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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">10.17285/0869-7035.2018.27.1.072-092</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-238</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>Аналитический алгоритм оценки пространственного положения и курса объекта</article-title><trans-title-group xml:lang="en"><trans-title>Analytical Algorithm for Attitude and Heading Estimation Aided by Maneuver Classification</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>Аль-Мансур</surname><given-names>М.</given-names></name><name name-style="western" xml:lang="en"><surname>Mansour</surname><given-names>Al</given-names></name></name-alternatives><bio xml:lang="ru"><p>Аль-Мансур Мехьяр. Аспирант, факультет электромеханических систем</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>M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шуаиб Ибрахим. Доктор наук, профессор</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>Джафар</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Jafar</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Джафар Асеф. Доктор наук, профессор</p></bio><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Потапов</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Potapov,</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Потапов Анатолий Андреевич. Доцент кафедры автоматики и управления</p></bio><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Высший институт прикладных наук и технологий (Дамаск, Сирия)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Department of Electronic &amp; Mechanical Systems, Higher Institute for Applied Sciences and Technology (HIAST)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Высший институт прикладных наук и технологий (Дамаск, Сирия)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>(Department of Electronic &amp; Mechanical Systems, Higher Institute for Applied Sciences and Technology (HIAST)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Высший институт прикладных наук и технологий (Дамаск, Сирия)..</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Department of Electronic &amp; Mechanical Systems, Higher Institute for Applied Sciences and Technology (HIAST)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Казанский национальный исследовательский технический университет им. А.Н. Туполева – КАИ (Казань, Россия)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Kazan National Research Technical University named after A. N. Tupolev – KAI</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>13</day><month>11</month><year>2025</year></pub-date><volume>27</volume><issue>1</issue><fpage>72</fpage><lpage>92</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Аль-Мансур М., Шуаиб И., Джафар А., Потапов А.А., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Аль-Мансур М., Шуаиб И., Джафар А., Потапов А.А.</copyright-holder><copyright-holder xml:lang="en">Mansour A., Chouaib M., Jafar A., Potapov, A.A.</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/238">https://www.gyroscopy.ru/jour/article/view/238</self-uri><abstract><p>В статье описывается модифицированный адаптивный аналитический алгоритм оценки пространственного положения и курса объекта, основанный на синтезе данных инерциального измерительного модуля (ИИМ), магнитометров и скорости, вырабатываемой приемником GPS. В первую очередь на основе выходной информации от датчиков угловой скорости (ДУС), входящих в состав ИИМ, рассчитываются кинематические углы Эйлера, после чего содержащиеся в них погрешности компенсируются с помощью выходных данных полученных от акселерометров и магнитометров, а также скоростных измерений. При этом нет необходимости в знании моделей систематической и случайной погрешностей используемых датчиков; фильтр Калмана не используется. Адаптация алгоритма производится на основе классификации маневра (отсутствие маневра, слабый маневр, сильный маневр), в зависимости от интенсивности которого настраиваются параметры соответствующих фильтров. Компьютерное моделирование с использованием смоделированных и реальных полетных данных показало, что предложенный алгоритм дает приемлемые результаты по сравнению с расширенным фильтром Калмана.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents a modified adaptive analytical algorithm for attitude and heading estimation. The analytical algorithm is based on the fusion of IMU, magnetometers and the velocity from GPS. The kinematic Euler angles are first calculated based on the output of the rate gyros, then the calculated angle errors are compensated using the output of each of the accelerometers, magnetometers, and the velocity taken from a GPS receiver, without the need to model the systematic and random errors of the used sensors; Kalman filter is not used. The algorithm will be adaptive based on the maneuver classification, the filters' parameters will be tuned depending on the maneuver intensity: No, Low, or High maneuver. The main contribution of this paper is to build an attitude and heading estimation algorithm (analytical algorithm) without using Kalman filter; this algorithm will be made adaptive based on the maneuver classification algorithm which was developed using logistic regression technique based on IMU output. Computer simulation with simulated and real flight data showed that the adaptive analytical algorithm has acceptable results compared to EKF.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Курсовертикаль</kwd><kwd>ИИМ на микроэлектромеханической системе (МЭМС)</kwd><kwd>магнитометры</kwd><kwd>GPS</kwd><kwd>синтез данных беспилотный летательный аппарат (БПЛА)</kwd><kwd>классификация маневра расширенный фильтр Калмана.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>AHRS</kwd><kwd>MEMS IMU</kwd><kwd>magnetometers</kwd><kwd>GPS</kwd><kwd>data fusion</kwd><kwd>UAV maneuver classification</kwd><kwd>extended Kalman filter.</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">Lai, Ying-Chih, and Jan, Shau-Shiun, Attitude estimation based on fusion of gyroscopes and single antenna GPS for small UAVs under the influence of vibration, GPS solutions, 2011, vol. 15 no. 1, pp. 67–77.</mixed-citation><mixed-citation xml:lang="en">Lai, Ying-Chih, and Jan, Shau-Shiun, Attitude estimation based on fusion of gyroscopes and single antenna GPS for small UAVs under the influence of vibration, GPS solutions, 2011, vol. 15 no. 1, pp. 67–77.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Wu, Yuanxin, et al., Strapdown inertial navigation system algorithms based on dual quaternions IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, no. 1, pp. 110–132.</mixed-citation><mixed-citation xml:lang="en">Wu, Yuanxin, et al., Strapdown inertial navigation system algorithms based on dual quaternions IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, no. 1, pp. 110–132.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Brunner, T., et al., Evaluation of attitude estimation algorithms using absolute magnetic reference data: methodology and results, Proc. of IEEE/ION Position, Location and Navigation SymposiumPLANS 2014, 2014, pp. 212–218.</mixed-citation><mixed-citation xml:lang="en">Brunner, T., et al., Evaluation of attitude estimation algorithms using absolute magnetic reference data: methodology and results, Proc. of IEEE/ION Position, Location and Navigation SymposiumPLANS 2014, 2014, pp. 212–218.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Khalaf, E.W., Chouaib, I., and Wainakh, M., Development of Unscented Kalman Filter for LooselyCoupled INS/GPS/Magnetometer/Barometer Integration, 2017, https://www.researchgate.net/ publication/ 282909368_Development_of_Unscented_Kalman_Filter_for_Loosely-coupled_INSGPS MagnetometerBarometer_Integration.</mixed-citation><mixed-citation xml:lang="en">Khalaf, E.W., Chouaib, I., and Wainakh, M., Development of Unscented Kalman Filter for LooselyCoupled INS/GPS/Magnetometer/Barometer Integration, 2017, https://www.researchgate.net/ publication/ 282909368_Development_of_Unscented_Kalman_Filter_for_Loosely-coupled_INSGPS MagnetometerBarometer_Integration.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Crow, W.T., and Van Loon, E., Impact of incorrect model error assumptions on the sequential assimilation of remotely sensed surface soil moisture, Journal of Hydrometeorology, 2006, vol. 7 no. 3, pp. 421–432.</mixed-citation><mixed-citation xml:lang="en">Crow, W.T., and Van Loon, E., Impact of incorrect model error assumptions on the sequential assimilation of remotely sensed surface soil moisture, Journal of Hydrometeorology, 2006, vol. 7 no. 3, pp. 421–432.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Stengel, R., Aircraft Flight Dynamics, Princeton University, 2014.</mixed-citation><mixed-citation xml:lang="en">Stengel, R., Aircraft Flight Dynamics, Princeton University, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Barton, J.D., Fundamentals of small unmanned aircraft flight, Johns Hopkins APL Technical Digest, 2012, vol 31, no. 2, pp. 132–149.</mixed-citation><mixed-citation xml:lang="en">Barton, J.D., Fundamentals of small unmanned aircraft flight, Johns Hopkins APL Technical Digest, 2012, vol 31, no. 2, pp. 132–149.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Jekeli, C., Inertial navigation systems with geodetic applications, Berlin: Walter de Gruyter GmbH &amp; 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