{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:19:57Z","timestamp":1760145597294,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T00:00:00Z","timestamp":1724025600000},"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":"publisher","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Qinglan Project of Jiangsu Province of China","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]},{"name":"the Science and Technology Innovation Project for the Selected Returned Overseas Chinese Scholars in Nanjing","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]},{"name":"the Foundation of Key Laboratory of Navigation, Guidance and Health-Management Technologies of Advanced Aircraft (Nanjing University of Aeronautics and Astronautics)","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]},{"name":"Ministry of Industry and Information Technology, the Foundation of Engineering Research Center of Autonomous Control Technology of Aircraft (Nanjing University of Aeronautics and Astronautics)","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]},{"name":"Ministry of Education, Jiangsu Key Laboratory \u201cInternet of Things and Control Technologies\u201d","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]},{"name":"the Priority Academic Program Development of Jiangsu Higher Education Institutions","award":["62073163","62388101","61703208","61873125"],"award-info":[{"award-number":["62073163","62388101","61703208","61873125"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Navigation system performance degrades significantly in complex environments. It is important to analyze satellite visibility through 3D terrain modelling and separate the satellite signals propagated by NLOS to suppress the NLOS error. However, the traditional 3D terrain modelling visibility analysis method based on the pure terrain cover angle is only suitable for determining the visibility of GNSS satellites and may incorrectly separate LOS propagate measurement signals from members with low relative ranges and elevation angles under air\u2013ground swarm conditions. To this end, this paper proposes a belief-propagating cooperative navigation method based on air\u2013ground visibility analysis, which avoids mistakenly separating close-range LOS cooperative navigation signals by simultaneously considering the distances, elevation angles, and azimuths of the signal sources relative to the air\u2013ground swarm members. The simulation shows that the cooperative navigation NLOS identification method based on air\u2013ground visibility analysis proposed in this paper can more accurately realize the separation of NLOS signals under cooperative conditions than the traditional pure angular 3D terrain modelling visibility analysis method can, and the localization error of the members to be assisted is significantly reduced.<\/jats:p>","DOI":"10.3390\/rs16163042","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T10:11:28Z","timestamp":1724062288000},"page":"3042","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Enhanced Collaborative Localization Method Based on Belief Propagation Aided by 3D Terrain Modelling"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5965-6958","authenticated-orcid":false,"given":"Rong","family":"Wang","sequence":"first","affiliation":[{"name":"Navigation Research Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Weicheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"Navigation Research Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"Shanghai Aerospace Control Technology Research Institute, Shanghai 201109, China"}]},{"given":"Zhi","family":"Xiong","sequence":"additional","affiliation":[{"name":"Navigation Research Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]},{"given":"Xiaoyi","family":"Chen","sequence":"additional","affiliation":[{"name":"Navigation Research Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9673","DOI":"10.1109\/TIE.2018.2880727","article-title":"Intelligent Collaborative Localization Among Air-Ground Robots for Industrial Environment Perception","volume":"66","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107458","DOI":"10.1016\/j.cie.2021.107458","article-title":"An air-ground cooperative scheduling model considering traffic environment and helicopter performance","volume":"158","author":"Zhang","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Shi, C., Xiong, Z., Chen, M., Wang, R., and Xiong, J. (2023). Cooperative Navigation for Heterogeneous Air-Ground Vehicles Based on Interoperation Strategy. Remote Sens., 15.","DOI":"10.3390\/rs15082006"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, R., Xiong, Z., and Liu, J. (2023). Collaborative Localization-Based Resilient Navigation Fusion. Resilient Fusion Navigation Techniques: Collaboration in Swarm, Springer Nature.","DOI":"10.1007\/978-981-19-8371-9"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, F., Wu, X., and Ma, P. (2022). Consistent Extended Kalman Filter-Based Cooperative Localization of Multiple Autonomous Underwater Vehicles. Sensors, 22.","DOI":"10.3390\/s22124563"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2880","DOI":"10.1109\/TITS.2017.2769488","article-title":"Angle of arrival-based cooperative positioning for smart vehicles","volume":"19","author":"Fascista","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1109\/JPROC.2008.2008853","article-title":"Cooperative localization in wireless networks","volume":"97","author":"Wymeersch","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Meyer, F., Etzlinger, B., Hlawatsch, F., and Springer, A. (2013, January 3\u20136). A distributed particle-based belief propagation algorithm for cooperative simultaneous localization and synchronization. Proceedings of the 2013 Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2013.6810334"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/LSP.2013.2290192","article-title":"Sigma point belief propagation","volume":"21","author":"Meyer","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_10","first-page":"832","article-title":"Cooperative localization using posterior linearization belief propagation","volume":"67","author":"Svensson","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"193695","DOI":"10.1109\/ACCESS.2020.3031605","article-title":"Collaborative Multiple UAVs Navigation With GPS\/INS\/UWB Jammers Using Sigma Point Belief Propagation","volume":"8","author":"Chen","year":"2022","journal-title":"IEEE Access."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106315","DOI":"10.1016\/j.ast.2020.106315","article-title":"GPS multipath and NLOS mitigation for relative positioning in urban environments","volume":"107","author":"Yuan","year":"2020","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Barral, V., Escudero, C.J., Garc\u00eda-Naya, J.A., and Maneiro-Catoira, R. (2019). NLOS identification and mitigation using low-cost UWB devices. Sensors, 19.","DOI":"10.3390\/s19163464"},{"key":"ref_14","unstructured":"Groves, P.D. (2016). It\u2019s time for 3D terrain modellingping\u2013aided GNSS. Inside GNSS Mag., 50\u201356."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1002\/navi.448","article-title":"Urban positioning: 3D terrain modellingping-aided GNSS using dual-frequency pseudorange measurements from smartphones","volume":"68","author":"Ng","year":"2021","journal-title":"Navigation"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"navi.515","DOI":"10.33012\/navi.515","article-title":"Multi-epoch 3D-mapping-aided positioning using bayesian filtering techniques","volume":"69","author":"Zhong","year":"2022","journal-title":"NAVIGATION J. Inst. Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/S0097-8493(99)00087-4","article-title":"The visibility octree: A data structure for 3D navigation","volume":"23","author":"Navazo","year":"1999","journal-title":"Comput. Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"8163","DOI":"10.1109\/TWC.2021.3090781","article-title":"Channel Measurement and Ray-Tracing-Statistical Hybrid Modeling for Low-Terahertz Indoor Communications","volume":"20","author":"Chen","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0373463317000509","article-title":"Intelligent Urban Positioning: Integration of Shadow Matching with 3D-Mapping-Aided GNSS Ranging","volume":"71","author":"Adjrad","year":"2018","journal-title":"J. Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1002\/rob.21988","article-title":"Radio propagation models for differential GNSS based on dense point clouds","volume":"37","author":"Kubelka","year":"2020","journal-title":"J. Field Robot."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1080\/01691864.2019.1642240","article-title":"Real-time autonomous navigation of an electric wheelchair in large-scale urban area with 3D terrain modelling","volume":"33","author":"Niijima","year":"2019","journal-title":"Adv. Robot."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"56822","DOI":"10.1109\/ACCESS.2023.3283610","article-title":"WiThRay: A Versatile Ray-Tracing Simulator for Smart Wireless Environments","volume":"11","author":"Choi","year":"2023","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Girindran, R., Boyd, D.S., Rosser, J., Vijayan, D., Long, G., and Robinson, D. (2020). On the reliable generation of 3D city models from open data. Urban Sci., 4.","DOI":"10.3390\/urbansci4040047"},{"key":"ref_24","first-page":"1119","article-title":"Mobile LiDAR mapping for 3D point cloud collection in urban areas\u2014A performance test","volume":"37","author":"Haala","year":"2008","journal-title":"Int. Arch. Photogram. Remote Sens. Spat. Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10514-012-9321-0","article-title":"OctoMap: An efficient probabilistic 3D terrain modellingping framework based on octrees","volume":"34","author":"Hornung","year":"2013","journal-title":"Auton. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1109\/TVT.2022.3202015","article-title":"Distributed Spatio-Temporal Information Based Cooperative 3D Positioning in GNSS-Denied Environments","volume":"72","author":"Cao","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","first-page":"12","article-title":"Morphological Operations on Unorganized Point Clouds Using Octree Graphs","volume":"16","author":"Pedro","year":"2023","journal-title":"ACM J. Comput. Cult. Herit. (JOCCH)"},{"key":"ref_28","first-page":"212","article-title":"An Efficient Parametric Algorithm for Octree Traversal","volume":"8","author":"Revelles","year":"2000","journal-title":"J. WSCG"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.23919\/JSEE.2021.000092","article-title":"An efficient adaptive space partitioning algorithm for electromagnetic scattering calculation of complex 3D models","volume":"32","author":"Huang","year":"2021","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5561","DOI":"10.1109\/TSP.2015.2454485","article-title":"Posterior linearization filter: Principles and implementation using sigma points","volume":"63","author":"Svensson","year":"2015","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/16\/3042\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:39:02Z","timestamp":1760110742000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/16\/3042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,19]]},"references-count":30,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["rs16163042"],"URL":"https:\/\/doi.org\/10.3390\/rs16163042","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,8,19]]}}}