{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T07:51:38Z","timestamp":1769068298601,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T00:00:00Z","timestamp":1642982400000},"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":["61403259, 61773266, 2019YFB2102703"],"award-info":[{"award-number":["61403259, 61773266, 2019YFB2102703"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Science and Technology Research and Development Foundation of Shenzhen","award":["20200813140339001, 20200809215801001, JCYJ20210324120209027"],"award-info":[{"award-number":["20200813140339001, 20200809215801001, JCYJ20210324120209027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Establishing a symmetrical model of surrounding vehicles and accurately obtaining the driving state of the surrounding vehicles in the driving environment can improve the safety of driving, which is an important issue that needs to be considered in the automatic driving system or auxiliary driving system. Therefore, we propose an adaptive unscented Kalman filter algorithm based on Interacting Multiple Model (IMM) theory to estimate the state of target vehicle in the high-speed driving environment. To be specific, we use the Constant Turn Rate and Acceleration (CTRA) theory to establish the target vehicle kinematics model, simultaneously, in order to overcome the problem of estimator failure when the yaw rate is close to zero, a simplified version of the CTRA model is also introduced into the estimation process. In addition, the parameter adaptation strategy is added, so the proposed estimator can overcome the uncertainty of the noise model and improve its accuracy. Finally, the effectiveness of proposed state estimation algorithm is verified on the Carsim and Simulink co-simulation platform. The results of simulations and experiments show that the accuracy and stability of IMM-based algorithm is better than the single-model algorithm in different scenarios, and the parameter adaptation strategy brings performance improvement.<\/jats:p>","DOI":"10.3390\/sym14020222","type":"journal-article","created":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T21:07:11Z","timestamp":1643144831000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Estimation of Vehicle State Based on IMM-AUKF"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2881-7093","authenticated-orcid":false,"given":"Ying","family":"Xu","sequence":"first","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Wenjie","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Wentao","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Chengxiang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Rong","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2935-0069","authenticated-orcid":false,"given":"Li","family":"He","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Yun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MITS.2011.942201","article-title":"Task-Based Environment Interpretation and System Architecture for Next Generation ADAS","volume":"3","author":"Kastner","year":"2011","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_2","first-page":"770","article-title":"A Research on Driving State Estimation for Distributed Drive Electric Vehicle Based on NA-EKF","volume":"40","author":"Geng","year":"2018","journal-title":"Qiche Gongcheng\/Automot. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4440","DOI":"10.1109\/TVT.2015.2496969","article-title":"A Reliable Fusion Methodology for Simultaneous Estimation of Vehicle Sideslip and Yaw Angles","volume":"65","author":"Li","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1080\/00423114.2015.1025082","article-title":"A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces","volume":"53","author":"Li","year":"2015","journal-title":"Veh. Syst. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1109\/TITS.2015.2401837","article-title":"The Driving Safety Field Based on Driver-Vehicle-Road Interactions","volume":"16","author":"Wang","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1002\/asjc.1449","article-title":"Estimation of Road Friction Coefficient and Vehicle States by 3-DOF Dynamic Model and HSRI Model Based on Information Fusion","volume":"20","author":"Ying","year":"2018","journal-title":"Asian J. Control"},{"key":"ref_7","unstructured":"Yi, Z., Li, L., Ling, S., and Matt, M. (2016, January 8\u201316). DAVE: A Unified Framework for Fast Vehicle Detection and Annotation. Proceedings of the European Conference on Computer Vision, Amsterdam, The Netherlands."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yang, L., Liu, J., and Tang, X. (2014, January 6\u201312). Object Detection and Viewpoint Estimation with Auto-masking Neural Network. Proceedings of the European Conference on Computer Vision, Zurich, Switzerland.","DOI":"10.1007\/978-3-319-10578-9_29"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1109\/TITS.2015.2402438","article-title":"Vehicle Type Classification Using a Semisupervised Convolutional Neural Network. Intelligent Transportation Systems","volume":"16","author":"Dong","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_10","unstructured":"Pino, I.D., Vaquero, V., Masini, B., Sol\u00e0, J., Moreno-Noguer, F., Sanfeliu, A., and Andrade-Cetto, J. (2017, January 22\u201324). Low resolution lidar-based multi object tracking for driving applications. Proceedings of the Iberian Robotics Conference, Seville, Spain."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, B. (2017, January 24\u201328). 3D fully convolutional network for vehicle detection in point cloud. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8205955"},{"key":"ref_12","unstructured":"Bo, L., Zhang, T., and Tian, X. (2016). Vehicle Detection from 3D Lidar Using Fully Convolutional Network. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chen, X., Ma, H., Wan, J., Li, B., and Xia, T. (2017, January 21\u201326). Multi-View 3D Object Detection Network for Autonomous Driving. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.691"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.measurement.2018.10.030","article-title":"Vehicle Dynamics Estimation via Augmented Extended Kalman Filtering","volume":"133","author":"Reina","year":"2018","journal-title":"Measurement"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.procs.2013.10.025","article-title":"Dynamic State Estimation in Vehicle Platoon System by Applying Particle Filter and Unscented Kalman Filter","volume":"24","author":"Suzuki","year":"2013","journal-title":"Procedia Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1109\/7.826326","article-title":"An interacting multiple model fixed-lag smoothing algorithm for Markovian switching systems","volume":"36","author":"Chen","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4122","DOI":"10.3390\/s130404122","article-title":"Multi-Sensor Fusion with Interacting Multiple Model Filter for Improved Aircraft Position Accuracy","volume":"13","author":"Cho","year":"2013","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TITS.2007.902642","article-title":"High-Integrity IMM-EKF-Based Road Vehicle Navigation with Low-Cost GPS\/SBAS\/INS","volume":"8","year":"2007","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1016\/j.sigpro.2009.04.033","article-title":"A novel interacting multiple model algorithm","volume":"89","author":"Qu","year":"2009","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1109\/TAES.2005.1561886","article-title":"Survey of maneuvering target tracking. Part V. Multiple-model methods","volume":"41","author":"Li","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1049\/ip-rsn:20041002","article-title":"Fuzzy-logic-based IMM algorithm for tracking a manoeuvring target","volume":"152","author":"Lee","year":"2005","journal-title":"IEEE Proc. Radar Sonar Navig."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/TAES.2005.1541443","article-title":"IMM estimator versus optimal estimator for hybrid systems","volume":"41","author":"Challa","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1109\/TVT.2014.2329497","article-title":"An IMM\/EKF Approach for Enhanced Multitarget State Estimation for Application to Integrated Risk Management System","volume":"64","author":"Kim","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1049\/ip-rsn:19951528","article-title":"Adaptive interacting multiple model algorithm for tracking a manoeuvring target","volume":"142","author":"Munir","year":"1995","journal-title":"Radar Sonar Navig. IEEE Proc."},{"key":"ref_25","unstructured":"Nie, Y., and Tao, Z. (2015, January 27\u201329). A self-adaptive scaling parameter selection algorithm for the Unscented Kalman Filter. Proceedings of the Chinese Automation Congress, Wuhan, China."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jo, K., Chu, K., Kim, J., and Sunwoo, M. (2011, January 5\u20137). Distributed vehicle state estimation system using information fusion of GPS and in-vehicle sensors for vehicle localization. Proceedings of the 2011 14th International IEEE Conference on Intelligent Transportation Systems, Washington, DC, USA.","DOI":"10.1109\/ITSC.2011.6083010"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"291913","DOI":"10.1155\/2015\/291913","article-title":"Centralized Fusion of Unscented Kalman Filter Based on Huber Robust Method for Nonlinear Moving Target Tracking","volume":"2015","author":"Huang","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Tsogas, M., Polychronopoulos, A., and Amditis, A. (2006, January 25\u201328). Unscented Kalman filter design for curvilinear motion models suitable for automotive safety applications. Proceedings of the 2005 7th International Conference on Information Fusion, Philadelphia, PA, USA.","DOI":"10.1109\/ICIF.2005.1592006"},{"key":"ref_29","unstructured":"Wan, E.A., and van der Merwe, R. (2000, January 4). The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373),  Lake Louise, AB, Canada."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5088","DOI":"10.3390\/en6105088","article-title":"Comparison Study on the Battery SoC Estimation with EKF and UKF Algorithms","volume":"6","author":"He","year":"2013","journal-title":"Energies"},{"key":"ref_31","first-page":"122","article-title":"A Hierarchical Track Fusion Algorithm Based on IMM-UKF","volume":"2","author":"Kong","year":"2018","journal-title":"Fire Control Command Control"},{"key":"ref_32","unstructured":"Huang, D., and Leung, H. (2004, January 3\u20136). EM-IMM based land-vehicle navigation with GPS\/INS. Proceedings of the 7th International IEEE Conference on Intelligent Transportation Systems (IEEE Cat. No.04TH8749), Washington, WA, USA."},{"key":"ref_33","unstructured":"Zheng, Z., Liu, S., and Zhang, B. (2012, January 25\u201327). An improved Sage-Husa adaptive filtering algorithm. Proceedings of the 31st Chinese Control Conference, Hefei, China."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/222\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:06:28Z","timestamp":1760133988000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/222"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,24]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020222"],"URL":"https:\/\/doi.org\/10.3390\/sym14020222","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,24]]}}}