{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T23:18:12Z","timestamp":1769555892845,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T00:00:00Z","timestamp":1630195200000},"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":["51977153, 51977161 , 51577046"],"award-info":[{"award-number":["51977153, 51977161 , 51577046"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.<\/jats:p>","DOI":"10.3390\/e23091124","type":"journal-article","created":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T21:45:16Z","timestamp":1630273516000},"page":"1124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-334X","authenticated-orcid":false,"given":"Wasiq","family":"Ali","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan"}]},{"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9953-822X","authenticated-orcid":false,"given":"Muhammad Asif Zahoor","family":"Raja","sequence":"additional","affiliation":[{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Yunlin 64002, Taiwan"}]},{"given":"Wasim Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}]},{"given":"Yigang","family":"He","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.arcontrol.2018.09.002","article-title":"Advanced state estimation for navigation of automated vehicles","volume":"46","author":"Konrad","year":"2018","journal-title":"Annu. 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