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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 / 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">KQZBSP</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-98</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>Оценка параметров относительного движения спутников при групповом полете с помощью АОФК</article-title><trans-title-group xml:lang="en"><trans-title>Estimation of the Relative States of Satellite Formation Flights Using the Adaptive Extended Kalman Filter</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3357-0985</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Эркек</surname><given-names>Т. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Erkec</surname><given-names>T. Y.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Эркек Тункай Юнус – доктор наук, Институт аэронавтики и космических технологий им. Хезарфена</p><p>Стамбул</p></bio><bio xml:lang="en"><p>Hezarfen Aeronautics and Space Technologies Instıtute</p><p>Istanbul</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/0000-0003-4115-341X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гаджиев</surname><given-names>Ч.</given-names></name><name name-style="western" xml:lang="en"><surname>Hajiyev</surname><given-names>Ch.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Гаджиев Чингиз – доктор наук, профессор, Факультет аэронавтики и астронавтики</p><p>Стамбул</p></bio><bio xml:lang="en"><p>Faculty of Aeronautics and Astronautics</p><p>Istanbul</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный университет обороны Турции</institution><country>Турция</country></aff><aff xml:lang="en"><institution>Turkish National Defence University</institution><country>Turkey</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Стамбульский технический университет</institution><country>Турция</country></aff><aff xml:lang="en"><institution>Istanbul Technical University</institution><country>Turkey</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>2</issue><fpage>86</fpage><lpage>105</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Эркек Т.Ю., Гаджиев Ч., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Эркек Т.Ю., Гаджиев Ч.</copyright-holder><copyright-holder xml:lang="en">Erkec T.Y., Hajiyev 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/98">https://www.gyroscopy.ru/jour/article/view/98</self-uri><abstract><p>В последнее время, чтобы снизить стоимость миссии, упростить требования к выполнению полета и устранить ограничения, связанные с применением одного космического аппарата, часто прибегают к групповым полетам спутников. В статье рассматривается навигация группы из двух спутников, в основу которой положен псевдодальномерный метод (модель определения дальности по данным GPS). Предлагаемый подход к построению схем относительной навигации космических аппаратов базируется на методе Ньютона–Рафсона (Newton–Raphson Method – NRM, МНР) с использованием данных глобальной системы позиционирования (GPS). Оценивание относительных положений спутника-цели и следящего спутника на основе МНР производится с помощью адаптивного обобщенного фильтра Калмана (АОФК) путем масштабирования ковариации шума измерений. Относительное положение и скорость спутников рассчитываются по уравнениям Хилла–Клохесси–Уилтшира (Hill–Clohessy–Wiltshire). В рамках расширенных исследований по обобщенному фильтру Калмана задача этой работы – повысить точность оценивания относительного движения спутников с помощью адаптивного фильтра с учетом погрешностей измерений или модели динамики.</p></abstract><trans-abstract xml:lang="en"><p>Using a satellite cluster design to reduce mission costs, mission request complexity, and single satellite utilization limits has grown in popularity in recent years. This paper presents two-satellite formation designs based on the pseudo-ranging model (GPS-based distance model). The Newton-Raphson Method (NRM) and the Global Positioning System (GPS) are used to create a novel approach to satellite relative navigation architecture. The Adaptive Extended Kalman filter (AEKF) with measurement noise covariance scaling is used to estimate the relative locations of the target and tracker satellites using the NRM technique. The relative location and velocity of the satellites are computed using the Hill-Clohessy-Wiltshire (HCW) equations. Within the scope of the advancement of studies with EKF in the literature, the focus of this research is to improve relative estimations with the adaptive filter by accounting for measurement or dynamic model problems.</p></trans-abstract><kwd-group xml:lang="en"><kwd>formation flight</kwd><kwd>satellite</kwd><kwd>relative navigation</kwd><kwd>Adaptive Extended Kalman Filter</kwd><kwd>GPS pseudo-ranging model</kwd><kwd>Newton-Raphson method</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">Alonso, R., Crassidis, J.L., Junkins, J.L., Vision-based relative navigation for formation flying of spacecraft, AIAA-2000-4439:2000, 2010, https://doi.org/10.2514/6.2000-4439.</mixed-citation><mixed-citation xml:lang="en">Alonso, R., Crassidis, J.L., Junkins, J.L., Vision-based relative navigation for formation flying of spacecraft, AIAA-2000-4439:2000, 2010, 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