<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">gyroscopy</journal-id><journal-title-group><journal-title xml:lang="ru">Гироскопия и навигация</journal-title><trans-title-group xml:lang="en"><trans-title>Giroskopiya i Navigatsiya / Gyroscopy and Navigation</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0869-7035</issn><issn pub-type="epub">2075-0927</issn><publisher><publisher-name>AO «Концерн «ЦНИИ «Электроприбор»</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="edn" pub-id-type="custom">XMYLOI</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-86</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Обзор методов инерциальной навигации на основе глубокого обучения для навигации АНПА на больших дистанциях</article-title><trans-title-group xml:lang="en"><trans-title>Deep Learning-Based Inertial Navigation Technology for Autonomous Underwater Vehicle Long-Distance Navigation – A Review</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хэ</surname><given-names>Цинь Юань</given-names></name><name name-style="western" xml:lang="en"><surname>He</surname><given-names>Qin Yuan</given-names></name></name-alternatives><bio xml:lang="ru"><p>Цинь Юань Хэ, доктор наук</p><p>Пекин</p></bio><bio xml:lang="en"><p>Qin Yuan He</p><p>Beijing</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ю</surname><given-names>Хуа Пэн</given-names></name><name name-style="western" xml:lang="en"><surname>Yu</surname><given-names>Hua Peng</given-names></name></name-alternatives><bio xml:lang="ru"><p>Хуа Пэн Ю, доктор наук</p><p>Пекин</p></bio><bio xml:lang="en"><p>Hua Peng Yu</p><p>Beijing</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фан</surname><given-names>Ю Чэнь</given-names></name><name name-style="western" xml:lang="en"><surname>Fang</surname><given-names>Yu Chen</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ю Чэнь Фан, доктор наук</p><p>факультет автоматизированного проектирования</p><p>Чэнду</p></bio><bio xml:lang="en"><p>Yu Chen Fang</p><p>Faculty of Computer-aided Design</p><p>Chengdu</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный институт инновационных оборонных технологий, Ака-&#13;
Доктор наук, Национальный институт инновационных оборонных технологий, Академия военных наук</institution><country>Китай</country></aff><aff xml:lang="en"><institution>National Innovation Institute of Defense Technology Academy of Military Science</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Национальный институт инновационных оборонных технологий, Академия военных наук</institution><country>Китай</country></aff><aff xml:lang="en"><institution>National Innovation Institute of Defense Technology Academy of Military Science</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Университет электронных наук и технологий Китая</institution><country>Китай</country></aff><aff xml:lang="en"><institution>School of Automation Engineering University of Electronic Science and Technology of China</institution><country>China</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>19</day><month>05</month><year>2025</year></pub-date><volume>31</volume><issue>3</issue><fpage>122</fpage><lpage>135</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Хэ Ц.Ю., Ю Х.П., Фан Ю.Ч., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Хэ Ц.Ю., Ю Х.П., Фан Ю.Ч.</copyright-holder><copyright-holder xml:lang="en">He Q.Y., Yu H.P., Fang Y.C.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.gyroscopy.ru/jour/article/view/86">https://www.gyroscopy.ru/jour/article/view/86</self-uri><abstract><p>   Инерциальные методы навигации автономных необитаемых подводных аппаратов (АНПА) позволяют обеспечить выполнение ими сложных задач в автоматическом режиме. Разработки в области традиционной инерциальной навигации ведутся в течение многих лет, и существует потребность в новых технических решениях. С помощью метода глубокого обучения можно автоматически выбирать и извлекать ключевые признаки в обрабатываемых данных, что широко применяется для распознавания изображений, речи, обработки текстов и в других областях. Хорошие результаты достигаются при обработке последовательно поступающих данных, например текста и речи. Очевидно, что выходные данные инерциальной навигации относятся к такому же типу информации. Многочисленные исследования показали, что модели на основе глубоких нейронных сетей можно использовать для снижения уровня шума инерциальных датчиков и дрейфа средств инерциальной навигации, а также комплексирования инерциальных данных с данными других датчиков. Кроме того, эти модели позволяют прогнозировать и уменьшать погрешности инерциальной навигации при длительном подводном плавании. В статье приводится обзор методов инерциальной навигации АНПА на основе глубокого обучения, включая новейшие достижения и тенденции развития.</p></abstract><trans-abstract xml:lang="en"><p>   Autonomous navigation technology is the key technology for Autonomous Underwater Vehicle (AUV) to achieve automated, intelligent operation and task processing. Inertial navigation technology is the core of autonomous navigation technology for AUV. Traditional inertial navigation technology has been developed for many years, and it is necessary to find new breakthroughs. Deep learning can automatically select and extract key features of input data, which has been widely used in image recognition, speech recognition, natural language processing and other fields, and has good results in processing sequential data such as text and speech. Inertial navigation data clearly belongs to this type of data, and many scholars in the industry have conducted related research and design, and found that deep neural network models can be used to calibrate the noise of inertial sensors, reduce the drift of inertial navigation mechanisms, and fuse inertial information with other sensor information, with good effects in solving the prediction and error suppression of inertial navigation during long-term underwater voyages. This article provides a comprehensive review of deep learning-based inertial navigation for AUV, including the latest research progress and development trend direction</p></trans-abstract><kwd-group xml:lang="ru"><kwd>инерциальная навигация</kwd><kwd>подводное позиционирование</kwd><kwd>глубокое обучение</kwd><kwd>АНПА</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Inertial Navigation</kwd><kwd>Underwater Localization</kwd><kwd>Deep Learning</kwd><kwd>AUV</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Matos, A. and Cruz, N., Development and implementation of a low-cost LBL navigation system for an AUV, Ocean ’99 MTS/IEEE. Riding the Crest into 21st Century, pp. 774–779.</mixed-citation><mixed-citation xml:lang="en">Matos, A. and Cruz, N., Development and implementation of a low-cost LBL navigation system for an AUV, Ocean ’99 MTS/IEEE. Riding the Crest into 21st Century, pp. 774–779.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Opderbecke, J.P. and Person, R., POSIDONIA 6000: A new long range highly accurate ultra short base line positioning system, Ocean MTS/IEEE Conference Proceedings, Halifax, 1998, pp. 1721–1727.</mixed-citation><mixed-citation xml:lang="en">Opderbecke, J.P. and Person, R., POSIDONIA 6000: A new long range highly accurate ultra short base line positioning system, Ocean MTS/IEEE Conference Proceedings, Halifax, 1998, pp. 1721–1727.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Thomas, H.G., GIB buoys: An interface between space and depths of the oceans, Proceedings of the 1998 Workshop on Autonomous Underwater Vehicles, Cambridge, pp. 181–184.</mixed-citation><mixed-citation xml:lang="en">Thomas, H.G., GIB buoys: An interface between space and depths of the oceans, Proceedings of the 1998 Workshop on Autonomous Underwater Vehicles, Cambridge, pp. 181–184.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Watanabe, Y. and Ochi, H., A tracking of AUV with integration of SSBL acoustic positioning and transmitted INS data, in Proc. OCEAN EUROPE, Bremen, 2009, pp. 1–6.</mixed-citation><mixed-citation xml:lang="en">Watanabe, Y. and Ochi, H., A tracking of AUV with integration of SSBL acoustic positioning and transmitted INS data, in Proc. OCEAN EUROPE, Bremen, 2009, pp. 1–6.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Toky, A. and Singh, R., Localization schemes for underwater acoustic sensor networks — A review, Comput. Sci. Rev., 2020, pp. 100241–100259.</mixed-citation><mixed-citation xml:lang="en">Toky, A. and Singh, R., Localization schemes for underwater acoustic sensor networks — A review, Comput. Sci. Rev., 2020, pp. 100241–100259.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Bresson, G. and Alsayed, Z., Simultaneous localization and mapping: A survey of current trends in autonomous driving, IEEE Trans. Intell., 2017, pp. 194–220.</mixed-citation><mixed-citation xml:lang="en">Bresson, G. and Alsayed, Z., Simultaneous localization and mapping: A survey of current trends in autonomous driving, IEEE Trans. Intell., 2017, pp. 194–220.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Qin, T. and Li, P., VINS-Mono: A robust and versatile monocular visual-inertial state estimator, IEEE Transactions on Robotics (ITOR) 2018, pp. 1004–1020.</mixed-citation><mixed-citation xml:lang="en">Qin, T. and Li, P., VINS-Mono: A robust and versatile monocular visual-inertial state estimator, IEEE Transactions on Robotics (ITOR) 2018, pp. 1004–1020.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Xu, W. and Cai, Y., Fast- LIO2: Fast direct LiDAR-inertial odometry, IEEE Transactions on Robotics, 2022.</mixed-citation><mixed-citation xml:lang="en">Xu, W. and Cai, Y., Fast- LIO2: Fast direct LiDAR-inertial odometry, IEEE Transactions on Robotics, 2022.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Feng, D. and Wang, C., Kalman-filter based integration of IMU and UWB for high-accuracy indoor positioning and navigation, IEEE Internet of Things Journal, 2020, pp. 3133–3146.</mixed-citation><mixed-citation xml:lang="en">Feng, D. and Wang, C., Kalman-filter based integration of IMU and UWB for high-accuracy indoor positioning and navigation, IEEE Internet of Things Journal, 2020, pp. 3133–3146.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Wagner, J. and Sorg, H.W., The Bohnenberger machine, Gyroscopy Navig., 2010, vol. 1, pp. 73–78.</mixed-citation><mixed-citation xml:lang="en">Wagner, J. and Sorg, H.W., The Bohnenberger machine, Gyroscopy Navig., 2010, vol. 1, pp. 73–78.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Allotta, B. and Caiti, A., A new AUV navigation system exploiting unscented Kalman filter, Ocean Eng., 2016, pp. 121–132.</mixed-citation><mixed-citation xml:lang="en">Allotta, B. and Caiti, A., A new AUV navigation system exploiting unscented Kalman filter, Ocean Eng., 2016, pp. 121–132.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Farrell, J.A., Aided Navigation Systems: GPS and High Rate Sensors, New York: McGraw-Hill, 2008, pp. 11–12.</mixed-citation><mixed-citation xml:lang="en">Farrell, J.A., Aided Navigation Systems: GPS and High Rate Sensors, New York: McGraw-Hill, 2008, pp. 11–12.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Petillo, S. and Schmidt, H., Exploiting adaptive and collaborative AUV autonomy for detection and characterization of internal waves, IEEE Journal of Oceanic Engineering Special Issue on Marine Vehicle Autonomy, 2014, pp. 150–164.</mixed-citation><mixed-citation xml:lang="en">Petillo, S. and Schmidt, H., Exploiting adaptive and collaborative AUV autonomy for detection and characterization of internal waves, IEEE Journal of Oceanic Engineering Special Issue on Marine Vehicle Autonomy, 2014, pp. 150–164.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Jalving, B., DVL velocity aiding in the HUGIN 1000 Integrated Inertial Navigation System, Modeling, Identification and Control, 2004, pp. 223–235.</mixed-citation><mixed-citation xml:lang="en">Jalving, B., DVL velocity aiding in the HUGIN 1000 Integrated Inertial Navigation System, Modeling, Identification and Control, 2004, pp. 223–235.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Stutters, L. and Liu, H., Navigation technologies for autonomous underwater vehicles, IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2008, pp. 581–589.</mixed-citation><mixed-citation xml:lang="en">Stutters, L. and Liu, H., Navigation technologies for autonomous underwater vehicles, IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, 2008, pp. 581–589.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Yu, S.-Ch., Ura, T., Fujii, T., and Kondo. H., Navigation of autonomous underwater vehicles based on artificial underwater landmarks, MTS/IEEE Oceans 2001. An Ocean Odyssey. Conference Proceedings (IEEE Cat. No. 01CH37295), Honolulu, 10.1109.</mixed-citation><mixed-citation xml:lang="en">Yu, S.-Ch., Ura, T., Fujii, T., and Kondo. H., Navigation of autonomous underwater vehicles based on artificial underwater landmarks, MTS/IEEE Oceans 2001. An Ocean Odyssey. Conference Proceedings (IEEE Cat. No. 01CH37295), Honolulu, 10.1109.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">LeCun, Y., Bengio, Y., and Hinton, G., Deep learning, Nature, 2015, pp. 436–44.</mixed-citation><mixed-citation xml:lang="en">LeCun, Y., Bengio, Y., and Hinton, G., Deep learning, Nature, 2015, pp. 436–44.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">McCulloch, W.S. and Pitts, W., A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics, 1943, pp. 115–133.</mixed-citation><mixed-citation xml:lang="en">McCulloch, W.S. and Pitts, W., A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics, 1943, pp. 115–133.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Rosenblatt, F., The perceptron: a probabilistic model for information storage and organization in the brain, Psychological review, 1958, p. 386.</mixed-citation><mixed-citation xml:lang="en">Rosenblatt, F., The perceptron: a probabilistic model for information storage and organization in the brain, Psychological review, 1958, p. 386.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Rumelhart, D.E. and Hinton, G.E., Learning representations by back-propagating errors, Nature, 1986, pp. 533–536.</mixed-citation><mixed-citation xml:lang="en">Rumelhart, D.E. and Hinton, G.E., Learning representations by back-propagating errors, Nature, 1986, pp. 533–536.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">LeCun, Y. and Bottou, L., Gradient-based learning applied to document recognition, Proceedings of the IEEE, 1998, pp. 2278–2324.</mixed-citation><mixed-citation xml:lang="en">LeCun, Y. and Bottou, L., Gradient-based learning applied to document recognition, Proceedings of the IEEE, 1998, pp. 2278–2324.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Goodfellow, I.J., Pouget-Abadie, J., Mirza, M. et al., Generative adversarial networks, Advances in Neural Information Processing Systems, 2014, pp. 2672–2680.</mixed-citation><mixed-citation xml:lang="en">Goodfellow, I.J., Pouget-Abadie, J., Mirza, M. et al., Generative adversarial networks, Advances in Neural Information Processing Systems, 2014, pp. 2672–2680.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Hinton, G.E., Osindero, S., and Teh, Y.-W., A fast learning algorithm for deep belief nets, Neural Computation, 2006, pp. 1527–1554.</mixed-citation><mixed-citation xml:lang="en">Hinton, G.E., Osindero, S., and Teh, Y.-W., A fast learning algorithm for deep belief nets, Neural Computation, 2006, pp. 1527–1554.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Sutskever, I., Martens, J., and Hinton, G.E., Generating text with Recurrent Neural Networks, International Conference on Machine Learning (ICML) 2016.</mixed-citation><mixed-citation xml:lang="en">Sutskever, I., Martens, J., and Hinton, G.E., Generating text with Recurrent Neural Networks, International Conference on Machine Learning (ICML) 2016.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Sutskever, I., Hinton, G.E., and Taylor, G.W., The Recurrent Temporal Restricted Boltzmann Machine, in Advances in Neural Information Processing Systems 21, 2008, pp. 1601–1608.</mixed-citation><mixed-citation xml:lang="en">Sutskever, I., Hinton, G.E., and Taylor, G.W., The Recurrent Temporal Restricted Boltzmann Machine, in Advances in Neural Information Processing Systems 21, 2008, pp. 1601–1608.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Graves, A. and Jaitly, N., Towards end-to-end speech recognition with recurrent neural networks, Proceedings of the 31&lt;sup&gt;st&lt;/sup&gt; International Conference on International Conference on Machine Learning, 2014, vol. 32, pp. 1164-1172.</mixed-citation><mixed-citation xml:lang="en">Graves, A. and Jaitly, N., Towards end-to-end speech recognition with recurrent neural networks, Proceedings of the 31&lt;sup&gt;st&lt;/sup&gt; International Conference on International Conference on Machine Learning, 2014, vol. 32, pp. 1164-1172.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Zhou, Y., Wang, M., Liu, D., and Hu, Z., More grounded image captioning by distilling image-text matching model, IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020.</mixed-citation><mixed-citation xml:lang="en">Zhou, Y., Wang, M., Liu, D., and Hu, Z., More grounded image captioning by distilling image-text matching model, IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Donahue, J, Hendricks, L.A., and Rohrbach, M., Long-term Recurrent Convolutional Networks for visual recognition and description, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, pp. 677–691.</mixed-citation><mixed-citation xml:lang="en">Donahue, J, Hendricks, L.A., and Rohrbach, M., Long-term Recurrent Convolutional Networks for visual recognition and description, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, pp. 677–691.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Hochreiter, S. and Schmidhuber, J., Long short-term memory, Neural Computation, 1997, pp. 1735–1780.</mixed-citation><mixed-citation xml:lang="en">Hochreiter, S. and Schmidhuber, J., Long short-term memory, Neural Computation, 1997, pp. 1735–1780.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Goodfellow, I.J. and Pouget-Abadie, J., Generative adversarial nets, in Proceedings of the 27&lt;sup&gt;th&lt;/sup&gt; International Conference on Neural Information Processing Systems – Volume 2 (NIPS’14): pp. 2672–2680.</mixed-citation><mixed-citation xml:lang="en">Goodfellow, I.J. and Pouget-Abadie, J., Generative adversarial nets, in Proceedings of the 27&lt;sup&gt;th&lt;/sup&gt; International Conference on Neural Information Processing Systems – Volume 2 (NIPS’14): pp. 2672–2680.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Vaswani, A. and Shazeer, N., Attention is all you need, Advances in Neural Information Processing Systems, 2017.</mixed-citation><mixed-citation xml:lang="en">Vaswani, A. and Shazeer, N., Attention is all you need, Advances in Neural Information Processing Systems, 2017.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Parmar, N., Vaswani, A., Uszkoreit, J. et al., Image transformer, International Conference on Machine Learning (ICML),2018, pp. 4055-4064.</mixed-citation><mixed-citation xml:lang="en">Parmar, N., Vaswani, A., Uszkoreit, J. et al., Image transformer, International Conference on Machine Learning (ICML),2018, pp. 4055-4064.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Chen, M., Radford, A. and Child, R., Generative pretraining from pixels, International Conference on Machine Learning (ICML), 2020, pp. 1691–1703.</mixed-citation><mixed-citation xml:lang="en">Chen, M., Radford, A. and Child, R., Generative pretraining from pixels, International Conference on Machine Learning (ICML), 2020, pp. 1691–1703.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Esser, P., Rombach, R., and Ommer, B., Taming transformers for high-resolution image synthesis, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 12873–12883.</mixed-citation><mixed-citation xml:lang="en">Esser, P., Rombach, R., and Ommer, B., Taming transformers for high-resolution image synthesis, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 12873–12883.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Chen, C., Lu, X., Markham, A., and Trigoni, N., IONet: Learning to cure the curse of drift in inertial odometry, in The Conference on Artificial Intelligence (AAAI) 2018.</mixed-citation><mixed-citation xml:lang="en">Chen, C., Lu, X., Markham, A., and Trigoni, N., IONet: Learning to cure the curse of drift in inertial odometry, in The Conference on Artificial Intelligence (AAAI) 2018.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Clark, R., Wang, S., Wen, H., Markham, A., and Trigoni, N., VINet: Visual-Inertial Odometry as a sequence-to-sequence learning problem, in The Conference on Artificial Intelligence (AAAI) 2017, pp. 3995– 4001.</mixed-citation><mixed-citation xml:lang="en">Clark, R., Wang, S., Wen, H., Markham, A., and Trigoni, N., VINet: Visual-Inertial Odometry as a sequence-to-sequence learning problem, in The Conference on Artificial Intelligence (AAAI) 2017, pp. 3995– 4001.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Lu, S., Liu, J., Guo, J. et al., Neural-network based AUV navigation for fast-changing environments, IEEE Internet of Things Journal, 2020, pp. 9773-9783.</mixed-citation><mixed-citation xml:lang="en">Lu, S., Liu, J., Guo, J. et al., Neural-network based AUV navigation for fast-changing environments, IEEE Internet of Things Journal, 2020, pp. 9773-9783.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Esfahani, M.A., Wang, H., and Wu, K., AbolDeepIO: A novel deep inertial odometry network for autonomous vehicles, IEEE Transactions on Intelligent Transportation Systems, 2020, pp. 1941–1950.</mixed-citation><mixed-citation xml:lang="en">Esfahani, M.A., Wang, H., and Wu, K., AbolDeepIO: A novel deep inertial odometry network for autonomous vehicles, IEEE Transactions on Intelligent Transportation Systems, 2020, pp. 1941–1950.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Topini, E. et al., LSTM-based dead reckoning navigation for Autonomous Underwater Vehicles, Global Oceans 2020, Singapore – U.S. Gulf Coast, Biloxi, pp. 1-7.</mixed-citation><mixed-citation xml:lang="en">Topini, E. et al., LSTM-based dead reckoning navigation for Autonomous Underwater Vehicles, Global Oceans 2020, Singapore – U.S. Gulf Coast, Biloxi, pp. 1-7.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Jiang, C. and Chen, S., A MEMS IMU de-noising method using Long Short Term Memory Recurrent Neural Networks (LSTM-RNN), Sensors, 2018.</mixed-citation><mixed-citation xml:lang="en">Jiang, C. and Chen, S., A MEMS IMU de-noising method using Long Short Term Memory Recurrent Neural Networks (LSTM-RNN), Sensors, 2018.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Chen, H., Aggarwal, P., Taha, T.M., and Chodavarapu, V.P., Improving inertial sensor by reducing errors using deep learning methodology, NAECON 2018 – IEEE National Aerospace and Electronics Conference (NAEC).</mixed-citation><mixed-citation xml:lang="en">Chen, H., Aggarwal, P., Taha, T.M., and Chodavarapu, V.P., Improving inertial sensor by reducing errors using deep learning methodology, NAECON 2018 – IEEE National Aerospace and Electronics Conference (NAEC).</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Ma, H., Mu, X., and He, B., Adaptive navigation algorithm with deep learning for Autonomous Underwater Vehicle, Sensors, 2021.</mixed-citation><mixed-citation xml:lang="en">Ma, H., Mu, X., and He, B., Adaptive navigation algorithm with deep learning for Autonomous Underwater Vehicle, Sensors, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Brossard, M., Bonnabel, S., and Barrau, A., Denoising IMU gyroscopes with deep learning for openloop attitude estimation, in IEEE Robotics and Automation Letters, 2020, pp. 4796–4803.</mixed-citation><mixed-citation xml:lang="en">Brossard, M., Bonnabel, S., and Barrau, A., Denoising IMU gyroscopes with deep learning for openloop attitude estimation, in IEEE Robotics and Automation Letters, 2020, pp. 4796–4803.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Martinelli, A., Vision and IMU data fusion: Closed-form solutions for attitude, speed, absolute scale, and bias determination, in IEEE Transactions on Robotics, 2011, pp. 44–60.</mixed-citation><mixed-citation xml:lang="en">Martinelli, A., Vision and IMU data fusion: Closed-form solutions for attitude, speed, absolute scale, and bias determination, in IEEE Transactions on Robotics, 2011, pp. 44–60.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Rao, B., Kazemi, E., and Ding, Y., CTIN: Robust Contextual Transformer Network for inertial navigation, Proceedings of the AAAI Conference on Artificial Intelligence, 2022, pp. 5413–5421.</mixed-citation><mixed-citation xml:lang="en">Rao, B., Kazemi, E., and Ding, Y., CTIN: Robust Contextual Transformer Network for inertial navigation, Proceedings of the AAAI Conference on Artificial Intelligence, 2022, pp. 5413–5421.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">Or, B. and Klein, I., ProNet: Adaptive process noise estimation for INS/DVL fusion, 2023 IEEE Underwater Technology (UT), Tokyo, Japan, pp. 1–5.</mixed-citation><mixed-citation xml:lang="en">Or, B. and Klein, I., ProNet: Adaptive process noise estimation for INS/DVL fusion, 2023 IEEE Underwater Technology (UT), Tokyo, Japan, pp. 1–5.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, X., He, B., Li, G., Mu, X., Zhou, Y. and Mang, T., Navnet: AUV navigation through deep sequential learning, in IEEE Access, 2020, vol. 8, pp. 59845–59861.</mixed-citation><mixed-citation xml:lang="en">Zhang, X., He, B., Li, G., Mu, X., Zhou, Y. and Mang, T., Navnet: AUV navigation through deep sequential learning, in IEEE Access, 2020, vol. 8, pp. 59845–59861.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">Carlucho, I., De Paula, M., Wang, S., Menna, B.V., Petillot, Y.R., and Acosta, G.G., AUV position tracking control using end-to-end deep reinforcement learning, OCEANS 2018 MTS/IEEE Charleston, Charleston, SC, USA , pp. 1–8.</mixed-citation><mixed-citation xml:lang="en">Carlucho, I., De Paula, M., Wang, S., Menna, B.V., Petillot, Y.R., and Acosta, G.G., AUV position tracking control using end-to-end deep reinforcement learning, OCEANS 2018 MTS/IEEE Charleston, Charleston, SC, USA , pp. 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">Li, D., Xu, J., He, H. and Wu, M., An underwater integrated navigation algorithm to deal with DVL malfunctions based on deep learning, in IEEE Access, 2021, vol. 9.</mixed-citation><mixed-citation xml:lang="en">Li, D., Xu, J., He, H. and Wu, M., An underwater integrated navigation algorithm to deal with DVL malfunctions based on deep learning, in IEEE Access, 2021, vol. 9.</mixed-citation></citation-alternatives></ref><ref id="cit50"><label>50</label><citation-alternatives><mixed-citation xml:lang="ru">Topini, E., Fanelli, F., and Topini, A., An experimental comparison of Deep Learning strategies for AUV navigation in DVL-denied environments, Ocean Engineering, 2023, vol. 274.</mixed-citation><mixed-citation xml:lang="en">Topini, E., Fanelli, F., and Topini, A., An experimental comparison of Deep Learning strategies for AUV navigation in DVL-denied environments, Ocean Engineering, 2023, vol. 274.</mixed-citation></citation-alternatives></ref><ref id="cit51"><label>51</label><citation-alternatives><mixed-citation xml:lang="ru">Zhu, J., Li, A., Qin, F., Che, H., and Wang, J., A novel hybrid method based on deep learning for an integrated navigation system during DVL signal failure, Electronics, 2022, vol. 11, no. 19, p. 2980.</mixed-citation><mixed-citation xml:lang="en">Zhu, J., Li, A., Qin, F., Che, H., and Wang, J., A novel hybrid method based on deep learning for an integrated navigation system during DVL signal failure, Electronics, 2022, vol. 11, no. 19, p. 2980.</mixed-citation></citation-alternatives></ref><ref id="cit52"><label>52</label><citation-alternatives><mixed-citation xml:lang="ru">Saksvik, I.B., Alcocer, A., and Hassani, V., A deep learning approach to dead-reckoning navigation for autonomous underwater vehicles with limited sensor payloads, OCEANS 2021, San Diego – Porto, pp. 1–9.</mixed-citation><mixed-citation xml:lang="en">Saksvik, I.B., Alcocer, A., and Hassani, V., A deep learning approach to dead-reckoning navigation for autonomous underwater vehicles with limited sensor payloads, OCEANS 2021, San Diego – Porto, pp. 1–9.</mixed-citation></citation-alternatives></ref><ref id="cit53"><label>53</label><citation-alternatives><mixed-citation xml:lang="ru">Yan, H., Shan, Q., and Furukawa, Y., RIDI: Robust IMU double integration, in Proceedings of the European Conference on Computer Vision (ECCV), 2018, pp. 621–636.</mixed-citation><mixed-citation xml:lang="en">Yan, H., Shan, Q., and Furukawa, Y., RIDI: Robust IMU double integration, in Proceedings of the European Conference on Computer Vision (ECCV), 2018, pp. 621–636.</mixed-citation></citation-alternatives></ref><ref id="cit54"><label>54</label><citation-alternatives><mixed-citation xml:lang="ru">Herath, S., Yan, H., and Furukawa, Y., RoNIN: Robust neural inertial navigation in the wild: Benchmark, evaluations, new methods, in 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 3146–3152</mixed-citation><mixed-citation xml:lang="en">Herath, S., Yan, H., and Furukawa, Y., RoNIN: Robust neural inertial navigation in the wild: Benchmark, evaluations, new methods, in 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 3146–3152</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
