{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T21:12:09Z","timestamp":1777669929453,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2019,10,10]],"date-time":"2019-10-10T00:00:00Z","timestamp":1570665600000},"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":["51775110, 61473085 , 51375088"],"award-info":[{"award-number":["51775110, 61473085 , 51375088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Fund of Key Laboratory of Inertial Technology","award":["614250607011709"],"award-info":[{"award-number":["614250607011709"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2242018K40065, 2242018K40066, 2242019K40035, 2242019K40040"],"award-info":[{"award-number":["2242018K40065, 2242018K40066, 2242019K40035, 2242019K40040"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology (Ministry of Education, China)","award":["SEU-MIAN-201803"],"award-info":[{"award-number":["SEU-MIAN-201803"]}]},{"name":"Foundation of Shanghai Key Laboratory of Navigation and Location Based Services","award":["have no Grant Number"],"award-info":[{"award-number":["have no Grant Number"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The USBL (Ultra-Short Base Line) positioning system is widely used in underwater acoustic positioning systems due to its small size and ease of use. The traditional USBL positioning system is based on \u2018slant range and azimuth\u2019. The positioning error is an increasing function with the increase in distance and the positioning accuracy depends on the ranging accuracy of the underwater target. This method is not suitable for long-distance underwater positioning operations. This paper proposes a USBL positioning calculation model based on depth information for \u2018rotating array and reusing elements\u2019. This method does not need to measure the distance between the USBL acoustic array and target, so it can completely eliminate the influence of long-distance ranging errors in USBL positioning. The theoretical analysis and simulation experiments show that the new USBL positioning model based on \u2018rotating array and reusing elements\u2019 can completely eliminate the influence of the wavelength error and spacing error of underwater acoustic signals on the positioning accuracy of USBL. The positioning accuracy can be improved by approximately 90%, and the horizontal positioning error within a positioning distance of 1000 m is less than 1.2 m. The positioning method has high precision performance in the long distance, and provides a new idea for the engineering design of a USBL underwater positioning system.<\/jats:p>","DOI":"10.3390\/s19204373","type":"journal-article","created":{"date-parts":[[2019,10,11]],"date-time":"2019-10-11T03:07:11Z","timestamp":1570763231000},"page":"4373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["An Ultra-Short Baseline Positioning Model Based on Rotating Array &amp; Reusing Elements and Its Error Analysis"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7061-7677","authenticated-orcid":false,"given":"Jinwu","family":"Tong","sequence":"first","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5165-0981","authenticated-orcid":false,"given":"Xiaosu","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lanhua","family":"Hou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yao","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instruments and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,10]]},"reference":[{"key":"ref_1","first-page":"8","article-title":"USBL Technology and Its Applications in Ocean Engineering","volume":"5","author":"Jin","year":"2018","journal-title":"Navig. Position. Timing"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"66923","DOI":"10.1109\/ACCESS.2018.2878756","article-title":"Study on Installation Error Analysis and Calibration of Acoustic Transceiver Array Based on SINS\/USBL Integrated System","volume":"6","author":"Tong","year":"2018","journal-title":"IEEE Access"},{"key":"ref_3","first-page":"331","article-title":"Development and Prospect for Underwater Acoustic Positioning and Navigation Technology","volume":"3","author":"Sun","year":"2019","journal-title":"J. Chin. Acad. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/JOE.2006.880585","article-title":"Simulation of an Inertial Acoustic Navigation System With Range Aiding for an Autonomous Underwater Vehicle","volume":"32","author":"Lee","year":"2007","journal-title":"IEEE J. Oceanic Eng."},{"key":"ref_5","unstructured":"Liu, P. (2007). Underwater Positioning and Navigation Technology, National Defense Industry Press."},{"key":"ref_6","unstructured":"Hu, H.Q. (2017). Research on AUV navigation technology based on USBL aided SINS. [Master\u2019s Thesis, Southeast University]."},{"key":"ref_7","unstructured":"Ixblue (2019, October 06). Gaps. Available online: https:\/\/www.ixblue.com\/products\/gaps-pre-calibrated-insusbl-system."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Morgado, M., Oliveira, P., Silvestre, C., and Vasconcelos, J.F. (2006, January 10\u201313). USBL\/INS Tightly-Coupled Integration Technique for Underwater Vehicles. Proceedings of the 9th International Conference on Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301607"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TCST.2013.2245133","article-title":"Embedded Vehicle Dynamics Aiding for USBL\/INS Underwater Navigation System","volume":"22","author":"Morgado","year":"2014","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1002\/rob.21442","article-title":"Tightly coupled ultrashort baseline and inertial navigation system for underwater vehicles: An experimental validation","volume":"30","author":"Morgado","year":"2013","journal-title":"J. Field Robotics"},{"key":"ref_11","unstructured":"Zhang, Y.W. (2016). An algorithm used in underwater SINS\/USBL integrated navigation. Navig. Position. Timing, 7\u201313."},{"key":"ref_12","unstructured":"Gao, B.B. (2015). Research on SINS\/USBL\/DVL integrated navigation system and high performance algorithm for underwater vehicles. [Master\u2019s Thesis, Northwestern Polytechnical University]."},{"key":"ref_13","first-page":"179","article-title":"INS\/USBL nonlinear integrated navigation method based on observations of relative information","volume":"41","author":"Dong","year":"2019","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.isatra.2014.10.006","article-title":"A derivative UKF for tightly coupled INS\/GPS integrated navigation","volume":"56","author":"Hu","year":"2015","journal-title":"ISA Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2016","DOI":"10.1109\/TMECH.2018.2834917","article-title":"Robust Initial Attitude Alignment for SINS\/DVL","volume":"23","author":"Chang","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1017\/S0373463313000222","article-title":"The Estimation of Angular Misalignments for Ultra Short Baseline Navigation Systems. Part I: Numerical Simulations","volume":"66","author":"Chen","year":"2013","journal-title":"J. Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1016\/j.oceaneng.2008.06.013","article-title":"In-situ alignment calibration of attitude and ultra short baseline sensors for precision underwater positioning","volume":"35","author":"Chen","year":"2008","journal-title":"Ocean Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"085001","DOI":"10.1063\/1.5100250","article-title":"A misalignment angle error calibration method of underwater acoustic array in strapdown inertial navigation system\/ultrashort baseline integrated navigation system based on single transponder mode","volume":"90","author":"Tong","year":"2019","journal-title":"Rev. Sci. Instrum."},{"key":"ref_19","unstructured":"Yu, M. (2005). Research on Long Range Ultra Short Baseline System. [Ph.D. Thesis, Harbin University of Engineering]."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, Y.H., Sun, G.Q., Lai, X.Q., and Liu, R.B. (2017, January 15\u201317). Research of ultrashort baseline positioning method based on depth information. Proceedings of the IEEE 2nd Information Technology, Networking, Electronic and Automation Control Conference, Chengdu, China.","DOI":"10.1109\/ITNEC.2017.8284770"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1017\/S0373463313000234","article-title":"The Estimation of Angular Misalignments for Ultra Short Baseline Navigation Systems. Part II: Experimental Results","volume":"66","author":"Chen","year":"2013","journal-title":"J. Navig."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yu, M. In-situ calibration of transceiver alignment for a high-precision USBL system, In Proceedings of the International Conference on Computer Application and System Modeling, Taiyuan, China. 22\u201324 October 2010.","DOI":"10.1109\/ICCASM.2010.5623256"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.apacoust.2018.10.004","article-title":"Array geometry calibration for underwater compact arrays","volume":"145","author":"Sun","year":"2019","journal-title":"Appl. Acoust."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4373\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:28:59Z","timestamp":1760189339000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,10]]},"references-count":23,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["s19204373"],"URL":"https:\/\/doi.org\/10.3390\/s19204373","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,10]]}}}