{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T14:49:22Z","timestamp":1772722162775,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"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":["62431023"],"award-info":[{"award-number":["62431023"]}],"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":["JCKYS2022604SSJS010"],"award-info":[{"award-number":["JCKYS2022604SSJS010"]}],"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":["SAST2022-011"],"award-info":[{"award-number":["SAST2022-011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Stable Supporting Fund of National Key Laboratory of Underwater Acoustic Technology","award":["62431023"],"award-info":[{"award-number":["62431023"]}]},{"name":"Stable Supporting Fund of National Key Laboratory of Underwater Acoustic Technology","award":["JCKYS2022604SSJS010"],"award-info":[{"award-number":["JCKYS2022604SSJS010"]}]},{"name":"Stable Supporting Fund of National Key Laboratory of Underwater Acoustic Technology","award":["SAST2022-011"],"award-info":[{"award-number":["SAST2022-011"]}]},{"DOI":"10.13039\/501100019082","name":"Shanghai Aerospace Science and Technology Innovation Foundation","doi-asserted-by":"publisher","award":["62431023"],"award-info":[{"award-number":["62431023"]}],"id":[{"id":"10.13039\/501100019082","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019082","name":"Shanghai Aerospace Science and Technology Innovation Foundation","doi-asserted-by":"publisher","award":["JCKYS2022604SSJS010"],"award-info":[{"award-number":["JCKYS2022604SSJS010"]}],"id":[{"id":"10.13039\/501100019082","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019082","name":"Shanghai Aerospace Science and Technology Innovation Foundation","doi-asserted-by":"publisher","award":["SAST2022-011"],"award-info":[{"award-number":["SAST2022-011"]}],"id":[{"id":"10.13039\/501100019082","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In view of the typical multi-target scenarios of underwater direction-of-arrival (DOA) tracking complicated by uncertain measurement noise in unknown underwater environments, a robust underwater multi-target DOA tracking method is proposed by incorporating Saga\u2013Husa (SH) noise estimation and a backward smoothing technique within the framework of the cardinalized probability hypothesis density (CPHD) filter. First, the kinematic model of underwater targets and the measurement model based on the received signals of a hydrophone array are established, from which the CPHD-based multi-target DOA tracking algorithm is derived. To mitigate the adverse impact of uncertain measurement noise, the Saga\u2013Husa approach is deployed for dynamic noise estimation, thereby reducing noise-induced performance degradation. Subsequently, a backward smoothing technique is applied to the forward filtering results to further enhance tracking robustness and precision. Finally, extensive simulations and experimental evaluations demonstrate that the proposed method outperforms existing DOA estimation and tracking techniques in terms of robustness and accuracy under uncertain measurement noise conditions.<\/jats:p>","DOI":"10.3390\/e27040438","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T08:24:07Z","timestamp":1744964647000},"page":"438","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust Smoothing Cardinalized Probability Hypothesis Density Filter-Based Underwater Multi-Target Direction-of-Arrival Tracking with Uncertain Measurement Noise"],"prefix":"10.3390","volume":"27","author":[{"given":"Xinyu","family":"Gu","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Hangzhou Applied Acoustic Research Institute, Hangzhou 310023, China"}]},{"given":"Xianghao","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Shaanxi Key Laboratory of Underwater Information Technology, Xi\u2019an 710072, China"}]},{"given":"Boxuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Precision Machinery Research Institute, Xi\u2019an 710077, China"}]},{"given":"Yixin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Shaanxi Key Laboratory of Underwater Information Technology, Xi\u2019an 710072, China"}]},{"given":"Shuanping","family":"Du","sequence":"additional","affiliation":[{"name":"Hangzhou Applied Acoustic Research Institute, Hangzhou 310023, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2007","DOI":"10.1109\/TSP.2007.893204","article-title":"Signal-Selective DOA Tracking for Wideband Cyclostationary Sources","volume":"55","author":"Yan","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131653","DOI":"10.1109\/ACCESS.2019.2940956","article-title":"Joint Algorithm Based on Interference Suppression and Kalman Filter for Bearing-Only Weak Target Robust Tracking","volume":"7","author":"Chen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4101","DOI":"10.1121\/10.0011730","article-title":"Robust Underwater Direction-of-Arrival Tracking with Uncertain Environmental Disturbances Using a Uniform Circular Hydrophone Array","volume":"151","author":"Zhang","year":"2022","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1109\/TSP.2015.2504349","article-title":"CPHD-DOA tracking of multiple extended sonar targets in impulsive environments","volume":"64","author":"Saucan","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1109\/TSP.2017.2768025","article-title":"A Covariance-Based Superpositional CPHD Filter for Multisource DOA Tracking","volume":"66","author":"Rao","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103228","DOI":"10.1016\/j.dsp.2021.103228","article-title":"A new measurement association mapping strategy for DOA tracking","volume":"118","author":"Zhao","year":"2021","journal-title":"Digit. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Battaglia, G.M., Isernia, T., Palmeri, R., Maisto, M.A., Solimene, R., and Morabito, A.F. (2025). Near-Field Synthesis of 1-D Shaped Patterns through Spectral Factorization and Minimally-Redundant Array-Like Representations. IEEE Trans. Antennas Propag.","DOI":"10.1109\/TAP.2024.3525137"},{"key":"ref_8","unstructured":"Kong, D., and Chun, J. (2000, January 10\u201312). A fast DOA tracking algorithm based on the extended Kalman filter. Proceedings of the IEEE 2000 National Aerospace and Electronics Conference. NAECON 2000. Engineering Tomorrow (Cat. No. 00CH37093), Dayton, OH, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/78.978377","article-title":"A Bayesian approach to tracking multiple targets using sensor arrays and particle filters","volume":"50","author":"Orton","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1109\/TAES.2003.1261119","article-title":"Multitarget Bayes filtering via first-order multitarget moments","volume":"39","author":"Mahler","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Clark, D.E., Panta, K., and Vo, B.N. (2006, January 10\u201313). The GM-PHD filter multiple target Tracker. Proceedings of the 2006 9th International Conference on Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301809"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1109\/TAES.2005.1561884","article-title":"Sequential Monte Carlo methods for multitarget filtering with random finite sets","volume":"41","author":"Vo","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/TAES.2007.4441756","article-title":"PHD filters of higher order in target number","volume":"43","author":"Mahler","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hou, X., Zhou, J., Yang, Y., Yang, L., and Qiao, G. (2021). Adaptive Two-Step Bearing-Only Underwater Uncooperative Target Tracking with Uncertain Underwater Disturbances. Entropy, 23.","DOI":"10.3390\/e23070907"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"014801","DOI":"10.1121\/10.0016837","article-title":"Robust Underwater Direction-of-Arrival Tracking Based on Variational Bayesian Extended Kalman Filter","volume":"3","author":"Hou","year":"2023","journal-title":"JASA Express Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hou, X., Qiao, Y., Zhang, B., and Yang, Y. (2023). Robust Underwater Direction-of-Arrival Tracking Based on AI-Aided Variational Bayesian Extended Kalman Filter. Remote Sens., 15.","DOI":"10.3390\/rs15020420"},{"key":"ref_17","unstructured":"Sage, A.P., and Husa, G.W. Adaptive filtering with unknown prior statistics. Joint Automatic Control Conference, Las Vegas, NV, USA, 5 August 1969, IEEE."},{"key":"ref_18","first-page":"605","article-title":"Robust underwater multi-target direction-of-arrival tracking with uncertain measurement noise","volume":"48","author":"Zhang","year":"2023","journal-title":"Acta Acust."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High-resolution frequency-wavenumber spectrum analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. IEEE"},{"key":"ref_20","first-page":"193","article-title":"A theory of PHD filters of higher order in target number","volume":"6235","author":"Mahler","year":"2006","journal-title":"Proc. SPIE Int. Soc. Opt. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Song, Y., Hu, Z., Li, T., and Fan, H. (2022). Performance evaluation metrics and approaches for target tracking: A survey. Sensors, 22.","DOI":"10.3390\/s22030793"},{"key":"ref_22","unstructured":"Booth, N.O., Hodgkiss, W.S., and Ensberg, D.E. (2015). SWellEx-96 Experiment Acoustic Data, UC San Diego Library Digital Collections."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/438\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:17:30Z","timestamp":1760030250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/438"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,18]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["e27040438"],"URL":"https:\/\/doi.org\/10.3390\/e27040438","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,18]]}}}