080\/01691864.2020.1819874","article-title":"Online Multi-Sensor Calibration Based on Moving Object Tracking","volume":"35","year":"2021","journal-title":"Adv. Robot."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wise, E., Cheng, Q., and Kelly, J. (2022). Spatiotemporal Calibration of 3D mm-Wave Radar-Camera Pairs. arXiv.","DOI":"10.1109\/TRO.2023.3311680"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"055118","DOI":"10.1088\/1361-6501\/ad29e6","article-title":"Automatic calibration and association for roadside radar and camera based on fluctuating traffic volume","volume":"35","author":"Jin","year":"2024","journal-title":"Meas. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"22278","DOI":"10.1109\/TITS.2021.3119079","article-title":"A Novel Spatiotemporal Synchronization Method of Roadside Asynchronous MMW Radar\u2013Camera for Sensor Fusion","volume":"23","author":"Du","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_18","first-page":"15502","article-title":"Trajectory-driven automatic extrinsic calibration for roadside radar\u2013camera fusion","volume":"25","author":"Zhu","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5715","DOI":"10.1109\/TVT.2022.3232135","article-title":"YOLO-ORE: A Deep Learning-Aided Object Recognition Approach for Radar Systems","volume":"72","author":"Huang","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","unstructured":"Ester, M., Kriegel, H., Sander, J., and Xu, X. (1996, January 2\u20134). A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Proceedings of the KDD, Portland, OR, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1145\/358669.358692","article-title":"Random Sample Consensus","volume":"24","author":"Fischler","year":"1981","journal-title":"Commun. ACM"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Olson, E. (2010, January 18\u201322). A Passive Solution to the Sensor Synchronization Problem. Proceedings of the IEEE\/RSJ IROS, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5650579"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"289","DOI":"10.37394\/23205.2024.23.29","article-title":"Exploring Radar-Camera Extrinsic Calibration: A Deep Learning Perspective and Challenges","volume":"23","author":"Ibrahim","year":"2024","journal-title":"Wseas Trans. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ren, F., Liu, H., and Wang, H. (2024). A LiDAR-Camera Joint Calibration Algorithm Based on Deep Learning. Sensors, 24.","DOI":"10.3390\/s24186033"},{"key":"ref_25","unstructured":"Texas Instruments (2025, December 10). IWR1843 Datasheet. Available online: https:\/\/www.ti.com\/product\/IWR1843."},{"key":"ref_26","unstructured":"(2025, December 10). RealSense D435i Product Specification. Available online: https:\/\/realsenseai.com\/products\/depth-camera-d435i\/."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1107\/S0567739476001873","article-title":"A solution for the best rotation to relate two sets of vectors","volume":"32","author":"Kabsch","year":"1976","journal-title":"Acta Crystallogr. Sect. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/34.88573","article-title":"Least-Squares Estimation of Transformation Parameters Between Two Point Patterns","volume":"13","author":"Umeyama","year":"1991","journal-title":"IEEE TPAMI"},{"key":"ref_29","unstructured":"NaturalPoint, Inc. (2025, December 10). OptiTrack Motion Capture System User Manual. Available online: https:\/\/optitrack.com\/."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, A., Nowruzi, F.E., and Laganiere, R. (2021, January 26\u201328). RadDet: Radar Range-Azimuth-Doppler Based Radar Object Detection. Proceedings of the IEEE CRV, Burnaby, BC, Canada.","DOI":"10.1109\/CRV52889.2021.00021"},{"key":"ref_31","unstructured":"Jocher, G. (2025, December 10). Ultralytics YOLOv5. Zenodo, Available online: https:\/\/github.com\/ultralytics\/yolov5."},{"key":"ref_32","unstructured":"Open Source Robotics Foundation (2025, December 10). ROS 2 Humble Hawksbill Documentation. Available online: https:\/\/docs.ros.org\/en\/humble."},{"key":"ref_33","first-page":"2633","article-title":"Pose Estimation for Augmented Reality: A Hands-On Survey","volume":"22","author":"Marchand","year":"2016","journal-title":"IEEE TVCG"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Luu, V.T., Cai, Y.L., Tran, V.H., Chiu, W.C., Chen, Y.T., and Huang, C.C. (2025, January 11\u201315). RC-AutoCalib: An End-to-End Radar-Camera Automatic Calibration Network. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR52734.2025.00628"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Liu, X., Deng, Z., and Zhang, G. (2025). Targetless Radar\u2013Camera Extrinsic Parameter Calibration Using Track-to-Track Association. Sensors, 25.","DOI":"10.3390\/s25030949"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/24\/7574\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T08:51:10Z","timestamp":1765875070000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/24\/7574"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,13]]},"references-count":35,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["s25247574"],"URL":"https:\/\/doi.org\/10.3390\/s25247574","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,13]]}}}