{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:31:38Z","timestamp":1778085098052,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000},"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":"crossref","award":["62173007"],"award-info":[{"award-number":["62173007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62203020"],"award-info":[{"award-number":["62203020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62473008"],"award-info":[{"award-number":["62473008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62433002"],"award-info":[{"award-number":["62433002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62476014"],"award-info":[{"award-number":["62476014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ministry of Education in China, MOC","award":["22YJCZH006"],"award-info":[{"award-number":["22YJCZH006"]}]},{"DOI":"10.13039\/501100005090","name":"Beijing Nova Program","doi-asserted-by":"crossref","award":["20240484710"],"award-info":[{"award-number":["20240484710"]}],"id":[{"id":"10.13039\/501100005090","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Beijing Scholars Program Grant","award":["099"],"award-info":[{"award-number":["099"]}]},{"name":"Project of ALL China Federation of Supply and Marketing Cooperatives","award":["202407"],"award-info":[{"award-number":["202407"]}]},{"name":"Project of Beijing Municipal University Teacher Team Construction Support Plan","award":["BPHR20220104"],"award-info":[{"award-number":["BPHR20220104"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Trajectory prediction in the Internet of Vehicles (IoV) is crucial for enhancing road safety and traffic efficiency; however, existing methods often fail to address the challenges of colored noise in GPS data and long-term dependency modeling. To overcome these limitations, this paper proposes AttSCNs, a probabilistic hybrid framework integrating stochastic configuration networks (SCNs) with an attention-based encoder to model trajectories while quantifying prediction uncertainty. The model leverages SCNs\u2019 stochastic neurons for adaptive noise filtering, attention mechanisms for dependency learning, and Bayesian hyperparameter optimization to infer robust configurations as a posterior distribution. Experimental results on real-world GPS datasets (10,000+ urban\/highway trajectories) demonstrate that AttSCNs significantly outperform conventional approaches, reducing RMSE by 36.51% compared to traditional SCNs and lowering MAE by 97.8% compared to Kalman filter baselines. Moreover, compared to the LSTM model, AttSCNs achieve a 52.5% reduction in RMSE and a 68.5% reduction in MAE, with real-time inference speed. These advancements position AttSCNs as a robust, noise-resistant solution for IoV applications, offering superior performance in autonomous driving and smart city systems.<\/jats:p>","DOI":"10.3390\/e27111094","type":"journal-article","created":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T00:47:36Z","timestamp":1761266856000},"page":"1094","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["AttSCNs: A Bayesian-Optimized Hybrid Model with Attention-Guided Stochastic Configuration Networks for Robust GPS Trajectory Prediction"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2230-0077","authenticated-orcid":false,"given":"Xue-Bo","family":"Jin","sequence":"first","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2102-4509","authenticated-orcid":false,"given":"Ye-Qing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0074-3467","authenticated-orcid":false,"given":"Jian-Lei","family":"Kong","sequence":"additional","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8047-1010","authenticated-orcid":false,"given":"Yu-Ting","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting-Li","family":"Su","sequence":"additional","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.62762\/TSCC.2025.291581","article-title":"Navigating Ethical Challenges in 6G-Enabled Smart Cities: Privacy, Equity, and Governance","volume":"2","author":"Rafique","year":"2025","journal-title":"ICCK Trans. Sens. Commun. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"85","DOI":"10.62762\/TSCC.2024.554721","article-title":"3D Holography Advertisement On Vehicle Using IoT","volume":"2","author":"Farooq","year":"2025","journal-title":"ICCK Trans. Sens. Commun. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Fu, R., Zhang, Z., and Li, L. (2016, January 11\u201313). Using LSTM and GRU neural network methods for traffic flow prediction. Proceedings of the 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), Wuhan, China.","DOI":"10.1109\/YAC.2016.7804912"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"112","DOI":"10.62762\/TIS.2024.300700","article-title":"Comparison of Deep Learning Algorithms for Retail Sales Forecasting","volume":"1","author":"Ahmed","year":"2024","journal-title":"ICCK Trans. Intell. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhang, Q., Yang, W., Zhao, A., Wang, X., Wang, Z., and Zhang, L. (2024). Short-term forecasting of vegetable prices based on LSTM model\u2014Evidence from Beijing\u2019s vegetable data. PLoS ONE, 19.","DOI":"10.1371\/journal.pone.0304881"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"126428","DOI":"10.1016\/j.eswa.2025.126428","article-title":"Ada-STGMAT: An adaptive spatio-temporal graph multi-attention network for intelligent time series forecasting in smart cities","volume":"269","author":"Jin","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3466","DOI":"10.1109\/TCYB.2017.2734043","article-title":"Stochastic configuration networks: Fundamentals and algorithms","volume":"47","author":"Wang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109","DOI":"10.62762\/TIS.2025.347925","article-title":"MamNet: A Novel Hybrid Model for Time-Series Forecasting and Frequency Pattern Analysis in Network Traffic","volume":"2","author":"Zhang","year":"2025","journal-title":"ICCK Trans. Intell. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"94176","DOI":"10.1109\/ACCESS.2020.2995672","article-title":"An adaptive turn rate estimation for tracking a maneuvering target","volume":"8","author":"Eltoukhy","year":"2020","journal-title":"IEEE Access"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3043","DOI":"10.1109\/TVT.2021.3065665","article-title":"Pseudo-spectrum based track-before-detect for weak maneuvering targets in range-Doppler plane","volume":"70","author":"Wang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"841","DOI":"10.21629\/JSEE.2017.05.03","article-title":"Highly maneuvering target tracking using multi-parameter fusion singer model","volume":"28","author":"Jia","year":"2017","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"02008","DOI":"10.1051\/matecconf\/201816002008","article-title":"Study on Maneuvering Target On-axis Tracking Algorithm of Modified Current Statistical Model","volume":"160","author":"Zhenkai","year":"2018","journal-title":"MATEC Web Conf."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, M., Shan, T., Zhang, W., and Huan, H. (2021). Analysis of BDS\/GPS signals\u2019 characteristics and navigation accuracy for a geostationary satellite. Remote Sens., 13.","DOI":"10.3390\/rs13101967"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"11863","DOI":"10.1109\/ACCESS.2025.3528348","article-title":"Adaptive Kalman Filtering: Measurement and Process Noise Covariance Estimation Using Kalman Smoothing","volume":"13","author":"Kruse","year":"2025","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1007\/s11063-021-10688-3","article-title":"Continuous positioning with recurrent auto-regressive neural network for unmanned surface vehicles in GPS outages","volume":"54","author":"Bai","year":"2022","journal-title":"Neural Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"191","DOI":"10.25103\/jestr.104.23","article-title":"Neural Networks Trained with Levenberg-Marquardt-Iterated Extended Kalman Filter for Mobile Robot Trajectory Tracking","volume":"10","author":"Aissa","year":"2017","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Markos, C., James, J., and Da Xu, R.Y. (2021, January 2\u20139). Capturing uncertainty in unsupervised GPS trajectory segmentation using Bayesian deep learning. Proceedings of the AAAI Conference on Artificial Intelligence, Virtual.","DOI":"10.1609\/aaai.v35i1.16115"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1049\/iet-its.2019.0017","article-title":"Convolutional LSTM based transportation mode learning from raw GPS trajectories","volume":"14","author":"Nawaz","year":"2020","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_20","unstructured":"Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. (2014). Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"202836","DOI":"10.1109\/ACCESS.2020.3035653","article-title":"Novel hybrid algorithm of improved CKF and GRU for GPS\/INS","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Donahue, J., Anne Hendricks, L., Guadarrama, S., Rohrbach, M., Venugopalan, S., Saenko, K., and Darrell, T. (2015, January 7\u201312). Long-term recurrent convolutional networks for visual recognition and description. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.21236\/ADA623249"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/TR.2020.3010970","article-title":"Remaining useful life prediction based on normalizing flow embedded sequence-to-sequence learning","volume":"70","author":"Yang","year":"2020","journal-title":"IEEE Trans. Reliab."},{"key":"ref_25","unstructured":"Nguyen, Q.M., Nguyen, L.M., and Das, S. (2023). Correlated Attention in Transformers for Multivariate Time Series. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/LSP.2021.3135793","article-title":"Learning sentimental and financial signals with normalizing flows for stock movement prediction","volume":"29","author":"Tai","year":"2021","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1109\/LRA.2021.3133862","article-title":"Unified and fast human trajectory prediction via conditionally parameterized normalizing flow","volume":"7","author":"Sun","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jin, X.B., Gong, W.T., Kong, J.L., Bai, Y.T., and Su, T.L. (2022). PFVAE: A planar flow-based variational auto-encoder prediction model for time series data. Mathematics, 10.","DOI":"10.3390\/math10040610"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2966","DOI":"10.1109\/TITS.2023.3276216","article-title":"A variational Bayesian inference-based en-decoder framework for traffic flow prediction","volume":"25","author":"Kong","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1109\/TMM.2017.2648498","article-title":"Diversified visual attention networks for fine-grained object classification","volume":"19","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Multimed."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1002\/for.2870","article-title":"Stochastic configuration network based on improved whale optimization algorithm for nonstationary time series prediction","volume":"41","author":"Chen","year":"2022","journal-title":"J. Forecast."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, J., Liu, Y., and Zhang, Q. (2023). A Gradient-Based Particle-Bat Algorithm for Stochastic Configuration Network. Appl. Sci., 13.","DOI":"10.3390\/app13052878"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4969","DOI":"10.1080\/15376494.2022.2110338","article-title":"Stochastic configuration network for structural reliability analysis","volume":"30","author":"Li","year":"2023","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"79","DOI":"10.62762\/TIS.2024.952592","article-title":"Long-term Traffic Flow Prediction using Stochastic Configuration Networks for Smart Cities","volume":"1","author":"Lin","year":"2024","journal-title":"ICCK Trans. Intell. Syst."},{"key":"ref_35","unstructured":"Wang, D., and Felicetti, M.J. (2023). Stochastic configuration machines for industrial artificial intelligence. arXiv."},{"key":"ref_36","unstructured":"Felicetti, M.J., and Wang, D. (2023). Stochastic configuration machines: FPGA implementation. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yan, S., Chen, F., Yang, J., and Zhao, Z. (2023). A Multistep Prediction Model for the Vibration Trends of Hydroelectric Generator Units Based on Variational Mode Decomposition and Stochastic Configuration Networks. Sensors, 23.","DOI":"10.3390\/s23249762"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3222","DOI":"10.1109\/TII.2023.3301059","article-title":"Online self-learning stochastic configuration networks for nonstationary data stream analysis","volume":"20","author":"Li","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.ins.2017.05.047","article-title":"Robust stochastic configuration networks with kernel density estimation for uncertain data regression","volume":"412","author":"Wang","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"106924","DOI":"10.1016\/j.knosys.2021.106924","article-title":"A stochastic configuration network based on chaotic sparrow search algorithm","volume":"220","author":"Zhang","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107143","DOI":"10.1016\/j.asoc.2021.107143","article-title":"Parallel stochastic configuration networks for large-scale data regression","volume":"103","author":"Zhang","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_42","first-page":"5998","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1094\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T04:27:28Z","timestamp":1761366448000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,23]]},"references-count":42,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["e27111094"],"URL":"https:\/\/doi.org\/10.3390\/e27111094","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,23]]}}}