{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T04:05:18Z","timestamp":1778904318317,"version":"3.51.4"},"reference-count":50,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,15]],"date-time":"2021-11-15T00:00:00Z","timestamp":1636934400000},"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":["91938203"],"award-info":[{"award-number":["91938203"]}],"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":["11874109"],"award-info":[{"award-number":["11874109"]}],"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":["12174053"],"award-info":[{"award-number":["12174053"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2242021k30019"],"award-info":[{"award-number":["2242021k30019"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology on Sonar Laboratory","award":["6142109180202"],"award-info":[{"award-number":["6142109180202"]}]},{"name":"National Defense Basis Scientific Research program of China","award":["JCKY2019110C143"],"award-info":[{"award-number":["JCKY2019110C143"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>To acquire the enhanced underwater ship-radiated noise signal in the presence of array shape distortion in a passive sonar system, the phase difference of the line-spectrum component in ship-radiated noise is often exploited to estimate the time-delay difference for the beamforming-based signal enhancement. However, the time-delay difference estimation performance drastically degrades with decreases of the signal-to-noise ratio (SNR) of the line-spectrum component. Meanwhile, although the time-delay difference estimation performance of the high-frequency line-spectrum components is generally superior to that of the low-frequency one, the phase difference measurements of the high-frequency line-spectrum component often easily encounter the issue of modulus 2\u03c0 ambiguity. To address the above issues, a novel time-frequency joint time-delay difference estimation method is proposed in this paper. The proposed method establishes a data-driven hidden Markov model with robustness to phase difference ambiguity by fully exploiting the underlying property of slowly changing the time-delay difference over time. Thus, the phase difference measurements available for time-delay difference estimation are extended from that of low-frequency line-spectrum components in a single frame to that of all detected line-spectrum components in multiple frames. By jointly taking advantage of the phase difference measurements in both time and frequency dimensions, the proposed method can acquire enhanced time-delay difference estimates even in a low SNR case. Both simulation and at-sea experimental results have demonstrated the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/rs13224586","type":"journal-article","created":{"date-parts":[[2021,11,15]],"date-time":"2021-11-15T20:46:47Z","timestamp":1637009207000},"page":"4586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Time-Frequency Joint Time-Delay Difference Estimation Method for Signal Enhancement in the Distorted towed Hydrophone Array"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3824-9453","authenticated-orcid":false,"given":"Chuanqi","family":"Zhu","sequence":"first","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiliang","family":"Fang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2114-7672","authenticated-orcid":false,"given":"Qisong","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"An","sequence":"additional","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1165-1522","authenticated-orcid":false,"given":"Xinwei","family":"Luo","sequence":"additional","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongli","family":"Cao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,15]]},"reference":[{"key":"ref_1","unstructured":"Van Trees, H.L. 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