{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T21:04:22Z","timestamp":1780088662982,"version":"3.54.0"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T00:00:00Z","timestamp":1678060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nature Science Foundations of China","award":["51879210"],"award-info":[{"award-number":["51879210"]}]},{"name":"Nature Science Foundations of China","award":["51979210"],"award-info":[{"award-number":["51979210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recent technological advancements facilitate the autonomous navigation of maritime surface ships. The accurate data given by a range of various sensors serve as the primary assurance of a voyage\u2019s safety. Nevertheless, as sensors have various sample rates, they cannot obtain information at the same time. Fusion decreases the accuracy and reliability of perceptual data if different sensor sample rates are not taken into account. Hence, it is helpful to increase the quality of the fusion information to precisely anticipate the motion status of ships at the sampling time of each sensor. This paper proposes a non-equal time interval incremental prediction method. In this method, the high dimensionality of the estimated state and nonlinearity of the kinematic equation are taken into consideration. First, the cubature Kalman filter is employed to estimate a ship\u2019s motion at equal intervals based on the ship\u2019s kinematic equation. Next, a ship motion state predictor based on a long short-term memory network structure is created, using the increment and time interval of the historical estimation sequence as the network input and the increment of the motion state at the projected time as the network output. The suggested technique can lessen the effect of the speed difference between the test set and the training set on the prediction accuracy compared with the traditional long short-term memory prediction method. Finally, comparison experiments are carried out to validate the precision and effectiveness of the proposed approach. The experimental results show that the root-mean-square error coefficient of the prediction error is decreased on average by roughly 78% for various modes and speeds when compared with the conventional non-incremental long short-term memory prediction approach. Additionally, the proposed prediction technology and the traditional approach have virtually the same algorithm times, which may fulfill the real engineering requirements.<\/jats:p>","DOI":"10.3390\/s23052852","type":"journal-article","created":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T04:29:58Z","timestamp":1678076998000},"page":"2852","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Non-Equal Time Interval Incremental Motion Prediction Method for Maritime Autonomous Surface Ships"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-1312-6207","authenticated-orcid":false,"given":"Zhijie","family":"Zhou","sequence":"first","affiliation":[{"name":"Key Laboratory of High-Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China"},{"name":"School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haixiang","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of High-Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China"},{"name":"School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Laboratory of High-Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China"},{"name":"School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjuan","family":"Li","sequence":"additional","affiliation":[{"name":"Marine Equipment Technology Institute, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"544","DOI":"10.4236\/blr.2022.133035","article-title":"The Development of Maritime Autonomous Surface Ships: Regulatory Challenges and the Way Forward","volume":"13","author":"Osaloni","year":"2022","journal-title":"Beijing Law Rev."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hannaford, E., and Hassel, E.V. (2021). Risks and Benefits of Crew Reduction and\/or Removal with Increased Automation on the Ship Operator: A Licensed Deck Officer\u2019s Perspective. Appl. Sci., 11.","DOI":"10.3390\/app11083569"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110555","DOI":"10.1016\/j.oceaneng.2022.110555","article-title":"Human\u2013machine cooperation research for navigation of maritime autonomous surface ships: A review and consideration","volume":"246","author":"Liu","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1017\/S0263574712000409","article-title":"Sensor fusion-based dynamic positioning of ships using Extended Kalman and Particle Filtering","volume":"31","author":"Rigatos","year":"2013","journal-title":"Robotica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.measurement.2014.02.019","article-title":"A fast and high-accuracy transfer alignment method between M\/S INS for ship based on iterative calculation","volume":"51","author":"Liu","year":"2014","journal-title":"Measurement"},{"key":"ref_6","first-page":"49","article-title":"Application research of state estimation algorithm for dynamic positioning ship on fusion of unscented Kalman filtering and particle filtering","volume":"39","author":"Cao","year":"2017","journal-title":"Ship Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1080\/03081079.2019.1659257","article-title":"Centralized, distributed and sequential fusion estimation from uncertain outputs with correlation between sensor noises and signal","volume":"48","year":"2019","journal-title":"Int. J. Gen. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1080\/00207160.2018.1554213","article-title":"Distributed fusion filtering for multi-sensor systems with correlated random transition and measurement matrices","volume":"97","year":"2020","journal-title":"Int. J. Comput. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Caballero-\u00c1guila, R., Hu, J., and Linares-P\u00e9rez, J. (2022). Two Compensation Strategies for Optimal Estimation in Sensor Networks with Random Matrices, Time-Correlated Noises, Deception Attacks and Packet Losses. Sensors, 22.","DOI":"10.3390\/s22218505"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109101","DOI":"10.1016\/j.measurement.2021.109101","article-title":"An improved RISS-GPS ship navigation approach via azimuth updates and magnetometer-calibration technology","volume":"175","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_11","unstructured":"Liu, Y.Q. (2017). Research on the Multi-sensor Asynchronous Fusion Methods of Dynamic Positioning System. [Master\u2019s Thesis, Harbin Engineering University]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.sigpro.2019.01.028","article-title":"Asynchronous multi-rate multi-sensor fusion based on random finite set","volume":"160","author":"Li","year":"2019","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"59511","DOI":"10.1109\/ACCESS.2020.2982682","article-title":"An asynchronous data fusion algorithm for target detection based on multi-sensor networks","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_14","first-page":"77","article-title":"An improved asynchronous fusion algorithm for multi-sensor integrated navigation system","volume":"41","author":"Liu","year":"2021","journal-title":"Chin. Space Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1109\/JSEN.2021.3128226","article-title":"Robust CPHD Fusion for Distributed Multitarget Tracking Using Asynchronous Sensors","volume":"22","author":"Yu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, G.C., Battistelli, G., Chisci, L., and Kong, L. (2020, January 21). Distributed multi-target tracking over an asynchronous multi-sensor network. Proceedings of the IEEE Radar Conference (RadarConf20), Florence, Italy.","DOI":"10.1109\/RadarConf2043947.2020.9266606"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhang, D., Duan, Z., and Hanebeck, U.D. (2022, January 4). Asynchronous Multi-Radar Tracking Fusion with Converted Measurements. Proceedings of the 25th International Conference on Information Fusion, Link\u00f6ping, Sweden.","DOI":"10.23919\/FUSION49751.2022.9841267"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1016\/j.proeng.2014.12.692","article-title":"An asynchronous track-to-track association algorithm without time alignment","volume":"99","author":"Yi","year":"2015","journal-title":"Procedia Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Giorgi, G., Davidson, J., Habib, G., Bracco, G., Mattiazzo, G., and Kalm\u00e1r-Nagy, T. (2020). Nonlinear dynamic and kinematic model of a Spar-Buoy: Parametric resonance and yaw numerical instability. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8070504"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"112524","DOI":"10.1016\/j.oceaneng.2022.112524","article-title":"Attitude prediction of ship coupled heave\u2013pitch motions using nonlinear innovation via full-scale test data","volume":"264","author":"Song","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_21","first-page":"1","article-title":"Performance of GPS and IMU sensor fusion using unscented Kalman filter for precise i-Boat navigation in infinite wide waters","volume":"95","author":"Cahyadi","year":"2022","journal-title":"Geod. Geodyn."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Guo, P., Li, J., Chen, T., and Wu, Z. (2021, January 18). Heave Motion Estimation Based on Cubature Kalman Filter. Proceedings of the International Conference on Cyber-Physical Social Intelligence (ICCSI), Beijing, China.","DOI":"10.1109\/ICCSI53130.2021.9736261"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, Z., Bai, M., Lei, J., Huang, Y., Wang, J., and Xia, X. (2018, January 9). Comparison of UKF and EKF Filter Algorithm in INS\/BDS Tightly Mode. Proceedings of the 30th Chinese Control and Decision Conference, Shenyang, China.","DOI":"10.1109\/CCDC.2018.8407589"},{"key":"ref_24","unstructured":"Sun, F., and Tang, L.J. (2013). Estimation precision comparison of Cubature Kalman filter and Unscented Kalman filter. Control Decis., 28."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Ni, G., and Xu, Y. (2020, January 12). Ship trajectory prediction based on LSTM neural network. Proceedings of the IEEE 5th Information Technology and Mechatronics Engineering Conference (ITOEC), Chongqing, China.","DOI":"10.1109\/ITOEC49072.2020.9141702"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"109066","DOI":"10.1016\/j.oceaneng.2021.109066","article-title":"Multiscale attention-based LSTM for ship motion prediction","volume":"230","author":"Zhang","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_27","first-page":"421","article-title":"Ship motion attitude prediction based on EMD-PSO-LSTM integrated model","volume":"27","author":"Peng","year":"2019","journal-title":"J. Chin. Inert. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/5\/2852\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:48:48Z","timestamp":1760122128000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/5\/2852"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,6]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["s23052852"],"URL":"https:\/\/doi.org\/10.3390\/s23052852","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,6]]}}}