{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:32:11Z","timestamp":1770748331062,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2022YFB3904702"],"award-info":[{"award-number":["2022YFB3904702"]}]},{"name":"National Key Research and Development Program of China","award":["2022YFB3904603"],"award-info":[{"award-number":["2022YFB3904603"]}]},{"name":"National Key Research and Development Program of China","award":["6220020330"],"award-info":[{"award-number":["6220020330"]}]},{"name":"National Natural Science Foundation of China","award":["2022YFB3904702"],"award-info":[{"award-number":["2022YFB3904702"]}]},{"name":"National Natural Science Foundation of China","award":["2022YFB3904603"],"award-info":[{"award-number":["2022YFB3904603"]}]},{"name":"National Natural Science Foundation of China","award":["6220020330"],"award-info":[{"award-number":["6220020330"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The Global Navigation Satellite System (GNSS) has been widely used in every area of our daily life to provide accurate Positioning, Navigation, and Timing (PNT) services. However, due to the multipatch effect and an obstructed view of the satellite, GNSS receivers are susceptible to large-ranging errors, which are particularly prevalent in urban areas where precise positioning is indispensable. The deployment of the high-spatial-density Fifth-Generation (5G) network makes it possible to provide a broad area with high-precision positioning service. Obviously, it promoting the deep integration of the GNSS system and the 5G mobile communication network and establishing a Highly Dependable Spatio-temporal Network (HDSN) have become an inevitable trend. The existing algorithm for the fusion of multiple signals has difficulty settling problems such as the fast fluctuation of available signal sources and the poor stability of multi-scale multi-type signal estimation in GNSS-5G hybrid networks. Here, we propose a Square Root Unscented Stable Filter (SRUSF) for GNSS and 5G joint positioning with a compact coupled filter group architecture in a highly dependable spatio-temporal network. A stabilized coefficient is added to guarantee positive covariance of the estimation error. The possibility of divergence of filtering results due to the variation in signal sources and the incomplete agreement between the system model and the actual situation are reduced. The simulation results show that the proposed SRUSF method substantially enhances the positioning accuracy and reliability compared with the other five joint estimation methods for multiple signals. This work will enable the terminal of mass users to provide timing and positioning services with unprecedented accuracy and dependability under the GNSS and 5 G-based spatio-temporal network\u2019s architecture.<\/jats:p>","DOI":"10.3390\/rs15174220","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T05:46:47Z","timestamp":1693201607000},"page":"4220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["GNSS-5G Hybrid Positioning Based on Joint Estimation of Multiple Signals in a Highly Dependable Spatio-Temporal Network"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5597-5150","authenticated-orcid":false,"given":"Jingrong","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Zhongliang","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Enwen","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Yunfei","family":"Huang","sequence":"additional","affiliation":[{"name":"China Telecom, Beijing 101399, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7239-2088","authenticated-orcid":false,"given":"Xiwen","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Zhichao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Zhenke","family":"Ding\u00a0","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Bingxun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"ref_1","unstructured":"(2023, May 15). Location-Based Services Global Market Report 2023. The Business Research Company. Available online: https:\/\/www.thebusinessresearchcompany.com\/report\/location-based-services-global-market-report."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1080\/10095020.2022.2144481","article-title":"Structure and performance analysis of fusion positioning system with a single 5G station and a single GNSS satellite","volume":"26","author":"Guo","year":"2023","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, X., Shen, Z., Li, X., Liu, G., Zhou, Y., Li, S., Lyu, H., and Zhang, Q. (2023). Continuous Decimeter-Level Positioning in Urban Environments Using Multi-Frequency GPS\/BDS\/Galileo PPP\/INS Tightly Coupled Integration. Remote Sens., 15.","DOI":"10.3390\/rs15082160"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/LRA.2022.3224367","article-title":"IC-GVINS: A Robust, Real-Time, INS-Centric GNSS-Visual-Inertial Navigation System","volume":"8","author":"Niu","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9818","DOI":"10.1109\/LRA.2022.3190093","article-title":"Rail Vehicle Localization and Mapping With LiDAR-Vision-Inertial-GNSS Fusion","volume":"7","author":"Wang","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10633","DOI":"10.1109\/TVT.2021.3110325","article-title":"Indoor and Outdoor Seamless Positioning Method Using UWB Enhanced Multi-Sensor Tightly-Coupled Integration","volume":"70","author":"Jiang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17205","DOI":"10.1109\/JSEN.2022.3192911","article-title":"Environment Perception Based Seamless Indoor and Outdoor Positioning System of Smartphone","volume":"22","author":"Liu","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/MITS.2020.2994110","article-title":"Robust Vehicular Localization and Map Matching in Urban Environments Through IMU, GNSS, and Cellular Signals","volume":"12","author":"Kassas","year":"2020","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8501415","DOI":"10.1109\/TIM.2022.3154821","article-title":"GNSS-5G Hybrid Positioning Based on Multi-Rate Measurements Fusion and Proactive Measurement Uncertainty Prediction","volume":"71","author":"Bai","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1109\/JSAC.2018.2804223","article-title":"A GNSS\/5G Integrated Positioning Methodology in D2D Communication Networks","volume":"36","author":"Yin","year":"2018","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8718","DOI":"10.1109\/JIOT.2022.3232221","article-title":"iPos-5G: Indoor Positioning via Commercial 5G NR CSI","volume":"10","author":"Ruan","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liu, J., Deng, Z., Deng, X., and Luo, K. (2022, January 9\u201312). BDS-5G Hybrid Positioning Based on Signal Quality Assessment and Adaptive Switchover Strategy based on Measurement Uncertainty Evaluation. Proceedings of the 2022 IEEE 8th International Conference on Computer and Communications, Chengdu, China.","DOI":"10.1109\/ICCC56324.2022.10065778"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10739","DOI":"10.1109\/JSEN.2023.3264782","article-title":"A Dynamic Continuous Constrained Phase Factor Graph Optimization Method for GNSS Kinematic Precise Point Positioning","volume":"23","author":"Shuai","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6385","DOI":"10.1109\/TGRS.2015.2438395","article-title":"Multi-GNSS Meteorology: Real-Time Retrieving of Atmospheric Water Vapor From BeiDou, Galileo, GLONASS, and GPS Observations","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8504011","DOI":"10.1109\/TIM.2023.3281565","article-title":"Robust Unscented Kalman Filter-Based Decentralized Multisensor Information Fusion for INS\/GNSS\/CNS Integration in Hypersonic Vehicle Navigation","volume":"72","author":"Hu","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1109\/JSEN.2022.3223974","article-title":"Enhanced EKF-Based Time Calibration for GNSS\/UWB Tight Integration","volume":"23","author":"Guo","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1109\/TCST.2015.2488597","article-title":"Adaptive EKF-Based Vehicle State Estimation With Online Assessment of Local Observability","volume":"24","author":"Katriniok","year":"2016","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented filtering and nonlinear estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Xu, Q., Gao, Z., Yang, C., and Lv, J. (2023). High-Accuracy Positioning in GNSS-Blocked Areas by Using the MSCKF-Based SF-RTK\/IMU\/Camera Tight Integration. Remote Sens., 15.","DOI":"10.3390\/rs15123005"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6677","DOI":"10.1109\/LRA.2022.3175600","article-title":"Variable Observability Constrained Visual-Inertial-GNSS EKF-Based Navigation","volume":"7","author":"Liu","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1177\/0954410015586860","article-title":"Modified federated Kalman filter for INS\/GNSS\/CNS integration","volume":"230","author":"Hu","year":"2016","journal-title":"Proc. Inst. Mech. Eng. G J. Aerosp. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2507908","DOI":"10.1109\/TIM.2021.3073440","article-title":"A Wearable Pedestrian Localization and Gait Identification System Using Kalman Filtered Inertial Data","volume":"70","author":"Hajati","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","unstructured":"der Merwe, R.V., and Wan, E.A. (2001, January 7\u201311). The square-root unscented Kalman filter for state and parameter-estimation. Proceedings of the 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, UT, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jafarzadeh, S., Lascu, C., and Fadali, M.S. (2011, January 17\u201322). Square Root Unscented Kalman Filters for state estimation of induction motor drives. Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, USA.","DOI":"10.1109\/ECCE.2011.6063751"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4000312","DOI":"10.1109\/TMAG.2023.3258541","article-title":"Tracking Magnetic Target Based on Internative Multi-Model Square Root Unscented Kalman Filter","volume":"59","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Magn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6966","DOI":"10.1109\/JSEN.2016.2591260","article-title":"A Variational Bayesian-Based Unscented Kalman Filter With Both Adaptivity and Robustness","volume":"16","author":"Li","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zou, X., Li, Z., Wang, Y., Deng, C., Li, Y., Tang, W., Fu, R., Cui, J., and Liu, J. (2021). Multipath Error Fusion Modeling Methods for Multi-GNSS. Remote Sens., 13.","DOI":"10.3390\/rs13152925"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"15191","DOI":"10.1109\/JSEN.2022.3185164","article-title":"Indoor Positioning With Adaptive Wavelet Denoise Enhancement and Trend Surface Analysis Based Multipath Map","volume":"22","author":"Ma","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/TNET.2011.2158656","article-title":"Tracking low-precision clocks with time-varying drifts using Kalman filtering","volume":"20","author":"Kim","year":"2012","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Koivisto, M., Costa, M., Hakkarainen, A., Leppanen, K., and Valkama, M. (2016, January 4\u20138). Joint 3D Positioning and Network Synchronization in 5G Ultra-Dense Networks Using UKF and EKF. Proceedings of the 2016 IEEE Globecom Workshops (GC Wkshps), Washington, DC, USA.","DOI":"10.1109\/GLOCOMW.2016.7848938"},{"key":"ref_31","unstructured":"ETSI (2020). Physical Channels and Modulation, 3GPP. Document TS 38.211."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1186\/s43020-020-00024-w","article-title":"Role, path, and vision of \u201c5G + BDS\/GNSS\u201d","volume":"1","author":"Liu","year":"2020","journal-title":"Satell. Navig."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/17\/4220\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:40:46Z","timestamp":1760128846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/17\/4220"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,28]]},"references-count":32,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["rs15174220"],"URL":"https:\/\/doi.org\/10.3390\/rs15174220","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,28]]}}}