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<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</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">DXLKCS</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-144</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>Усовершенствованный алгоритм многоальтернативной фильтрации на основе байесовских сетей и его применение в интегрированной навигационной системе</article-title><trans-title-group xml:lang="en"><trans-title>Bayesian Network Enhanced Multi-model Algorithm and its Application in Integrated Navigation System</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7090-8506</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ван</surname><given-names>Лэй</given-names></name><name name-style="western" xml:lang="en"><surname>Wang</surname><given-names>Lei</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ван Лэй. Профессор</p><p>Хэфэй</p><p>Уху, Аньхой</p></bio><bio xml:lang="en"><p>Wuhu, Anhui</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0002-4462-5785</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Яо</surname><given-names>Гуй Тин</given-names></name><name name-style="western" xml:lang="en"><surname>Yao</surname><given-names>Guiting</given-names></name></name-alternatives><bio xml:lang="ru"><p>Яо Гуй Тин. Аспирант</p><p>Хэфэй</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0000-1004-8890</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ли</surname><given-names>Тин</given-names></name><name name-style="western" xml:lang="en"><surname>Li</surname><given-names>Ting</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ли Тин. Преподаватель</p><p>Хэфэй</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0009-4311-4327</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чжан</surname><given-names>Мин Юй</given-names></name><name name-style="western" xml:lang="en"><surname>Zhang</surname><given-names>Mingyu</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжан Мин Юй. Студент</p><p>Хэфэй</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Колледж радиоэлектроники, Университет Чаоху; Аньхойский центр технических исследований по комплексированию информации и управлению интеллектуальными роботами</institution><country>Китай</country></aff><aff xml:lang="en"><institution>School of electronic engineering, Chaohu University, Hefei, China; Anhui Engineering Research Center on Information Fusion and Control of Intelligent Robot</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Колледж радиоэлектроники, Университет Чаоху</institution><country>Китай</country></aff><aff xml:lang="en"><institution>School of electronic engineering, Chaohu University</institution><country>China</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>30</day><month>07</month><year>2025</year></pub-date><volume>33</volume><issue>2</issue><fpage>48</fpage><lpage>71</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ван Л., Яо Г., Ли Т., Чжан М., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ван Л., Яо Г., Ли Т., Чжан М.</copyright-holder><copyright-holder xml:lang="en">Wang L., Yao G., Li T., Zhang M.</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/144">https://www.gyroscopy.ru/jour/article/view/144</self-uri><abstract><p>Неопределенность параметров и нестабильность модели интегрированной навигационной системы типичны для неупорядоченной среды. В таких системах большие погрешности оценивания чаще всего возникают тогда, когда для решения навигационных задач используется одна модель. Для устранения этой проблемы предложен алгоритм взаимосвязанной многоальтернативной фильтрации (interacting multimodel – IMM), усовершенствованный за счет использования байесовских сетей (BNIMM). Алгоритм предусматривает введение параметров движения, определенных с помощью многоальтернативной оценки, и формирование байесовских сетей на основе причинно-следственной связи между переменными и моделью системы. Характеристики байесовской сети используются для модификации вероятностей переключения моделей при многоальтернативном оценивании, что может снизить зависимость распознавания действительной модели от априорной информации, задействуемой в алгоритме IMM.Предлагаемый подход позволяет решать такие проблемы, как запаздывание смены модели и вероятное изменение модели в алгоритме IMM, и повышать адаптивность алгоритма IMM. Метод BNIMM использовался в качестве локального субфильтра в федеративном фильтре, что дало возможность сформировать архитектуру объединения информации, полученной от интегрированной навигационной системы в составе бесплатформенной инерциальной навигационной системы (БИНС), глобальной навигационной спутниковой системы (GPS) и одометра. В ходе испытаний выходные данные гироскопа и акселерометра были взяты в качестве характеристических переменных для построения байесовской сети, которая применялась для прогнозирования в динамическом режиме неопределенности в интегрированной навигационной системе. Полевые тесты на дорогах показали, что предложенный федеративный алгоритм BNIMM может значительно повысить стабильность и точность оценки состояния интегрированной навигационной системы.</p></abstract><trans-abstract xml:lang="en"><p>The uncertainty of the model parameters of integrated navigation system and the instability of the system model are characteristic of unstructured environment. For these systems, large estimation errors are likely to occur if a fixed single model is used for navigation solutions. To solve this problem, a Bayesian network enhanced interacting multiple model (BN-IMM) filtering algorithm is proposed. In the proposed algorithm, certain motion characteristic variables are introduced on the basis of multi-model estimation, and Bayesian networks are established according to the causal relationship between variables and the system model. Bayesian network parameters are used to modify the model switching probability in multi-model estimation, which can reduce the dependence of real model recognition on prior knowledge in multi-model algorithm. The proposed algorithm can solve the problems such as model conversion lag and model probability mutation in the interacting multi-model (IMM) algorithm, and enhance the adaptive ability of the multi-model algorithm. The proposed BN-IMM was utilized as a local sub-filter within a federated filter, establishing an information fusion algorithm architecture for the strapdown inertial navigation system (SINS)/global positioning system (GPS)/odometer integrated navigation system. In the test, the output of gyro and accelerometer was taken as characteristic variables to build a Bayesian network. The established Bayesian network was used to dynamically predict the uncertainties in the integrated navigation system. The actual road tests demonstrate that the proposed federated BN-IMM algorithm can significantly enhance the stability and accuracy of state estimation in the integrated navigation system.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>беспилотное транспортное средство</kwd><kwd>интегрированная навигационная система</kwd><kwd>многоальтернативная фильтрация</kwd><kwd>байесовская сеть</kwd></kwd-group><kwd-group xml:lang="en"><kwd>unmanned vehicle</kwd><kwd>integrated navigation</kwd><kwd>Multiple Model</kwd><kwd>Bayesian Network</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке Естественнонаучного фонда провинции Аньхой (№ 2208085MF169), Фонда Аньхойский центр технических исследований по комплексированию информации и управлению интеллектуальными роботами (Foundation of Anhui Engineering Research Center on Information Fusion and Control of Intelligent Robot) (№ IFCIR2024020), Инновационной программы взаимодействия университетов провинции Аньхой (University Synergy Innovation Program of Anhui Province) (№ GXXT2023010), Ключевого научно-исследовательского проекта развития естественных наук в университетах провинции Аньхой (Key Scientific Research Project of Natural Science in Universities of Anhui Province) (№ 2024AH051329) и Фонда пилотных исследовательских проектов Университета Чаоху (Research Launch Fund Project of Chaohu University) (№KYQD2023038).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Lu, H., Wang, P., Qu, T., Chen, H., Zhang, L., and Hu Y., Moving horizon estimation with variable structure interacting multiple model for surrounding vehicle states in complex environments, IEEE Transactions on Intelligent Transportation Systems, 2024, vol. 25(12), pp. 19943–19961, https://doi.org/10.1109/TITS.2024.3467042.</mixed-citation><mixed-citation xml:lang="en">Lu, H., Wang, P., Qu, T., Chen, H., Zhang, L., and Hu Y., Moving horizon estimation with variable structure interacting multiple model for surrounding vehicle states in complex environments, IEEE Transactions on Intelligent Transportation Systems, 2024, vol. 25(12), pp. 19943–19961, https://doi.org/10.1109/TITS.2024.3467042.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Lei, W., Shicheng, X., Hengliu, X., Shuangxi, L., and Le, W., Robust visual inertial odometry estimation based on adaptive interacting multiple model algorithm, International Journal of Control, Automation and Systems, 2022, vol. 20, pp. 3335–3346, https://doi.org/10.1007/s1255502007812.</mixed-citation><mixed-citation xml:lang="en">Lei, W., Shicheng, X., Hengliu, X., Shuangxi, L., and Le, W., Robust visual inertial odometry estimation based on adaptive interacting multiple model algorithm, International Journal of Control, Automation and Systems, 2022, vol. 20, pp. 3335–3346, https://doi.org/10.1007/s1255502007812.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Gomaa, M. 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