{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T07:13:24Z","timestamp":1760426004508,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T00:00:00Z","timestamp":1632441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Cooperative localization (CL) of underwater multi-AUVs is vital for numerous underwater operations. Single-transponder-aided cooperative localization (STCL) is regarded as a promising scheme for multi-AUVs CL, benefiting from the fact that an accurate reference is adopted. To improve the positioning accuracy and robustness of STCL, a novel Factor Graph and Cubature Kalman Filter (FGCKF)-integrated algorithm is proposed in this paper. In the proposed FGCKF, historical information can be efficiently used in measurement updating to overcome uncertain observation environments, which greatly helps to improve the performance of filtering progress. Furthermore, Adaptive CKF, sum product, and Maximum Correntropy Criterion (MCC) methods are designed to deal with outliers of acoustic transmission delay, sound velocity, and motion velocity, respectively. Simulations and experiments are conducted, and it is verified that the proposed FGCKF algorithm can improve positioning accuracy and robustness greatly than traditional filtering methods.<\/jats:p>","DOI":"10.3390\/e23101244","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T01:59:47Z","timestamp":1632707987000},"page":"1244","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Novel Factor Graph and Cubature Kalman Filter Integrated Algorithm for Single-Transponder-Aided Cooperative Localization"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8932-7960","authenticated-orcid":false,"given":"Wanlong","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huifeng","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deyue","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Dalian University of Technology, Dalian 116081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1002\/rob.21986","article-title":"Wimust: A cooperative marine robotic system for autonomous geotechnical surveys","volume":"38","author":"Simetti","year":"2021","journal-title":"J. Field Robot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3987","DOI":"10.1109\/LRA.2019.2926947","article-title":"Sampling-Based Path Planning for Cooperative Autonomous Maritime Vehicles to Reduce Uncertainty in Range-Only Localization","volume":"4","author":"Willners","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhao, W., Zhao, H., and Liu, L. (July, January 28). A Single Beacon-aided Cooperative Localization Algorithm based on Maximum Correntropy Criterion. Proceedings of the 2021 International Wireless Communications and Mobile Computing (IWCMC), Harbin, China.","DOI":"10.1109\/IWCMC51323.2021.9498651"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1109\/TVT.2015.2398874","article-title":"Least Square Cooperative Localization","volume":"64","author":"Nguyen","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1966","DOI":"10.1109\/TAES.2019.2942704","article-title":"Cooperative Localization of a GPS-Denied UAV Using Direction-of-Arrival Measurements","volume":"56","author":"Russell","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2543","DOI":"10.1109\/TVT.2017.2764265","article-title":"Asynchronous Localization with Mobility Prediction for Underwater Acoustic Sensor Networks","volume":"67","author":"Yan","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1109\/JOE.2020.3041123","article-title":"Collaborating Underwater Vehicles Conducting Large-Scale Geospatial Tasks","volume":"46","author":"Kuhlman","year":"2021","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/JAS.2014.7004622","article-title":"Cooperative localization of AUVs using moving horizon estimation","volume":"1","author":"Wang","year":"2014","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106197","DOI":"10.1016\/j.asoc.2020.106197","article-title":"Cooperative localization for multiple AUVs based on the rough estimation of the measurements","volume":"91","author":"Lu","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liao, Y., Xie, J., Wang, Z., and Shen, X. (2019). Multisensor Estimation Fusion with Gaussian Process for Nonlinear Dynamic Systems. Entropy, 21.","DOI":"10.3390\/e21111126"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106068","DOI":"10.1016\/j.ast.2020.106068","article-title":"Cooperative positioning for low-cost close formation flight based on relative estimation and belief propagation","volume":"106","author":"Xiong","year":"2020","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"205669","DOI":"10.1109\/ACCESS.2020.3035470","article-title":"Cooperative Relative Localization Using Range Measurements without a Priori Information","volume":"8","author":"Chakraborty","year":"2020","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1177\/0278364910380760","article-title":"Cooperative AUV Navigation using a Single Maneuvering Surface Craft","volume":"29","author":"Fallon","year":"2010","journal-title":"Int. J. Robot. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1982","DOI":"10.1109\/TSP.2017.2788419","article-title":"Optimal Bayesian Kalman Filtering with Prior Update","volume":"66","author":"Dehghannasiri","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature Kalman Filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.1109\/TII.2020.3015001","article-title":"A Novel Heavy-Tailed Mixture Distribution Based Robust Kalman Filter for Cooperative Localization","volume":"17","author":"Bai","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","first-page":"1","article-title":"A Novel Robust Gaussian Approximate Smoother Based on EM for Cooperative Localization with Sensor Fault and Outliers","volume":"70","author":"Xu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1109\/TIM.2018.2809139","article-title":"Robust Student\u2019s t-Based Cooperative Navigation for Autonomous Underwater Vehicles","volume":"67","author":"Li","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1109\/TAES.2017.2756763","article-title":"A New Adaptive Extended Kalman Filter for Cooperative Localization","volume":"54","author":"Huang","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4221","DOI":"10.1109\/TVT.2014.2312195","article-title":"Real-Time Estimation of Center of Gravity Position for Lightweight Vehicles Using Combined AKF-EKF Method","volume":"63","author":"Huang","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","first-page":"1","article-title":"A Novel Measurement Information Anomaly Detection Method for Cooperative Localization","volume":"70","author":"Xu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3958","DOI":"10.1109\/TAES.2020.2985316","article-title":"Cooperative Terrain Navigation Using Hybrid GMM\/SMC Message Passing on Factor Graphs","volume":"56","author":"Oliveira","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1109\/18.910572","article-title":"Factor graphs and the sum-product algorithm","volume":"47","author":"Kschischang","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"67006","DOI":"10.1109\/ACCESS.2019.2918586","article-title":"An Advanced Cooperative Positioning Algorithm Based on Improved Factor Graph and Sum-Product Theory for Multiple AUVs","volume":"7","author":"Fan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4753","DOI":"10.1109\/JIOT.2018.2812179","article-title":"Cooperative Localization Algorithm Based on Hybrid Topology Architecture for Multiple Mobile Robot System","volume":"5","author":"Sun","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"64634","DOI":"10.1109\/ACCESS.2020.2983083","article-title":"Gaussian Parameterized Information Aided Distributed Cooperative Underwater Positioning Algorithm","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"12044","DOI":"10.1109\/ACCESS.2021.3051715","article-title":"A Multi-Sensor Information Fusion Method Based on Factor Graph for Integrated Navigation System","volume":"9","author":"Xu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6952","DOI":"10.1109\/TCOMM.2019.2930517","article-title":"TOA-Based Passive Localization Constructed Over Factor Graphs: A Unified Framework","volume":"67","author":"Yuan","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"107484","DOI":"10.1016\/j.oceaneng.2020.107484","article-title":"A variational bayesian approximation based adaptive single transponder navigation method with unknown ESV","volume":"209","author":"Qin","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2365","DOI":"10.1109\/LRA.2020.2972889","article-title":"Cooperative Localization and Unknown Currents Estimation Using Multiple Autonomous Underwater Vehicles","volume":"5","author":"Kim","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8855","DOI":"10.1109\/TVT.2020.2996513","article-title":"AUV-Aided Localization for Underwater Acoustic Sensor Networks with Current Field Estimation","volume":"69","author":"Yan","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3376","DOI":"10.1109\/TSP.2016.2539127","article-title":"Generalized Correntropy for Robust Adaptive Filtering","volume":"64","author":"Chen","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1109\/TASLP.2020.2982030","article-title":"Robust Generalized Maximum Correntropy Criterion Algorithms for Active Noise Control","volume":"28","author":"Zhu","year":"2020","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1109\/JOE.2017.2771898","article-title":"Modeling AUV Localization Error in a Long Baseline Acoustic Positioning System","volume":"43","author":"Thomson","year":"2018","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Li, X., Lu, B., Ali, W., and Jin, H. (2021). Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment. Entropy, 23.","DOI":"10.3390\/e23081082"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-002-0256-7","article-title":"Robust estimator for correlated observations based on bifactor equivalent weights","volume":"76","author":"Yang","year":"2002","journal-title":"J. Geod."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:04:45Z","timestamp":1760166285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,24]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["e23101244"],"URL":"https:\/\/doi.org\/10.3390\/e23101244","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,9,24]]}}}