{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T11:06:35Z","timestamp":1784027195922,"version":"3.55.0"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T00:00:00Z","timestamp":1783728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Training Fund Project of the Hanjiang National Laboratory","award":["HJLJ20230406"],"award-info":[{"award-number":["HJLJ20230406"]}]},{"name":"basic research funds for central universities","award":["3072024YY0401"],"award-info":[{"award-number":["3072024YY0401"]}]},{"name":"National Key Laboratory of the Underwater Robot Technology Fund","award":["JCKYS2022SXJQR-09"],"award-info":[{"award-number":["JCKYS2022SXJQR-09"]}]},{"name":"special program to guide high-level scientific research","award":["3072022QBZ0403"],"award-info":[{"award-number":["3072022QBZ0403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>The advancing perception capabilities of an individual unmanned underwater vehicle (UUV) pose new challenges for multi-target perceptual consistency in underwater bearing-only tracking (BOT) systems. Accurate target state estimation necessitates two key prerequisites: sensor bias compensation and precise data association. The biases encompass both sensor spatial bias and signal propagation delay between the target and sensor. This paper introduces a measurement model that explicitly accounts for these factors. To address the lack of prior target information, an initial target state estimation algorithm is developed based on maximum likelihood estimation (MLE), with a refined bio-inspired variant incorporating particle swarm optimization (PSO). To this end, a cost function is formulated to transform the BOT data association problem into an assignment problem. Thereafter, an iterative multi-target data association (MDA) algorithm, integrated with the expectation-maximization (EM) method, is designed to jointly mitigate the effects of signal delay and spatial bias. Monte Carlo simulation scenarios validate the overall effectiveness of the proposed MDA framework. Specifically, the EM-based spatial bias estimation method demonstrates accurate bias estimation capability.<\/jats:p>","DOI":"10.3390\/biomimetics11070489","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T08:53:58Z","timestamp":1783932838000},"page":"489","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Target Data Association Algorithm in Underwater BOT System with Spatial Bias and Signal Delay"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8407-4714","authenticated-orcid":false,"given":"Naifu","family":"Luo","sequence":"first","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1187-0135","authenticated-orcid":false,"given":"Hongjian","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9666-7740","authenticated-orcid":false,"given":"Zhenwei","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1949-5440","authenticated-orcid":false,"given":"Xinyang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0614-1731","authenticated-orcid":false,"given":"Jingfei","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MAES.2024.3366144","article-title":"Underwater inspection and monitoring: Technologies for autonomous operations","volume":"39","author":"Ioannou","year":"2024","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113861","DOI":"10.1016\/j.oceaneng.2023.113861","article-title":"Autonomous underwater vehicle navigation: A review","volume":"273","author":"Zhang","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1109\/7.543850","article-title":"Observability in passive target motion analysis","volume":"32","author":"Jauffret","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/JOE.2018.2817268","article-title":"At-sea evaluation of an underwater vehicle behavior for passive target tracking","volume":"44","author":"Wolek","year":"2018","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.inffus.2020.03.005","article-title":"Radar networks: A review of features and challenges","volume":"61","author":"Javadi","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/7.826319","article-title":"Broadband passive acoustic technique for target motion parameter estimation","volume":"36","author":"Lo","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1109\/JOE.2020.3039354","article-title":"Target bearing estimation for ship-borne HFSWR using Doppler effect and very small antenna array","volume":"46","author":"Tian","year":"2021","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107581","DOI":"10.1016\/j.sigpro.2020.107581","article-title":"Underwater angle-only tracking with propagation delay and time-offset between observers","volume":"176","author":"Su","year":"2020","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1049\/rsn2.12269","article-title":"Underwater passive manoeuvring target tracking with isogradient sound speed profile","volume":"16","author":"Su","year":"2022","journal-title":"IET Radar Sonar Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6488","DOI":"10.1109\/TSP.2021.3129599","article-title":"Analysis of propagation delay effects on bearings-only fusion of heterogeneous sensors","volume":"69","author":"Arulampalam","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1109\/TAES.2019.2917992","article-title":"CRLB for estimating time-varying rotational biases in passive sensors","volume":"56","author":"Kowalski","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5038","DOI":"10.1109\/TSP.2012.2205923","article-title":"Distributed maximum likelihood for simultaneous self-localization and tracking in sensor networks","volume":"60","author":"Kantas","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/TAES.2019.2929972","article-title":"Distributed joint sensor registration and multitarget tracking via sensor network","volume":"56","author":"Gao","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5865","DOI":"10.1109\/LRA.2021.3084891","article-title":"Robust data association for multi-object detection in maritime environments using camera and radar measurements","volume":"6","author":"Kim","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, T.Y., Chen, W.N., Wei, F.F., and Wang, Y. (2025). Decentralized evolutionary optimization for multi-target tracking and data association with bearing-only measurements. Proceedings of the IEEE INFOCOM 2025\u2014IEEE Conference on Computer Communications, IEEE.","DOI":"10.1109\/INFOCOM55648.2025.11044752"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4544","DOI":"10.1109\/LRA.2021.3068709","article-title":"Bearing-only active sensing under merged measurements","volume":"6","author":"Calkins","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, Q., Huang, X., Tao, H., Xia, Z., Liu, C., and Ren, X. (2024). Marine navigation radar multi-target tracking using adaptive innovation sequence-based joint probability data association. Proceedings of the 2024 IEEE 13th Data Driven Control and Learning Systems Conference (DDCLS), IEEE.","DOI":"10.1109\/DDCLS61622.2024.10606901"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/JSAS.2024.3517513","article-title":"Nonparametric multitarget data association and tracking for multistatic radars","volume":"2","author":"Sruti","year":"2024","journal-title":"IEEE J. Sel. Areas Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108909","DOI":"10.1016\/j.sigpro.2022.108909","article-title":"Joint sensor registration and multi-object tracking with PHD filter in distributed multi-sensor networks","volume":"206","author":"Chai","year":"2023","journal-title":"Signal Process."},{"key":"ref_20","first-page":"5102012","article-title":"Track-to-track association based on maximum likelihood estimation for T\/RR composite compact HFSWR","volume":"61","author":"Sun","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3092","DOI":"10.1109\/LRA.2024.3364842","article-title":"CLIPPER: Robust data association without an initial guess","volume":"9","author":"Lusk","year":"2024","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9902","DOI":"10.1109\/JSEN.2025.3533894","article-title":"Joint matching and fusion with sensor bias and clutter for decentralized multi-target tracking","volume":"25","author":"Hao","year":"2025","journal-title":"IEEE Sens. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1109\/TSP.2023.3268472","article-title":"Joint data association, spatiotemporal bias compensation and fusion for multisensor multitarget tracking","volume":"71","author":"Bu","year":"2023","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1109\/JOE.2025.3585627","article-title":"A novel adaptive initial state estimation method for underwater bearings-only target tracking","volume":"50","author":"Niu","year":"2025","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_25","unstructured":"Yang, R., Ng, G.W., and Bar-Shalom, Y. (2015). Bearings-only tracking with fusion from heterogenous passive sensors: ESM\/EO and acoustic. Proceedings of the 2015 18th International Conference on Information Fusion (Fusion), IEEE."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1109\/TAC.1984.1103664","article-title":"Fundamental properties and performance of conventional bearings-only target motion analysis","volume":"29","author":"Nardone","year":"1984","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"108248","DOI":"10.1016\/j.sigpro.2021.108248","article-title":"A novel bearing-only localization for generalized Gaussian noise","volume":"189","author":"Naseri","year":"2021","journal-title":"Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4045","DOI":"10.1109\/TAES.2024.3503559","article-title":"Target motion analysis with passive measurements and partial prior information","volume":"61","author":"Lowney","year":"2024","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/JSEN.2024.3493935","article-title":"Multi-observer trajectories optimization based on APSO algorithm in underwater BOT system","volume":"25","author":"Luo","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/7.192098","article-title":"Nth-order dynamics target observability from angle measurements","volume":"24","author":"Fogel","year":"1988","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1109\/7.210096","article-title":"Simple linear theory approach to TMA observability","volume":"29","author":"Becker","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","first-page":"9002812","article-title":"A maritime multi-target tracking method with non-Gaussian measurement noises based on joint probabilistic data association","volume":"74","author":"Chen","year":"2025","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/489\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T10:44:03Z","timestamp":1784025843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/489"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,11]]},"references-count":32,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["biomimetics11070489"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11070489","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,11]]}}}