{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T17:19:40Z","timestamp":1782321580996,"version":"3.54.5"},"reference-count":41,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2020,7,10]],"date-time":"2020-07-10T00:00:00Z","timestamp":1594339200000},"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":["11574250"],"award-info":[{"award-number":["11574250"]}],"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":["11874302"],"award-info":[{"award-number":["11874302"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Research and Development Program of Shaanxi Province","award":["2020SF-391"],"award-info":[{"award-number":["2020SF-391"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The traditional target tracking is a process of estimating the state of a moving target using measurement information obtained by sensors. However, underwater passive acoustic target tracking will confront further challenges, among which the system incomplete observability and time delay caused by the signal propagation create a great impact on tracking performance. Passive acoustic sensors cannot accurately obtain the target range information. The introduction of Doppler frequency measurement can improve the system observability performance; signal time delay cannot be ignored in underwater environments. It varies with time, which has a continuous negative impact on the tracking accuracy. In this paper, the Gauss\u2013Helmert model is introduced to solve this problem by expanding the unknown signal emission time as an unknown variable to the state. This model allows the existence of the previous state and current state at the same time, while handling the implicit equations. To improve the algorithm accuracy, this paper further takes advantage of the estimated state and covariance for the second stage iteration and propose the Gauss\u2013Helmert iterated Unscented Kalman filter under a three-dimensional environment. The simulation shows that the proposed method in this paper shows superior estimation accuracy and more stable performance compared with other filtering algorithms in underwater environments.<\/jats:p>","DOI":"10.3390\/s20143869","type":"journal-article","created":{"date-parts":[[2020,7,14]],"date-time":"2020-07-14T09:30:49Z","timestamp":1594719049000},"page":"3869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Underwater 3D Doppler-Angle Target Tracking with Signal Time Delay"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9143-7467","authenticated-orcid":false,"given":"Jun","family":"Su","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5973-9780","authenticated-orcid":false,"given":"Yaan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-334X","authenticated-orcid":false,"given":"Wasiq","family":"Ali","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohua","family":"Li","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3285-6490","authenticated-orcid":false,"given":"Jing","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/TASSP.1985.1164665","article-title":"Adaptive underwater target tracking using passive multipath time-delay measurements","volume":"33","author":"Moose","year":"1985","journal-title":"IEEE Trans. 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