{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T14:58:14Z","timestamp":1785855494334,"version":"3.56.0"},"reference-count":22,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T00:00:00Z","timestamp":1720828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62073163"],"award-info":[{"award-number":["62073163"]}]},{"name":"National Natural Science Foundation of China","award":["62103285"],"award-info":[{"award-number":["62103285"]}]},{"name":"National Natural Science Foundation of China","award":["62203228"],"award-info":[{"award-number":["62203228"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Cooperative localization (CL) for air-to-ground robots in a satellite-denial environment has become a current research hotspot. The traditional distance-based heterogeneous multiple-robot CL method requires at least four unmanned aerial vehicles (UAVs) with known positions. When the number of known-position UAVs in a cluster collaborative network is insufficient, the traditional distance-based CL method has a certain inapplicability. A novel adaptive CL method for air-to-ground robots based on relative distance constraints is proposed in this paper. Based on a dynamically changing number of known-position UAVs in the cluster collaborative network, the adaptive fusion estimation threshold is set. When the number of known-position UAVs in the cluster cooperative network is large, the real-time dynamic topology characteristics of multiple robots\u2019 spatial geometric configurations are considered. The optimal spatial geometric configuration between UAVs and unmanned ground vehicles (UGVs) is utilized to achieve a high-precision CL solution for UGVs. Otherwise, in the event that the number of known-position UAVs in a cluster collaborative network is insufficient, distance observation constraint information between UAVs and UGVs is retained in real time. Position observation equations for UGVs\u2019 inertial navigation system (INS) have been constructed using inertial-based high-precision relative position constraints and relative distance constraints from historical to current times. The experimental results show that the proposed method achieves adaptive fusion estimation with a dynamically changing number of known-position UAVs in the cluster collaborative network, effectively verifying the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s24144543","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T14:15:49Z","timestamp":1721052949000},"page":"4543","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Adaptive Cooperative Localization Method for Heterogeneous Air-to-Ground Robots Based on Relative Distance Constraints in a Satellite-Denial Environment"],"prefix":"10.3390","volume":"24","author":[{"given":"Shidong","family":"Han","sequence":"first","affiliation":[{"name":"Navigation Research Center, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"College of Intelligent Engineering, Nanjing Vocational Institute of Railway Technology, Nanjing 210031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi","family":"Xiong","sequence":"additional","affiliation":[{"name":"Navigation Research Center, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9581-002X","authenticated-orcid":false,"given":"Chenfa","family":"Shi","sequence":"additional","affiliation":[{"name":"Navigation Research Center, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.2514\/1.33721","article-title":"Unmanned aerial vehicles cooperative tracking of moving ground target in urban environments","volume":"31","author":"Shaferman","year":"2008","journal-title":"J. Guid. Control Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Wu, J., Dai, J., Ying, J., and He, C. (2020, January 27\u201329). Cooperative Tactical Planning Method for UAV Formation. Proceedings of the 39th Chinese Control Conference, Shenyang, China.","DOI":"10.23919\/CCC50068.2020.9189211"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"121444","DOI":"10.1016\/j.eswa.2023.121444","article-title":"A decentralized decision-making algorithm of UAV swarm with information fusion strategy","volume":"237","author":"Wang","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/B978-0-444-64235-6.50035-8","article-title":"Modeling of an air quality monitoring network with high space-time resolution","volume":"43","author":"Sofia","year":"2018","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sun, J., Li, B., Jiang, Y., and Wen, C.-Y. (2016). A camera-based target detection and positioning UAV system for search and rescue (SAR) purposes. Sensors, 16.","DOI":"10.3390\/s16111778"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1049\/cje.2019.12.006","article-title":"Review on the technological development and application of UAV systems","volume":"29","author":"Fan","year":"2020","journal-title":"Chin. J. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhu, X., Lai, J., and Chen, S. (2022). Cooperative Location Method for Leader-Follower UAV Formation Based on Follower UAV\u2019s Moving Vector. Sensors, 22.","DOI":"10.3390\/s22197125"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"642","DOI":"10.14419\/ijet.v7i2.7.10914","article-title":"Improvement of position and orientation of Unmanned Arial Vehicle (UAV) with INS\/GPS","volume":"7","author":"Raju","year":"2018","journal-title":"Int. J. Eng. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1134\/S2075108717040083","article-title":"Novel adaptive UKF for tightly coupled INS\/GPS integration with experimental validation on an UAV","volume":"8","author":"Khalaf","year":"2017","journal-title":"Gyroscopy Navig."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Huang, S., Huang, J., Tang, D., and Chen, F. (2018, January 28\u201330). Research on UAV flight performance test method based on dual antenna GPS\/ins integrated system. Proceedings of the 3rd Communication and Information Systems (ICCIS), Singapore.","DOI":"10.1109\/ICOMIS.2018.8644961"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.inffus.2023.01.025","article-title":"Multi-sensor integrated navigation\/positioning systems using data fusion: From analytics-based to learning-based approaches","volume":"95","author":"Zhuang","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1109\/TMECH.2022.3192985","article-title":"Camera-based lane-aided multi-information integration for land vehicle navigation","volume":"28","author":"Niu","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yang, C., Strader, J., Gu, Y., Hypes, A., Canciani, A., and Brink, K. (2018, January 8\u201312). Cooperative UAV navigation using Inter-Vehicle Ranging and Magnetic Anomaly Measurements. Proceedings of the 2018 AIAA Guidance, Navigation and Control Conference, Kissimmee, FL, USA.","DOI":"10.2514\/6.2018-1595"},{"key":"ref_14","unstructured":"Qu, Y., and Zhang, Y. (2010, January 2\u20135). Cooperative localization of low-cost UAV using relative range measurements in multi-UAV flight. Proceedings of the AIAA Guidance, Navigation and Control Conference, Toronto, ON, Canada."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1729881420932717","DOI":"10.1177\/1729881420932717","article-title":"Cooperative navigation of unmanned aerial vehicle swarm based on cooperative dilution of precision","volume":"17","author":"Chen","year":"2020","journal-title":"Int. J. Adv. Rob. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hanasz, S., Kuklewski, M., Kasprowicz, G., Bieda, M.S., and Traczyk, K. (2020, January 7\u201314). Concept of an enhanced accuracy onboard time synchronization via communication link. Proceedings of the 2020 IEEE Aerospace Conference, Big Sky, MT, USA.","DOI":"10.1109\/AERO47225.2020.9172378"},{"key":"ref_17","first-page":"830","article-title":"A High Precision Time Synchronization Scheme for Avionics System","volume":"54","author":"Duan","year":"2014","journal-title":"Telecommun. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1017\/S0373463300013060","article-title":"Principles of JTIDS relative navigation","volume":"49","author":"Ranger","year":"1996","journal-title":"J. Navig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"13037","DOI":"10.1109\/JSEN.2023.3252019","article-title":"Weight factor graph co-location method for UAV formation based on navigation performance evaluation","volume":"23","author":"Zhu","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1017\/S0373463318000565","article-title":"A dynamic vector-formed information-sharing algorithm based on two-state chi square detection in an adaptive federated filter","volume":"72","author":"Xu","year":"2019","journal-title":"J. Navig."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1109\/TMECH.2022.3203875","article-title":"Adaptive extended Kalman filter-based fusion approach for high-precision UAV positioning in extremely confined environments","volume":"28","author":"Yang","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zhou, W., and Wang, X. (2021). UAV swarm navigation using dynamic adaptive Kalman filter and network navigation. Sensors, 21.","DOI":"10.3390\/s21165374"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/14\/4543\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:16:19Z","timestamp":1760109379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/14\/4543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,13]]},"references-count":22,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["s24144543"],"URL":"https:\/\/doi.org\/10.3390\/s24144543","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,13]]}}}