{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:51:06Z","timestamp":1760709066100,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,13]],"date-time":"2016-05-13T00:00:00Z","timestamp":1463097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundations of China","award":["61272061 and 61301148"],"award-info":[{"award-number":["61272061 and 61301148"]}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["14JJ7023"],"award-info":[{"award-number":["14JJ7023"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student\u2019s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.<\/jats:p>","DOI":"10.3390\/s16050692","type":"journal-article","created":{"date-parts":[[2016,5,13]],"date-time":"2016-05-13T11:53:16Z","timestamp":1463140396000},"page":"692","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5645-160X","authenticated-orcid":false,"given":"Zhu","family":"Xiao","sequence":"first","affiliation":[{"name":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"},{"name":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3545-7639","authenticated-orcid":false,"given":"Vincent","family":"Havyarimana","sequence":"additional","affiliation":[{"name":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"},{"name":"Department of Applied Sciences, Ecole Normale Sup\u00e9rieure, 6983 Bujumbura, Burundi"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30199","DOI":"10.3390\/s151229795","article-title":"Passive Sensor Integration for Vehicle Self-Localization in Urban Traffic Environment","volume":"15","author":"Gu","year":"2015","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"28807","DOI":"10.3390\/s151128807","article-title":"Vehicle Position Estimation Based on Magnetic Markers: Enhanced Accuracy by Compensation of Time Delays","volume":"15","author":"Byun","year":"2015","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Almaz\u00e1n, J., Bergasa, L.M., Yebes, J.J., Barea, R., and Arroyo, R. 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