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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 pub-id-type="doi">10.17285/0869-7035.2019.27.2.003-027</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-241</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>Новый адаптивный нечеткий обобщенный фильтр Калмана для оценивания ориентации при отсутствии GPS-сигналов</article-title><trans-title-group xml:lang="en"><trans-title>Novel Adaptive Fuzzy Extended Kalman Filter for Attitude Estimation in GPS-Denied Environment</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>Ассад</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Assad</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ассад Аммар. Инженер, лаборатория навигации</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>Халаф</surname><given-names>В.</given-names></name><name name-style="western" xml:lang="en"><surname>Khalaf</surname><given-names>W.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Халаф Вассим. Начальник лаборатории навигации</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>Шуаиб</surname><given-names>И.</given-names></name><name name-style="western" xml:lang="en"><surname>Chouaib</surname><given-names>I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шуаиб Ибрахим. Доктор наук, заместитель по научной работе</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт прикладных наук и технологий, Дамаск, Сирия</institution><country>Сирия</country></aff><aff xml:lang="en"><institution>Department of Electronic &amp; Mechanical Systems, Higher Institute for Applied Sciences and Technology (HIAST), Damascus, Syria</institution><country>Syrian Arab Republic</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>14</day><month>11</month><year>2025</year></pub-date><volume>27</volume><issue>2</issue><fpage>3</fpage><lpage>27</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ассад А., Халаф В., Шуаиб И., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ассад А., Халаф В., Шуаиб И.</copyright-holder><copyright-holder xml:lang="en">Assad A., Khalaf W., Chouaib I.</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/241">https://www.gyroscopy.ru/jour/article/view/241</self-uri><abstract><p>В статье описывается новый адаптивный нечеткий обобщенный фильтр Калмана (НАНОФК), предназначенный для оценки ориентации объекта по выходным данным бес платформенного инерциально-измерительного модуля (ИИМ, гироскопов и акселерометров) и бесплатформенного магнитометра. НАНОФК, разработанный на основе обобщенного фильтра Калмана (ОФК) с использованием системы нечеткого логического вывода (СНЛВ), проверен в среде Matlab как на смоделированных траекториях беспилотного летательного аппарата (БЛА), так и на реальных данных, снятых в процессе полета. НАНОФК обеспечивает более точную по сравнению с ОФК оценку ориентации и настройку ковариационной матрицы измерительных шумов. В предлагаемом фильтре в модели измерений присутствует мультипликативная погрешность в уравнениях, описывающих динамику объекта. Результаты моделирования показывают, что ковариационная матрица оценки измерительных шумов близка к своему истинному значению в крейсерском режиме полета (стационарная фаза), а в нестационарной фазе полета достоверность модели измерений акселерометра оценивается в НАНОФК и измерения акселерометров могут не учитываться.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents a Novel Adaptive Fuzzy Extended Kalman Filter namely (NAFEKF) which has been developed and applied for attitude estimation using only the outputs of strap-down IMU (Gyroscopes and Accelerometers) and strapdown magnetometer.</p><p>The NAFEKF, which is based on EKF (Extended Kalman Filter) aided by FIS (Fuzzy Inference System), is validated in Matlab environment on simulated trip data and real data acquired during an UAV’s trip. Accuracy of estimated attitude is increased using NAFEKF compared to typical EKF and in addition the measurement noise covariance matrix is tuned, the proposed filter uses multiplicative error for quaternion.</p><p>Simulation results show that estimated measurement noise covariance matrix is closed to its true value in cruise phase of flight (stationary phase), while in nonstationary phase it refers to the validity of accelerometer measurement model in the filter in NAFEKF; it neglects measurements from accelerometers in this case.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Обобщенный фильтр Калмана (ОФК)</kwd><kwd>система нечеткого логического вывода (СНЛВ)</kwd><kwd>оценка ориентации</kwd><kwd>мультипликативная погрешность измерений.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Extended Kalman Filter (EKF)</kwd><kwd>Fuzzy Inference System (FIS)</kwd><kwd>Attitude Estimation</kwd><kwd>multiplicative quaternion.</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">Bonilla, M.N.I., Pedestrian Dead Reckoning: a neuro-fuzzy approach with inertial measurements fusion based on Kalman filter and DWT, M. 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