{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T15:40:11Z","timestamp":1778686811751,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,8]],"date-time":"2018-12-08T00:00:00Z","timestamp":1544227200000},"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":["U1713205"],"award-info":[{"award-number":["U1713205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51809062"],"award-info":[{"award-number":["51809062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology on Underwater Vehicle Laboratory","award":["SXJQR2018WDKT07"],"award-info":[{"award-number":["SXJQR2018WDKT07"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the single-beacon underwater tracking system, vehicles rely on slant range measurements from an acoustic beacon to bound errors accumulated by dead reckoning. Ranges are usually obtained based on a presumed known effective sound velocity (ESV). Since the ESV is difficult to determine accurately, traditional methods suffer from large positioning error. By treating the unknown ESV as a state variable, a novel single-beacon tracking model (the so called \u201c5-sv\u201d model) and an extended Kalman filter (EKF)-based solution method have been discussed to solve the problem of ESV estimation. However, due to the uncertainty of underwater acoustic propagation, the probabilistic characteristics of the ESV uncertainty and acoustic measurement noise are unknown and varying both with time and location. EKF, which runs with presupposed noise parameters, cannot describe the practical noise specifications. To overcome the divergence issue of EKF-based single-beacon tracking methods, this paper proposes an adaptive Kalman filter-based single-beacon tracking algorithm which employs the \u201c5-sv\u201d model as the baseline model. Through numerical examples using simulated and field data, both the filter and smoother results show that while implementing the proposed algorithm, the tracking accuracy can be significantly improved, and the estimated noise parameter agrees well with its true value.<\/jats:p>","DOI":"10.3390\/s18124339","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T03:36:41Z","timestamp":1544413001000},"page":"4339","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Adaptive Kalman Filter-Based Single-Beacon Underwater Tracking with Unknown Effective Sound Velocity"],"prefix":"10.3390","volume":"18","author":[{"given":"Zhong-Chao","family":"Deng","sequence":"first","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang","family":"Yu","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong-De","family":"Qin","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhong-Ben","family":"Zhu","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9528313","DOI":"10.1155\/2018\/9528313","article-title":"Virtual Submerged Floating Operational System for Robotic Manipulation","volume":"2018","author":"Zhang","year":"2018","journal-title":"Complexity"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1007\/s40815-017-0401-3","article-title":"Survey on FuzzyLogicBased Guidance and Control of Marine Surface Vehicles and Underwater Vehicles","volume":"20","author":"Xiang","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.isatra.2017.09.008","article-title":"On decentralized adaptive full-order sliding mode control of multiple UAVs","volume":"71","author":"Xiang","year":"2017","journal-title":"ISA Trans."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.oceaneng.2017.06.020","article-title":"On intelligent risk analysis and critical decision of underwater robotic vehicle","volume":"140","author":"Xiang","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Roper, D.T., Phillips, A.B., Harris, C.A., Salavasidis, G., Pebody, M., Templeton, R., Amma, S.V.S., Smart, M., and McPhail, S. (2017, January 19\u201322). Autosub long range 1500: An ultra-endurance AUV with 6000 Km range. Proceedings of the OCEANS 2017, Aberdeen, UK.","DOI":"10.1109\/OCEANSE.2017.8084928"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/JOE.2018.2792278","article-title":"Sparus II AUV\u2014A Hovering Vehicle for Seabed Inspection","volume":"43","author":"Carreras","year":"2018","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JOE.2013.2278891","article-title":"AUV Navigation and Localization: A Review","volume":"39","author":"Paull","year":"2014","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ferreira, B., Matos, A., and Cruz, N. (2010, January 20\u201323). Single beacon navigation: Localization and control of the MARES AUV. Proceedings of the OCEANS 2010 MTS\/IEEE SEATTLE, Seattle, WA, USA.","DOI":"10.1109\/OCEANS.2010.5664518"},{"key":"ref_9","unstructured":"Wang, S., Chen, L., Hu, H., and Gu, D. (2013, January 3\u20137). Single beacon based localization of AUVs using moving horizon estimation. Proceedings of the 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Harris, Z.J., and Whitcomb, L.L. (2016, January 16\u201321). Preliminary study of cooperative navigation of underwater vehicles without a DVL utilizing range and range-rate observations. Proceedings of the IEEE International Conference on Robotics and Automation, Stockholm, Sweden.","DOI":"10.1109\/ICRA.2016.7487420"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/rob.21746","article-title":"Closed loop one way travel time navigation using low grade odometry for autonomous underwater vehicles","volume":"35","author":"Claus","year":"2017","journal-title":"J. Field Robot."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1109\/TCST.2014.2321973","article-title":"GES Long Baseline Navigation With Unknown Sound Velocity and Discrete-Time Range Measurements","volume":"23","author":"Batista","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TCST.2015.2429613","article-title":"Underwater Inertial Navigation With Long Baseline Transceivers: A Near-Real-Time Approach","volume":"24","author":"Chen","year":"2016","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/JOE.2010.2052691","article-title":"Autonomous Underwater Vehicle Navigation","volume":"35","author":"Miller","year":"2010","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_16","unstructured":"Larsen, M.B. (2000, January 11\u201314). Synthetic long baseline navigation of underwater vehicles. Proceedings of the Oceans, Providence, RI, USA."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Casey, T., Guimond, B., and Hu, J. (October, January 29). Underwater vehicle positioning based on time of arrival measurements from a single beacon. Proceedings of the OCEANS 2007, Vancouver, BC, Canada.","DOI":"10.1109\/OCEANS.2007.4449186"},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1177\/0278364914532390","article-title":"An origin state method for communication constrained cooperative localization with robustness to packet loss","volume":"33","author":"Walls","year":"2014","journal-title":"Int. J. Robot. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1109\/JOE.2017.2754018","article-title":"Model and Algorithm Improvement on Single Beacon Underwater Tracking","volume":"43","author":"Zhu","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_21","unstructured":"Zhu, Z., Hu, S.L.J., and Li, H. (2016, January 19\u201323). Kalman-based underwater tracking with unknown effective sound velocity. Proceedings of the Oceans, Monterey, CA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhu, Z., Hu, S.L.J., and Li, H. (2016, January 6\u20139). Effect on Kalman based underwater tracking due to ocean current uncertainty. Proceedings of the Autonomous Underwater Vehicles, Tokyo, Japan.","DOI":"10.1109\/AUV.2016.7778660"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s001900050236","article-title":"Adaptive Kalman Filtering for INS\/GPS","volume":"73","author":"Mohamed","year":"1999","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.asoc.2016.02.034","article-title":"An adaptive modeling and asset allocation approach to financial markets based on discrete microstructure model","volume":"43","author":"Qin","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jpowsour.2015.04.148","article-title":"Adaptive unscented Kalman filter based state of energy and power capability estimation approach for lithium-ion battery","volume":"289","author":"Zhang","year":"2015","journal-title":"J. Power Sources"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, John Wiley & Sons.","DOI":"10.1002\/0470045345"},{"key":"ref_27","unstructured":"Sarkka, S. (2013). Bayesian Filtering and Smoothing, Institute of Mathematical Statistics Textbooks, Cambridge University Press."},{"key":"ref_28","unstructured":"Gelb, A. (1974). Applied Optimal Estimation, MIT Press."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4339\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:32:11Z","timestamp":1760196731000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,8]]},"references-count":28,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["s18124339"],"URL":"https:\/\/doi.org\/10.3390\/s18124339","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,8]]}}}