{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T07:43:23Z","timestamp":1791272603498,"version":"4.1.0"},"reference-count":47,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T00:00:00Z","timestamp":1768435200000},"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>Three-dimensional multi-object tracking (3D MOT) plays a vital role in enabling reliable perception for LiDAR-based autonomous systems. However, LiDAR measurements often exhibit sparsity, occlusion, and sensor noise that lead to uncertainty and instability in downstream tracking. To address these challenges, we propose FGO-PMB, a unified probabilistic framework that integrates the Poisson Multi-Bernoulli (PMB) filter from Random Finite Set (RFS) theory with Factor Graph Optimization (FGO) for robust LiDAR-based object tracking. In the proposed framework, object states, existence probabilities, and association weights are jointly formulated as optimizable variables within a factor graph. Four factors, including state transition, observation, existence, and association consistency, are formulated to uniformly encode the spatio-temporal constraints among these variables. By unifying the uncertainty modeling capability of RFS with the global optimization strength of FGO, the proposed framework achieves temporally consistent and uncertainty-aware estimation across continuous LiDAR scans. Experiments on KITTI and nuScenes indicate that the proposed method achieves competitive 3D MOT accuracy while maintaining real-time performance.<\/jats:p>","DOI":"10.3390\/s26020591","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T12:31:41Z","timestamp":1768480301000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["FGO-PMB: A Factor Graph Optimized Poisson Multi-Bernoulli Filter for Accurate Online 3D Multi-Object Tracking"],"prefix":"10.3390","volume":"26","author":[{"given":"Jingyi","family":"Jin","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5660-1281","authenticated-orcid":false,"given":"Jindong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun 130012, China"},{"name":"Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiming","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yitong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun 130012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bewley, A., Ge, Z., Ott, L., Ramos, F., and Upcroft, B. (2016, January 25\u201328). Simple online and realtime tracking. Proceedings of the 2016 IEEE International Conference on Image Processing (ICIP), Phoenix, AZ, USA.","DOI":"10.1109\/ICIP.2016.7533003"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Weng, X., Wang, J., Held, D., and Kitani, K. (2020, January 25\u201329). 3d multi-object tracking: A baseline and new evaluation metrics. Proceedings of the 2020 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9341164"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chiu, H.k., Prioletti, A., Li, J., and Bohg, J. (2020). Probabilistic 3d multi-object tracking for autonomous driving. arXiv.","DOI":"10.1109\/ICRA48506.2021.9561754"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Pang, Z., Li, Z., and Wang, N. (2022). Simpletrack: Understanding and rethinking 3d multi-object tracking. Proceedings of the European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-031-25056-9_43"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Weng, X., Wang, Y., Man, Y., and Kitani, K.M. (2020, January 14\u201319). Gnn3dmot: Graph neural network for 3d multi-object tracking with 2d-3d multi-feature learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00653"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/TSP.2023.3314275","article-title":"Neural enhanced belief propagation for multiobject tracking","volume":"72","author":"Liang","year":"2023","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","unstructured":"Zhang, P., Li, X., He, L., and Lin, X. (2023). 3d multiple object tracking on autonomous driving: A literature review. arXiv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109544","DOI":"10.1016\/j.sigpro.2024.109544","article-title":"3D multi-object tracking based on informatic divergence-guided data association","volume":"222","author":"He","year":"2024","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liu, K., Jin, S., Fu, Z., Chen, Z., Jiang, R., and Ye, J. (2023, January 4\u20136). Uncertainty-aware unsupervised multi-object tracking. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Paris, France.","DOI":"10.1109\/ICCV51070.2023.00917"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1007\/s42154-022-00185-1","article-title":"PTMOT: A probabilistic multiple object tracker enhanced by tracklet confidence for autonomous driving","volume":"5","author":"Jiang","year":"2022","journal-title":"Automot. Innov."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pang, S., Morris, D., and Radha, H. (June, January 30). 3d multi-object tracking using random finite set-based multiple measurement models filtering (rfs-m 3) for autonomous vehicles. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9561852"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/TIV.2022.3217490","article-title":"GNN-PMB: A simple but effective online 3D multi-object tracker without bells and whistles","volume":"8","author":"Liu","year":"2022","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.1109\/TAES.2018.2805153","article-title":"Poisson multi-Bernoulli mixture filter: Direct derivation and implementation","volume":"54","author":"Williams","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"P\u00f6schmann, J., Pfeifer, T., and Protzel, P. (2020, January 25\u201329). Factor graph based 3d multi-object tracking in point clouds. Proceedings of the 2020 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9340932"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1109\/JSEN.2023.3336221","article-title":"Accurate and real-time 3D-LiDAR multiobject tracking using factor graph optimization","volume":"24","author":"Feng","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng. Mar."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/nav.3800020109","article-title":"The Hungarian method for the assignment problem","volume":"2","author":"Kuhn","year":"1955","journal-title":"Nav. Res. Logist. Q."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yin, T., Zhou, X., and Krahenbuhl, P. (2021, January 19\u201325). Center-based 3d object detection and tracking. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.01161"},{"key":"ref_19","unstructured":"Zhang, W., Zhou, H., Sun, S., Wang, Z., Shi, J., and Loy, C.C. (November, January 27). Robust multi-modality multi-object tracking. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huang, K., and Hao, Q. (October, January 27). Joint multi-object detection and tracking with camera-LiDAR fusion for autonomous driving. Proceedings of the 2021 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic.","DOI":"10.1109\/IROS51168.2021.9636311"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kim, A., O\u0161ep, A., and Leal-Taix\u00e9, L. (June, January 30). Eagermot: 3d multi-object tracking via sensor fusion. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9562072"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, K., Liu, Y., Mei, F., Jin, J., and Wang, Y. (2023). Boost correlation features with 3D-MiIoU-based camera-LiDAR fusion for MODT in autonomous driving. Remote Sens., 15.","DOI":"10.3390\/rs15040874"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Luo, C., Yang, X., and Yuille, A. (2021, January 11\u201317). Exploring simple 3d multi-object tracking for autonomous driving. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Montreal, QC, Canada.","DOI":"10.1109\/ICCV48922.2021.01032"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8793","DOI":"10.1109\/TMM.2023.3241548","article-title":"CenterTube: Tracking multiple 3D objects with 4D tubelets in dynamic point clouds","volume":"25","author":"Liu","year":"2023","journal-title":"IEEE Trans. Multimed."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kini, J., Mian, A., and Shah, M. (June, January 29). 3DMODT: Attention-Guided Affinities for Joint Detection & Tracking in 3D Point Clouds. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK.","DOI":"10.1109\/ICRA48891.2023.10160305"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hairui, S., Ran, Z., Huiyan, C., Xiaodi, M., Lin, L., and Jingya, Q. (2024, January 24\u201326). A review of point target and extended target tracking algorithms. Proceedings of the 2024 3rd International Conference on Image Processing and Media Computing (ICIPMC), Hefei, China.","DOI":"10.1109\/ICIPMC62364.2024.10586568"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1109\/TSP.2015.2505683","article-title":"Multiple extended target tracking with labeled random finite sets","volume":"64","author":"Beard","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Xia, Y., Granstr\u00f6m, K., Svensson, L., Garc\u00eda-Fern\u00e1ndez, \u00c1.F., and Williams, J.L. (2019, January 2\u20135). Extended target Poisson multi-Bernoulli mixture trackers based on sets of trajectories. Proceedings of the 2019 22th International Conference on Information Fusion (FUSION), Ottawa, ON, Canada.","DOI":"10.23919\/FUSION43075.2019.9011181"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Pang, S., and Radha, H. (2021, January 6\u201311). Multi-object tracking using poisson multi-bernoulli mixture filtering for autonomous vehicles. Proceedings of the ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toronto, ON, Canada.","DOI":"10.1109\/ICASSP39728.2021.9415072"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5256","DOI":"10.1109\/TAES.2022.3168252","article-title":"An efficient labeled\/unlabeled random finite set algorithm for multiobject tracking","volume":"58","author":"Kropfreiter","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Shim, C., and Kim, D.Y. (2021, January 14\u201317). Space-oriented Label Partitioning for Multi-object Tracking. Proceedings of the 2021 International Conference on Control, Automation and Information Sciences (ICCAIS), Xi\u2019an, China.","DOI":"10.1109\/ICCAIS52680.2021.9624509"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11668","DOI":"10.1109\/TITS.2023.3294519","article-title":"Interaction-aware labeled multi-bernoulli filter","volume":"24","author":"Ishtiaq","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"P\u00f6schmann, J., Pfeifer, T., and Protzel, P. (2021, January 11\u201317). Optimization based 3D multi-object tracking using camera and radar data. Proceedings of the 2021 IEEE Intelligent Vehicles Symposium (IV), Nagoya, Japan.","DOI":"10.1109\/IV48863.2021.9575636"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4880","DOI":"10.1109\/TPAMI.2024.3362401","article-title":"Learnable Graph Matching: A Practical Paradigm for Data Association","volume":"46","author":"He","year":"2024","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5619513","DOI":"10.1109\/TGRS.2022.3152250","article-title":"Multi-object tracking in satellite videos with graph-based multitask modeling","volume":"60","author":"He","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","first-page":"1","article-title":"Factor graph aided multiple hypothesis tracking","volume":"56","author":"Wang","year":"2013","journal-title":"Sci. China Inf. Sci."},{"key":"ref_37","unstructured":"Schubert, R., Richter, E., and Wanielik, G. (July, January 30). Comparison and evaluation of advanced motion models for vehicle tracking. Proceedings of the 2008 11th International Conference on Information Fusion, Cologne, Germany."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1007\/s11263-020-01375-2","article-title":"Hota: A higher order metric for evaluating multi-object tracking","volume":"129","author":"Luiten","year":"2021","journal-title":"Int. J. Comput. Vis."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"246309","DOI":"10.1155\/2008\/246309","article-title":"Evaluating multiple object tracking performance: The clear mot metrics","volume":"2008","author":"Bernardin","year":"2008","journal-title":"EURASIP J. Image Video Process."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kim, A., Bras\u00f3, G., O\u0161ep, A., and Leal-Taix\u00e9, L. (2022). PolarMOT: How far can geometric relations take us in 3D multi-object tracking?. Proceedings of the European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-031-20047-2_3"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5704511","DOI":"10.1109\/TGRS.2022.3203163","article-title":"CasA: A cascade attention network for 3-D object detection from LiDAR point clouds","volume":"60","author":"Wu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5668","DOI":"10.1109\/TITS.2021.3055616","article-title":"3D multi-object tracking in point clouds based on prediction confidence-guided data association","volume":"23","author":"Wu","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Wu, H., Wen, C., Shi, S., Li, X., and Wang, C. (2023, January 17\u201324). Virtual sparse convolution for multimodal 3d object detection. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada.","DOI":"10.1109\/CVPR52729.2023.02074"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Cho, M., and Kim, E. (2023). 3D LiDAR multi-object tracking with short-term and long-term multi-level associations. Remote Sens., 15.","DOI":"10.3390\/rs15235486"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"109367","DOI":"10.1016\/j.sigpro.2023.109367","article-title":"3D multi-object tracking with boosting data association and improved trajectory management mechanism","volume":"218","author":"Jin","year":"2024","journal-title":"Signal Process."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1109\/LRA.2024.3511438","article-title":"A Multi-Modal Fusion-Based 3D Multi-Object Tracking Framework with Joint Detection","volume":"10","author":"Wang","year":"2025","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"4744","DOI":"10.1109\/TITS.2025.3542269","article-title":"Co-MOT: Exploring the Collaborative Relations in Traffic Flow for 3D Multi-Object Tracking","volume":"26","author":"Liu","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/2\/591\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T05:13:47Z","timestamp":1768626827000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/2\/591"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,15]]},"references-count":47,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["s26020591"],"URL":"https:\/\/doi.org\/10.3390\/s26020591","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,15]]}}}