{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:36:54Z","timestamp":1760240214165,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T00:00:00Z","timestamp":1554854400000},"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>A problem of tracking surface shape-shifting extended target by using gray scale pixels on optical image is considered. The measurement with amplitude information (AI) is available to the proposed method. The target is regarded as a convex hemispheric object, and the amplitude distribution of the extended target is represented by a solid radial function. The Gaussian process (GP) is applied and the covariance function of GP is modified to fit the convex hemispheric shape. The points to be estimated on the target surface are selected reasonably in the hemispheric space at the azimuth and pitch directions. Analytical representation of the estimated target extent is provided and the recursive process is implemented by the extended Kalman filter (EKF). In order to demonstrate the algorithm\u2019s ability of tracking complex shaped targets, a trailing target characterized by two feature parameters is simulated and the two feature parameters are extracted with the estimated points. The simulations verify the validity of the proposed method with compared to classical algorithms.<\/jats:p>","DOI":"10.3390\/s19071704","type":"journal-article","created":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T03:47:36Z","timestamp":1554868056000},"page":"1704","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Extended Target Tracking and Feature Estimation for Optical Sensors Based on the Gaussian Process"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1708-9892","authenticated-orcid":false,"given":"Haoyang","family":"Yu","sequence":"first","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"An","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ran","family":"Zhu","sequence":"additional","affiliation":[{"name":"Institute of Systems Engineering, AMS, PLA, Beijing 100141, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gilholm, K., Maskell, S., Salmond, D., and Godsill, S. (August, January 31). Poisson models for extended target and group tracking. Proceedings of the Signal and Data Processing of Small Targets 2005, San Diego, CA, USA.","DOI":"10.1117\/12.618730"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Granstr\u00f6m, K., Lundquist, C., and Orguner, U. (2011, January 26\u201329). A gaussian mixture phd filter for extended target tracking. Proceedings of the IEEE International Conference on Information Fusion, Edinburgh, UK.","DOI":"10.1109\/ICIF.2010.5711885"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3827","DOI":"10.1109\/TSP.2012.2192927","article-title":"A variational measurement update for extended target tracking with random matrices","volume":"60","author":"Orguner","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1409","DOI":"10.1109\/TSP.2010.2101064","article-title":"Tracking of extended objects and group targets using random matrices","volume":"59","author":"Feldmann","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1109\/TAES.2008.4655362","article-title":"Bayesian approach to extended object and cluster tracking using random matrices","volume":"44","author":"Koch","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","unstructured":"Lan, J., and Li, X.R. (2012, January 9\u201312). Tracking of extended object or target group using random matrix\u2014Part I: New model and approach. Proceedings of the International Conference on Information Fusion, Singapore."},{"key":"ref_7","unstructured":"Schuster, M., Reuter, J., and Wanielik, G. (2015, January 6\u20139). Probabilistic data association for tracking extended group targets under clutter using random matrices. Proceedings of the International Conference on Information Fusion, Washington, DC, USA."},{"key":"ref_8","unstructured":"Lan, J., and Li, X.R. (2012, January 9\u201312). Tracking of extended object or target group using random matrix\u2014Part II: Irregular object. Proceedings of the International Conference on Information Fusion, Singapore."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1109\/TSP.2014.2309561","article-title":"Tracking of Maneuvering Non-Ellipsoidal Extended Object or Target Group Using Random Matrix","volume":"62","author":"Lan","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","unstructured":"Granstr\u00f6m, K., Willett, P., and Bar-Shalom, Y. (2015, January 6\u20139). An extended target tracking model with multiple random matrices and unified kinematics. Proceedings of the International Conference on Information Fusion, Washington, DC, USA."},{"key":"ref_11","unstructured":"Granstr\u00f6m, K., Lundquist, C., and Orguner, U. (2011, January 5\u20138). Tracking rectangular and elliptical extended targets using laser measurements. Proceedings of the International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_12","unstructured":"Granstr\u00f6m, K., Reuter, S., Meissner, D., and Scheel, A. (2014, January 7\u201310). A multiple model PHD approach to tracking of cars under an assumed rectangular shape. Proceedings of the International Conference on Information Fusion, Salamanca, Spain."},{"key":"ref_13","unstructured":"Granstr\u00f6m, K., and Lundquist, C. (2013, January 9\u201312). On the Use of Multiple Measurement Models for Extended Target Tracking. Proceedings of the International Conference on Information Fusion, Istanbul, Turkey."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Baum, M., and Hanebeck, U. (2010, January 14\u201317). Random hypersurface models for extended object tracking. Proceedings of the IEEE International Symposium on Signal Processing and Information Technology, Ajman, UAE.","DOI":"10.1109\/ISSPIT.2009.5407526"},{"key":"ref_15","unstructured":"Baum, M., and Hanebeck, U. (2011, January 5\u20138). Shape tracking of extended objects and group targets with starconvex RHMs. Proceedings of the International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Steinbring, J., Baum, M., Zea, A., Faion, F., and Hanebeck, U. (2015, January 14\u201316). A Closed-Form Likelihood for Particle Filters to Track Extended Objects with Star-Convex RHMs. Proceedings of the IEEE International Conference on Multisensor Fusion and Information Integration, San Diego, CA, USA.","DOI":"10.1109\/MFI.2015.7295740"},{"key":"ref_17","unstructured":"\u00d6zkan, E., Wahlstr\u00f6m, N., and Godsill, S. (2016, January 5\u20138). Rao-blackwellised particle filter for star-convex extended target tracking models. Proceedings of the International Conference on Information Fusion, Heidelberg, Germany."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4165","DOI":"10.1109\/TSP.2015.2424194","article-title":"Extended target tracking using Gaussian processes","volume":"63","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","unstructured":"Hirscher, T., Scheel, A., Reuter, S., and Dietmayer, K. (2016, January 5\u20138). Multiple extended object tracking using Gaussian processes. Proceedings of the International Conference on Information Fusion, Heidelberg, Germany."},{"key":"ref_20","unstructured":"Granstr\u00f6m, K., Baum, M., and Reuter, S. (arXiv, 2016). Extended Object Tracking: Introduction, Overview and Applications, arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mahler, J., Patil, S., Kehoe, B., Van Den Berg, J., Ciocarlie, M., Abbeel, P., and Goldberg, K. (2015, January 26\u201330). Gp-gpis-opt: Grasp planning with shape uncertainty using Gaussian process implicit surfaces and sequential convex programming. Proceedings of the IEEE International Conference on Robotics and Automation, Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139882"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1109\/LRA.2016.2631260","article-title":"Geometric priors for Gaussian process implicit surfaces","volume":"2","author":"Martens","year":"2017","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kumru, M., and \u00d6zkan, E. (2018, January 10\u201313). 3D Extended Object Tracking Using Recursive Gaussian Processes. Proceedings of the 21st International Conference on Information Fusion, Cambridge, UK.","DOI":"10.23919\/ICIF.2018.8455480"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huber, M.F. (2013, January 26\u201331). Recursive Gaussian process regression. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638281"},{"key":"ref_25","unstructured":"Chen, X., Wang, X., and Xuan, J. (arXiv, 2018). Tracking Multiple Moving Objects Using Unscented Kalman Filtering Techniques, arXiv."},{"key":"ref_26","unstructured":"Chen, X., Wang, W., Meng, W., and Zhang, Z. (2010, January 8\u201310). A novel UKF based scheme for GPS signal tracking in high dynamic environment. Proceedings of the International Symposium on Systems and Control in Aeronautics and Astronautics, Harbin, China."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1704\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:44:10Z","timestamp":1760186650000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1704"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,10]]},"references-count":26,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19071704"],"URL":"https:\/\/doi.org\/10.3390\/s19071704","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,4,10]]}}}