{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:23:51Z","timestamp":1760239431799,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T00:00:00Z","timestamp":1605225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773184"],"award-info":[{"award-number":["61773184"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cooperative target tracking by multiple vehicles connected through inter-vehicle communication is a promising way to improve the estimation of target state. The effectiveness of cooperative tracking closely depends on the accuracy of relative localization between host and cooperative vehicles. However, the localization signal usually provided by the satellite-based navigation system is rather susceptible to dynamic driving environment, thus influencing the effectiveness of cooperative tracking. In order to implement reliable cooperative tracking, especially when the statistical characteristic of the relative localization noise is time-varying and uncertain, this paper presents a recursive Bayesian framework which jointly estimates the state of the target and the cooperative vehicle as well as the localization noise parameter. An online variational Bayesian inference algorithm is further developed to achieve efficient recursive estimate. The simulation results verify that our proposed algorithm can effectively boost the accuracy of target tracking when the localization noise dynamically changes over time.<\/jats:p>","DOI":"10.3390\/s20226487","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:44:02Z","timestamp":1605257042000},"page":"6487","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-Vehicle Cooperative Target Tracking with Time-Varying Localization Uncertainty via Recursive Variational Bayesian Inference"],"prefix":"10.3390","volume":"20","author":[{"given":"Xiaobo","family":"Chen","sequence":"first","affiliation":[{"name":"Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China"}]},{"given":"Yanjun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China"}]},{"given":"Ling","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China"}]},{"given":"Jianyu","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, H., Yu, Y., Cai, Y., Chen, X., Chen, L., and Li, Y. (2020). Soft-weighted-average ensemble vehicle detection method based on single-stage and two-stage deep learning models. IEEE Trans. Intell. Veh., 1.","DOI":"10.1109\/TIV.2020.3010832"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/MITS.2019.2903518","article-title":"A comparative study of state-of-the-art deep learning algorithms for vehicle detection","volume":"11","author":"Wang","year":"2019","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/MITS.2015.2409883","article-title":"The impact of cooperative perception on decision making and planning of autonomous vehicles","volume":"7","author":"Kim","year":"2015","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/TITS.2014.2337316","article-title":"Multivehicle cooperative driving using cooperative perception: Design and experimental validation","volume":"16","author":"Kim","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1109\/TIV.2019.2938110","article-title":"No blind spots: Full-surround multi-object tracking for autonomous vehicles using cameras and LiDARs","volume":"4","author":"Rangesh","year":"2019","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, H., Fang, J., Cui, S., Xu, H., and Xue, J. (2019, January 11\u201314). Multi-3D-object tracking by fusing RGB and 3D-LiDAR data. Proceedings of the IEEE International Conference on Unmanned Aircraft Systems (ICUAS), Atlanta, GA, USA.","DOI":"10.1109\/ICUS48101.2019.8995984"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"G\u00fcnther, H.-J., Mennenga, B., Trauer, O., Riebl, R., and Wolf, L.C. (2016, January 8\u201310). Realizing collective perception in a vehicle. Proceedings of the IEEE Vehicular Networking Conference (VNC), Columbus, OH, USA.","DOI":"10.1109\/VNC.2016.7835930"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1109\/JPROC.2011.2132790","article-title":"Dedicated short-range communications (DSRC) standards in the United States","volume":"99","author":"Kenney","year":"2011","journal-title":"Proc. IEEE"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1109\/JIOT.2016.2611605","article-title":"LTE-V: A TD-LTE-based V2X solution for future vehicular network","volume":"3","author":"Chen","year":"2016","journal-title":"IEEE Internet Things J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.measurement.2016.10.018","article-title":"Millimeter wave radio channel characterization for 5G vehicle-to-vehicle communications","volume":"95","author":"Cid","year":"2017","journal-title":"Measurement"},{"key":"ref_11","first-page":"63","article-title":"Data analytics for cooperative intelligent transport systems","volume":"15","author":"Javed","year":"2019","journal-title":"Veh. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liggins, M., Hall, D., and Llinas, J. (2017). Handbook of Multisensor Data Fusion: Theory and Practice, CRC Press.","DOI":"10.1201\/9781420053098"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Marvasti, E.E., Raftari, A., Marvasti, A.E., Fallah, Y.P., Guo, R., and Lu, H. (2020). Cooperative LIDAR object detection via feature sharing in deep networks. arXiv.","DOI":"10.1109\/VTC2020-Fall49728.2020.9348723"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/0967-0661(94)90349-2","article-title":"Data fusion in decentralized sensor networks","volume":"2","author":"Grime","year":"1994","journal-title":"Control. Eng. Pract."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gabb, M., Digel, H., Muller, T., and Henn, R.-W. (2019, January 9). Infrastructure-supported perception and track-level fusion using edge computing. Proceedings of the IV IEEE Intelligent Vehicles Symposium, Paris, France.","DOI":"10.1109\/IVS.2019.8813886"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, Q., Tang, S., Yang, Q., and Fu, S. (2019, January 7\u20139). Cooper: Cooperative perception for connected autonomous vehicles based on 3D point clouds. Proceedings of the 39th IEEE International Conference on Distributed Computing Systems (ICDCS), Dalas, TX, USA.","DOI":"10.1109\/ICDCS.2019.00058"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Vasic, M., and Martinoli, A. (2015, January 15\u201318). A collaborative sensor fusion algorithm for multi-object tracking using a Gaussian mixture probability hypothesis density filter. Proceedings of the 18th IEEE International Conference on Intelligent Transportation Systems, Las Palmas, Spain.","DOI":"10.1109\/ITSC.2015.87"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4091","DOI":"10.1109\/TSP.2006.881190","article-title":"The Gaussian mixture probability hypothesis density filter","volume":"54","author":"Vo","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/ICIF.2002.1021196","article-title":"An information theoretic justification for covariance intersection and its generalization","volume":"1","author":"Hurley","year":"2002","journal-title":"Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997)"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Vasic, M., Lederrey, G., Navarro, I., and Martinoli, A. (2016, January 19\u201322). An overtaking decision algorithm for networked intelligent vehicles based on cooperative perception. Proceedings of the IV IEEE Intelligent Vehicles Symposium, Gothenburg, Sweden.","DOI":"10.1109\/IVS.2016.7535519"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Thomaidis, G., Vassilis, K., Lytrivis, P., Tsogas, M., Karaseitanidis, G., and Amditis, A. (2011, January 5\u20139). Target tracking and fusion in vehicular networks. Proceedings of the IV IEEE Intelligent Vehicles Symposium, Baden, Germany.","DOI":"10.1109\/IVS.2011.5940535"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Soatti, G., Nicoli, M., Garcia, N., Denis, B., Raulefs, R., and Wymeersch, H. (2017, January 16\u201319). Enhanced vehicle positioning in cooperative ITS by joint sensing of passive features. Proceedings of the 20th IEEE International Conference on Intelligent Transportation Systems (ITSC), Yokohama, Japan.","DOI":"10.1109\/ITSC.2017.8317801"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s00190-013-0686-4","article-title":"Instantaneous BeiDou+GPS RTK positioning with high cut-off elevation angles","volume":"88","author":"Teunissen","year":"2014","journal-title":"J. Geodesy"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huang, C., and Wu, X. (2019, January 20\u201324). Cooperative vehicle tracking using particle filter integrated with interacting multiple models. Proceedings of the IEEE International Conference on Communications (ICC), Shanghai, China.","DOI":"10.1109\/ICC.2019.8761905"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/TIV.2019.2938093","article-title":"Multisensor poisson multi-bernoulli filter for joint target\u2013sensor state tracking","volume":"4","author":"Lindberg","year":"2019","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_26","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_27","unstructured":"Kakinuma, K., Ozaki, M., Hashimoto, M., and Takahashi, K. (2012, January 20\u201323). Cooperative pedestrian tracking by multi-vehicles in GPS-denied environments. Proceedings of the SICE Annual Conference (SICE), Akita, Japan."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Chen, X., Ji, J., and Wang, Y. (2020). Robust cooperative multi-vehicle tracking with inaccurate self-localization based on on-board sensors and inter-vehicle communication. Sensors, 20.","DOI":"10.3390\/s20113212"},{"key":"ref_29","unstructured":"Hu, X., Sun, Y., Gao, J., Hu, Y., Ju, F., and Yin, B. (2020). Probabilistic linear discriminant analysis based on L1-norm and its Bayesian variational inference. IEEE Trans. Cybern., 1\u201312."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1109\/TNNLS.2014.2387376","article-title":"L1-norm low-rank matrix factorization by variational Bayesian method","volume":"26","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TAC.2008.2008348","article-title":"Recursive noise adaptive Kalman filtering by variational Bayesian approximations","volume":"54","author":"Sarkka","year":"2009","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"124","DOI":"10.5772\/64012","article-title":"Recursive variational Bayesian inference to simultaneous registration and fusion","volume":"13","author":"Zhu","year":"2016","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.ins.2012.09.017","article-title":"A variational Bayesian approach to robust sensor fusion based on Student-t distribution","volume":"221","author":"Zhu","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_34","unstructured":"Koller, D., and Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques, MIT Press."},{"key":"ref_35","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.measurement.2018.02.055","article-title":"Variational Bayesian adaptation of noise covariances in multiple target tracking problems","volume":"122","author":"Hosseini","year":"2018","journal-title":"Measurement"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6487\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:33:06Z","timestamp":1760178786000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6487"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,13]]},"references-count":36,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20226487"],"URL":"https:\/\/doi.org\/10.3390\/s20226487","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,11,13]]}}}