<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Cosmic Research</journal-id><journal-title-group><journal-title xml:lang="en">Cosmic Research</journal-title><trans-title-group xml:lang="ru"><trans-title>Космические исследования</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0023-4206</issn><issn publication-format="electronic">3034-5502</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">692314</article-id><article-id pub-id-type="doi">10.31857/S0023420625040066</article-id><article-id pub-id-type="edn">qnmace</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Parametric analysis and estimation of the worst attitude accuracy of a satellite</article-title><trans-title-group xml:lang="ru"><trans-title>Параметрический анализ и оценка наихудшей точности ориентации космического аппарата</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Drobysheva</surname><given-names>A. S.</given-names></name><name xml:lang="ru"><surname>Дробышева</surname><given-names>А. С.</given-names></name></name-alternatives><email>stevens_L@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Tkachev</surname><given-names>S. S.</given-names></name><name xml:lang="ru"><surname>Ткачев</surname><given-names>С. С.</given-names></name></name-alternatives><email>stevens_L@mail.ru</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Space Research Institute of the Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Институт космических исследований РАН</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Keldysh Institute of Applied Mathematics</institution></aff><aff><institution xml:lang="ru">Институт прикладной математики им. М.В. Келдыша РАН</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-08-15" publication-format="electronic"><day>15</day><month>08</month><year>2025</year></pub-date><volume>63</volume><issue>4</issue><issue-title xml:lang="en">VOL 63, NO4 (2025)</issue-title><issue-title xml:lang="ru">ТОМ 63, №4 (2025)</issue-title><fpage>407</fpage><lpage>422</lpage><history><date date-type="received" iso-8601-date="2025-10-07"><day>07</day><month>10</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Российская академия наук</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0023-4206/article/view/692314">https://journals.eco-vector.com/0023-4206/article/view/692314</self-uri><abstract xml:lang="en"><p>The paper considers the angular motion of a spacecraft under the influence of various disturbing torques. A method for studying the space of disturbing parameters is proposed to estimate the probability of attitude accuracy falling within a certain interval, as well as to identify the worst accuracy and the corresponding disturbing parameters. To analyze the structure of the entire set of disturbing parameters, a method for obtaining a statistical ensemble and further interpretation of the data is used. The worst value of the attitude accuracy is sought using the particle swarm optimization method, which takes into account the restrictions on the disturbing parameters. A numerical example of analyzing the attitude accuracy in the orbital stabilization mode by both methods is given.</p></abstract><trans-abstract xml:lang="ru"><p>В работе рассматривается угловое движение космического аппарата под воздействием различных возмущающих факторов. Предлагается методика исследования пространства возмущающих параметров для оценки вероятности попадания точности ориентации в некоторый интервал, а также выявления наихудшей точности и соответствующих ей возмущающих параметров. Для анализа структуры всего множества возмущающих параметров используется способ получения статистического ансамбля и дальнейшей интерпретации данных. Наихудшее значение точности ориентации ищется с помощью метода роя частиц, в котором учитываются ограничения на возмущающие параметры. Приведен численный пример анализа точности ориентации в режиме орбитальной стабилизации обоими способами.</p></trans-abstract><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке гранта РНФ № 23-72-30002, https://rscf.ru/en/project/23-72-30002/</funding-statement></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Brasoveanu D., Hashmall J. Spacecraft Attitude Determination Accuracy From Mission Experience // Flight Mech. Theory, NASA, 1994. P. 153–168. https://www.tib.eu/de/suchen/id/BLCP %3ACN003744905</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Игнатов А.И., Иванов Г.А., Коломиец Е.С. и др.Реализация режима солнечной ориентации космического аппарата с помощью системы двигателей-маховиков // Косм. исслед. 2023. Т. 61. С. 143–156. https://journals.rcsi.science/0023-4206/article/view/137338</mixed-citation></ref><ref id="B3"><label>3.</label><mixed-citation>Boussadia H., Mohammed M., Abdelkrim M. et al.Estimation of satellite attitude dynamics and external torques via mixed Kalman/H-infinity filter under inertia uncertainties // Aerosp. Syst. 2023. V. 6. P. 633–640. https://doi.org/10.1007/s42401-023-00235-4</mixed-citation></ref><ref id="B4"><label>4.</label><mixed-citation>Kim J., Bang H.Observer-Based Disturbance Estimation for a Spacecraft Inertial Pointing Using Magnetic Torquers // Trans. JAPAN Soc. Aeronaut. Sp. Sci. Aerosp. Technol. JAPAN. 2019. V. 17. https://doi.org/10.2322/tastj.17.447</mixed-citation></ref><ref id="B5"><label>5.</label><mixed-citation>Ivanov D., Roldugin D. Nanosatellite Three-Axis Attitude Control and Determination Using Two Magnetorquers Only // Proc. 9th International Conference on Recent Advances in Space Technologies. Istanbul, Turkey. 2019. P. 761–768. https://doi.org/10.1109/RAST.2019.8767828</mixed-citation></ref><ref id="B6"><label>6.</label><mixed-citation>Ivanov D., Roldugin D., Ovchinnikov M. Three-Axis Attitude Determination Using Magnetorquers // J. Guid. Control Dyn. 2018. V. 41. P. 1–24. https://doi.org/10.2514/1.G003698</mixed-citation></ref><ref id="B7"><label>7.</label><mixed-citation>Ivanov D.S., Ovchinnikov M.Y., Penkov V.I. et al. Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties // Acta Astronaut. 2017. V. 132. P. 103–110. https://doi.org/10.1016/j.actaastro.2016.11.045</mixed-citation></ref><ref id="B8"><label>8.</label><mixed-citation>Ulrich S., Côté J., de Lafontaine J.In-Flight Attitude Perturbation Estimation for Earth-Orbiting Spacecraft // J. Astronaut. Sci. 2009. V. 57. https://doi.org/10.1007/BF03321520</mixed-citation></ref><ref id="B9"><label>9.</label><mixed-citation>Khurshid O., Selkäinaho J., Soken H. et al.Small satellite attitude determination during plasma brake deorbiting experiment // Acta Astronaut. 2016. V. 129. https://doi.org/10.1016/j.actaastro.2016.08.035</mixed-citation></ref><ref id="B10"><label>10.</label><mixed-citation>Wertz J.Spacecraft Attitude Determination And Control. Springer, 1978. https://doi.org/10.1007/978-94-009-9907-7</mixed-citation></ref><ref id="B11"><label>11.</label><mixed-citation>ECSS-E-ST-60-10C, Space engineering — Control performance, ECSS Secretariat ESA-ESTEC Requirements &amp; Standards Division, Noordwijk, The Netherlands, 2008.</mixed-citation></ref><ref id="B12"><label>12.</label><mixed-citation>ECSS-E-HB-60-10A, Space engineering — Control performance guidelines, ECSS Secretariat ESA-ESTEC Requirements &amp; Standards Division, Noordwijk, The Netherlands, 2010.</mixed-citation></ref><ref id="B13"><label>13.</label><mixed-citation>Kennedy J., Eberhart R.Particle swarm optimization // Proc. ICNN’95-International Conf. Neural Networks. Perth, WA, Australia. 1995. P. 1942–1948.</mixed-citation></ref><ref id="B14"><label>14.</label><mixed-citation>Guerman A.D., Ivanov D.S., Roldugin D.S. et al.Orbital and Angular Dynamics Analysis of the Small Satellite SAR Mission INFANTE // Cosmic Research. 2020. V. 58. P. 206–217. https://doi.org/10.1134/S0010952520030016</mixed-citation></ref><ref id="B15"><label>15.</label><mixed-citation>Зубов В.И.Лекции по теории управления. М.: Главная редакция физико-математической литературы изд-ва “Наука”, 1975.</mixed-citation></ref><ref id="B16"><label>16.</label><mixed-citation>Tsiotras P.New Control Laws for the Attitude Stabilization of Rigid Bodies // IFAC Proc. 1994. V. 27. P. 321–326. https://doi.org/10.1016/S1474-6670(17)45820-4</mixed-citation></ref><ref id="B17"><label>17.</label><mixed-citation>Овчинников М.Ю., Ткачев С.С., Карпенко С.О.Исследование углового движения микроспутника Чибис-М с трехосным маховичным управлением // Косм. исслед. 2012. Т. 50. С. 462–471.</mixed-citation></ref><ref id="B18"><label>18.</label><mixed-citation>Барбашин Е.А. Введение в теорию устойчивости. М.: Наука, 1967.</mixed-citation></ref><ref id="B19"><label>19.</label><mixed-citation>Annenkova A., Abdelrahman N., Ivanov D. et al. CubeSat Magnetic Atlas and in-Orbit Compensation of Residual Magnetic Dipole // Proc. 71th International Astronautical Congress. The CyberSpace Edition. 12–14 October 2020.</mixed-citation></ref><ref id="B20"><label>20.</label><mixed-citation>Ovchinnikov M., Ivanov D.Approach to study satellite attitude determination algorithms // Acta Astronaut. 2014. V. 98. P. 133–137. https://doi.org/10.1016/j.actaastro.2014.01.024</mixed-citation></ref><ref id="B21"><label>21.</label><mixed-citation>Ivanov D., Ovchinnikov M., Ivlev N. et al.Analytical study of microsatellite attitude determination algorithms // Acta Astronaut. 2015. V. 116 P. 339–348. https://doi.org/10.1016/j.actaastro.2015.07.001</mixed-citation></ref><ref id="B22"><label>22.</label><mixed-citation>Chasset C., Noteborn R., Bodin P. et al.3-Axis magnetic control: flight results of the TANGO satellite in the PRISMA mission // CEAS Sp. J. 2013. V. 5. P. 1–17. https://doi.org/10.1007/s12567-013-0034-9</mixed-citation></ref><ref id="B23"><label>23.</label><mixed-citation>Bodin P., Larsson R., Nilsson F. et al.PRISMA: An In-Orbit Test Bed for Guidance, Navigation, and Control Experiments // J. Spacecr. Rockets. 2009. V. 46. P. 615–623. https://doi.org/10.2514/1.40161</mixed-citation></ref><ref id="B24"><label>24.</label><mixed-citation>Ovchinnikov M.Y., Roldugin D.S., Penkov V.I. et al. Fully magnetic sliding mode control for acquiring three-axis attitude // Acta Astronaut. 2016. V. 121. P. 59–62. https://doi.org/10.1016/j.actaastro.2015.12.031</mixed-citation></ref><ref id="B25"><label>25.</label><mixed-citation>Tkachev S., Mashtakov Y., Ivanov D. et al.Effect of Reaction Wheel Imbalances on Attitude and Stabilization Accuracy // Aerosp. 2021. V. 8. https://doi.org/10.3390/aerospace8090252</mixed-citation></ref><ref id="B26"><label>26.</label><mixed-citation>Alcorn J., Allard C., Schaub H.Fully Coupled Reaction Wheel Static and Dynamic Imbalance for Spacecraft Jitter Modeling // J. Guid. Control. Dyn. 2018. V. 41. P. 1380–1388. https://doi.org/10.2514/1.G003277</mixed-citation></ref><ref id="B27"><label>27.</label><mixed-citation>Hoeffding W.Probability Inequalities for Sums of Bounded Random Variables // J. Am. Stat. Assoc. 1963. V. 58. P. 13–30. https://doi.org/10.1080/01621459.1963.10500830</mixed-citation></ref><ref id="B28"><label>28.</label><mixed-citation>Dvoretzky A., Kiefer J., Wolfowitz J.Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator // Ann. Math. Stat. 1956. V. 27. P. 642–669. https://doi.org/10.1214/aoms/1177728174</mixed-citation></ref><ref id="B29"><label>29.</label><mixed-citation>Kuzin S., Bogachev S., Pertsov A. et al. EUV telescope for a Cubesat nanosatellite // Appl. Opt. 2023. 62. P. 8462–8471. https://doi.org/10.1364/AO.501437</mixed-citation></ref><ref id="B30"><label>30.</label><mixed-citation>Kennedy R., Eberhart J.Particle swarm optimization // Proc. Int. Conf. Neural Networks. IEEE. Perth, Australia. 1995. V. 4. P. 1942–1948.</mixed-citation></ref><ref id="B31"><label>31.</label><mixed-citation>Trelea I.C.The particle swarm optimization algorithm: convergence analysis and parameter selection // Inf. Process. Lett. 2003. V. 85. P. 317–325. https://doi.org/10.1016/S0020-0190(02)00447-7</mixed-citation></ref><ref id="B32"><label>32.</label><mixed-citation>Vanderbergh F., Engelbrecht A.A study of particle swarm optimization particle trajectories // Inf. Sci. 2006. V. 176. P. 937–971.</mixed-citation></ref><ref id="B33"><label>33.</label><mixed-citation>Okhitina A., Roldugin D., Tkachev S.Application of the PSO for the construction of a 3-axis stable magnetically actuated satellite angular motion // Acta Astronaut. 2022. V. 195. P. 86–97. https://doi.org/10.1016/J.ACTAASTRO.2022.03.001</mixed-citation></ref><ref id="B34"><label>34.</label><mixed-citation>Okhitina A., Roldugin D., Tkachev S.Magnetically controllable attitude trajectory constructed using the particle swarm optimization method // 72nd Int. Astronaut. Congr.Dubai,UAE.2021.</mixed-citation></ref><ref id="B35"><label>35.</label><mixed-citation>Okhitina A., Tkachev S., Roldugin D.Comparative cost functions analysis in the construction of a reference angular motion implemented by magnetorquers // Aerospace. 2023. V. 10. Art.ID. 468.</mixed-citation></ref><ref id="B36"><label>36.</label><mixed-citation>Белецкий В.В., Яншин А.М.Влияние аэродинамических сил на вращательное движение искусственных спутников. Киев: Наук. думк, 1984.</mixed-citation></ref><ref id="B37"><label>37.</label><mixed-citation>Dutoit S.H.C.Graphical Exploratory Data Analysis. Springer, 2012.</mixed-citation></ref></ref-list></back></article>
