{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T15:33:14Z","timestamp":1760369594712,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Funds of Chongqing Science and Technology Commission","award":["cstc2017jcyjAX0293"],"award-info":[{"award-number":["cstc2017jcyjAX0293"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Track-to-track association (T2TA) is a challenging task in situational awareness in intelligent vehicles and surveillance systems. In this paper, the problem of track-to-track association with sensor bias (T2TASB) is considered. Traditional T2TASB algorithms only consider a statistical distance cost between local tracks from different sensors, without exploiting the geometric relationship between one track and its neighboring ones from each sensor. However, the relative geometry among neighboring local tracks is usually stable, at least for a while, and thus helpful in improving the T2TASB. In this paper, we propose a probabilistic method, called the local track geometry preservation (LTGP) algorithm, which takes advantage of the geometry of tracks. Assuming that the local tracks of one sensor are represented by Gaussian mixture model (GMM) centroids, the corresponding local tracks of the other sensor are fitted to those of the first sensor. In this regard, a geometrical descriptor connectivity matrix is constructed to exploit the relative geometry of these tracks. The track association problem is formulated as a maximum likelihood estimation problem with a local track geometry constraint, and an expectation\u2013maximization (EM) algorithm is developed to find the solution. Simulation results demonstrate that the proposed methods offer better performance than the state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/s20051412","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T10:46:08Z","timestamp":1583318768000},"page":"1412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Track-to-Track Association for Intelligent Vehicles by Preserving Local Track Geometry"],"prefix":"10.3390","volume":"20","author":[{"given":"Ke","family":"Zou","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2215-9667","authenticated-orcid":false,"given":"Hao","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allan","family":"De Freitas","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Hatfield 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfu","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamid","family":"Esmaeili Najafabadi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2584","DOI":"10.1109\/TITS.2017.2658662","article-title":"Overview of Environment Perception for Intelligent Vehicles","volume":"18","author":"Zhu","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, Y., Chen, W., Peeta, S., and Wang, Y. (2019). Platoon Control of Connected Multi-Vehicle Systems Under V2X Communications: Design and Experiments. IEEE Trans. Intell. Transp. Syst.","DOI":"10.1109\/TITS.2019.2905039"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhu, H., Zou, K., Li, Y., Cen, M., and Mihaylova, L. (2019). Robust Non-Rigid Feature Matching for Image Registration Using Geometry Preserving. Sensors, 19.","DOI":"10.3390\/s19122729"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhu, H., Guo, B., Zou, K., Li, Y., Yuen, K., and Mihaylova, L. (2019). A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration. Sensors, 19.","DOI":"10.3390\/s19051191"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4618","DOI":"10.1109\/TIE.2018.2864708","article-title":"Integral-Sliding-Mode Braking Control for a Connected Vehicle Platoon: Theory and Application","volume":"66","author":"Li","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2209","DOI":"10.1109\/TITS.2018.2865546","article-title":"Nonlinear Consensus-Based Connected Vehicle Platoon Control Incorporating Car-Following Interactions and Heterogeneous Time Delays","volume":"20","author":"Li","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1109\/TITS.2017.2771820","article-title":"L-Shape Model Switching-Based Precise Motion Tracking of Moving Vehicles Using Laser Scanners","volume":"19","author":"Kim","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/TITS.2017.2784486","article-title":"Multi-Perspective Tracking for Intelligent Vehicle","volume":"19","author":"Ji","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1109\/TITS.2017.2787101","article-title":"Vehicle Tracking Using Surveillance With Multimodal Data Fusion","volume":"19","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/TITS.2006.888597","article-title":"Vehicle and Guard Rail Detection Using Radar and Vision Data Fusion","volume":"8","author":"Alessandretti","year":"2007","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/0005-1098(71)90096-3","article-title":"Computer control of multiple site track correlation","volume":"7","author":"Singer","year":"1971","journal-title":"Automatica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/0020-0255(80)90033-X","article-title":"An efficient track association algorithm for the multitarget tracking problem","volume":"21","author":"Sorenson","year":"1980","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/TAC.1981.1102635","article-title":"On the track-to-track correlation problem","volume":"26","year":"1981","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1109\/TAES.2006.314577","article-title":"New track correlation algorithms in a multisensor data fusion system","volume":"42","author":"He","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chong, C.Y., and Mori, S. (2006, January 10\u201313). Metrics for Feature-Aided Track Association. Proceedings of the 9th International Conference on Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301700"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2593","DOI":"10.1109\/TAES.2014.120687","article-title":"Performance prediction of feature-aided track-to-track association","volume":"50","author":"Mori","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TAES.2008.4560213","article-title":"Assignment costs for multiple sensor track-to-track association","volume":"44","author":"Kaplan","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1870","DOI":"10.1109\/TAES.2012.6237567","article-title":"A Comparison of Methods for Estimating Track-to-Track Assignment Probabilities","volume":"48","author":"Kragel","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","first-page":"58","article-title":"Performance of track-to-track association algorithms based on Mahalanobis distance","volume":"22","author":"Liu","year":"2013","journal-title":"Sens. Transducers"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bar-Shalom, Y., and Chen, H. (2004, January 14\u201317). Multisensor track-to-track association for tracks with dependent errors. Proceedings of the 2004 IEEE Conference on Decision and Control, Nassau, Bahamas.","DOI":"10.1109\/CDC.2004.1428864"},{"key":"ref_21","unstructured":"Osbome, R.W., Bar-Shalom, Y., and Willett, P. (2011, January 5\u20138). Track-to-track association with augmented state. Proceedings of the 2011 International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_22","first-page":"49","article-title":"Track-to-Track Association Using Attributes","volume":"2","author":"Chen","year":"2007","journal-title":"J. Adv. Inf. Fusion"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1016\/j.automatica.2012.04.001","article-title":"Smoothing innovations and data association with IPDA","volume":"48","author":"Song","year":"2012","journal-title":"Automatica"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1109\/TCYB.2014.2309632","article-title":"Optimal Object Association in the Dempster-Shafer Framework","volume":"44","author":"Dencux","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lee, K.H., Kanzawa, Y., Derry, M., and Jamesy, M.R. (2018, January 26\u201330). Multi-Target Track-to-Track Fusion Based on Permutation Matrix Track Association. Proceedings of the 2018 IEEE Conference on Intelligent Vehicles Symposium, Changshu, China.","DOI":"10.1109\/IVS.2018.8500433"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TITS.2011.2175218","article-title":"Detection and Tracking of Moving Objects at Intersections Using a Network of Laser Scanners","volume":"13","author":"Zhao","year":"2012","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1109\/TITS.2016.2533542","article-title":"On-Road Vehicle Detection and Tracking Using MMW Radar and Monovision Fusion","volume":"17","author":"Wang","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3068","DOI":"10.1109\/TITS.2017.2759904","article-title":"Track Fusion and Behavioral Reasoning for Moving Vehicles Based on Curvilinear Coordinates of Roadway Geometries","volume":"19","author":"Jo","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Papageorgiou, D.J., and Sergi, J.D. (2008, January 1\u20138). Simultaneous Track-to-Track Association and Bias Removal Using Multistart Local Search. Proceedings of the IEEE Aerospace Confence, Big Sky, MT, USA.","DOI":"10.1109\/AERO.2008.4526430"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1109\/TAES.2004.1337456","article-title":"Joint sensor registration and track-to-track fusion for distributed tracks","volume":"40","author":"Okello","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1109\/TAES.2012.6237594","article-title":"A Pseudo-Measurement Approach to Simultaneous Registration and Track Fusion","volume":"48","author":"Huang","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ins.2015.06.042","article-title":"A joint data association, registration, and fusion approach for distributed tracking","volume":"324","author":"Zhu","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/LSP.2014.2305305","article-title":"Track-to-Track Association for Biased Data Based on the Reference Topology Feature","volume":"21","author":"Tian","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/TAES.2015.140433","article-title":"Reference pattern-based track-to-track association with biased data","volume":"52","author":"Tian","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1109\/LSP.2017.2682857","article-title":"Track-to-Track Association by Coherent Point Drift","volume":"24","author":"Zhu","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.jprocont.2019.12.010","article-title":"Fault detection for uncertain LPV systems using probabilistic set-membership parity relation","volume":"87","author":"Wan","year":"2020","journal-title":"J. Process. Control."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2262","DOI":"10.1109\/TPAMI.2010.46","article-title":"Point Set Registration: Coherent Point Drift","volume":"32","author":"Myronenko","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Singer, R.A., and Stein, J.J. (1971, January 15\u201317). An optimal tracking filter for processing sensor data of imprecisely determined origin in surveillance systems. Proceedings of the 1971 IEEE Conference on Decision and Control, Miami Beach, FL, USA.","DOI":"10.1109\/CDC.1971.270971"},{"key":"ref_39","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":"1995","journal-title":"Nav. Res. Logist."},{"key":"ref_40","unstructured":"Bar-Shalom, Y., Li, X., and Kirubarajan, T. (2001). Estimation, Tracking and Navigation: Theory, Algorithms and Software, John Wiley & Sons."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1145\/361002.361007","article-title":"Multidimensional Binary Search Trees Used for Associative Searching","volume":"18","author":"Bentley","year":"1975","journal-title":"Commun. ACM"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2601","DOI":"10.1109\/TAES.2013.6621839","article-title":"State Estimation in Unknown Non-Gaussian Measurement Noise using Variational Bayesian Technique","volume":"49","author":"Zhu","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_43","unstructured":"Geiger, A. (2013). Probabilistic Models for 3D Urban Scene Understanding from Movable Platforms. [Ph.D. Thesis, University of T\u00fcbingen]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1109\/TPAMI.2009.167","article-title":"Object Detection with Discriminatively Trained Part-Based Models","volume":"32","author":"Felzenszwalb","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/5\/1412\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:04:09Z","timestamp":1760173449000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/5\/1412"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,4]]},"references-count":44,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["s20051412"],"URL":"https:\/\/doi.org\/10.3390\/s20051412","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,3,4]]}}}