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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">10.17285/0869-7035.0082</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-121</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>Новое решение задачи фильтрации для внутритрубной навигации при применении в снаряде микромеханического инерциального модуля</article-title><trans-title-group xml:lang="en"><trans-title>A Novel Constrained Filter Integrated with an Extended Kalman Filter in Underground Pipeline Navigation Using MEMS IMU</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0950-7038</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Афшар</surname><given-names>И. Х.</given-names></name><name name-style="western" xml:lang="en"><surname>Afshar</surname><given-names>I. H.</given-names></name></name-alternatives><bio xml:lang="ru"><sec><title>Афшар Исмаил Хатефи. Аспирант</title></sec></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9654-6491</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Делавар</surname><given-names>М. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Delavar</surname><given-names>M. R.</given-names></name></name-alternatives><bio xml:lang="ru"><sec><title>Делавар Махмуд Реза. Доктор наук, профессор</title></sec></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8390-4093</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мошири</surname><given-names>Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Moshiri</surname><given-names>B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мошири Бехзад. Доктор наук, профессор</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Технический колледж, Тегеранский университет</institution><country>Иран</country></aff><aff xml:lang="en"><institution>College of Engineering, University of Tehran</institution><country>Islamic Republic of Iran</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>20</day><month>05</month><year>2025</year></pub-date><volume>30</volume><issue>1</issue><fpage>12</fpage><lpage>38</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Афшар И.Х., Делавар М.Р., Мошири Б., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Афшар И.Х., Делавар М.Р., Мошири Б.</copyright-holder><copyright-holder xml:lang="en">Afshar I.H., Delavar M.R., Moshiri B.</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/121">https://www.gyroscopy.ru/jour/article/view/121</self-uri><abstract><p>В статье исследуется задача позиционирования первого в Тегеране магистрального газопровода (Тегеран–Кухнамак) с использованием бесплатформенной инерциальной навигационной системы (БИНС) на базе инерциального измерительного модуля (ИИМ) с микромеханическими чувствительными элементами (МЭМС), установленного на внутритрубном инспекционном (диагностическом) снаряде (далее – снаряд). Снаряд позволяет выработать координаты трубопровода протяженностью 111 км с дискретностью 4 мм. За основу решения навигационной задачи принят обобщенный фильтр Калмана (ОФК) с применением вариации Аллана для анализа и уточнения исходных данных. Одновременно используется специальный фильтр, данные которого комплексируются с данными ОФК, что обеспечивает коррекцию углов рыскания и тангажа, вырабатываемых снарядом. Для повышения надежности решения задачи вдоль трубопровода размещены 98 магнитных маркеров, координированные по данным GPS, а также в качестве измерений в ОФК привлекаются данные одометра. Полученные результаты свидетельствуют о том, что такой гибридный подход позволяет повысить точность позиционирования трубопровода примерно на 81% по сравнению с базовым алгоритмом ОФК. Кроме того, предложенный алгоритм позволяет повысить точность позиционирования на 32% и быстродействие на 55% по сравнению с разработанным в настоящее время другим интегрированным решением ОФК/РСТ, в котором также регистрируются соединения труб (РСТ).</p></abstract><trans-abstract xml:lang="en"><p>To produce a 3D map of the Tehran’s first gas transfer pipeline (Tehran—Kuhnamak), a methodology has been developed in this research, in which a strapdown inertial navigation system (SINS) based on micro-electro-mechanical system (MEMS) and inertial measurement unit (IMU) is applied on pipeline inspection gauges (PIGs) to sense data every 4 millimeters of 111 kilometers of the whole pipeline. The navigation solution is based on an extended Kalman filter (EKF) using Allan variance (AVAR) to analyze and tune the EKF initial inputs. A new constrained PIG filter (CPF) is proposed in this paper in integration with EKF, in which two Euler angles (pitch and yaw) of the PIG are updated due to non-holonomic state constraints between pipe junctions. Besides, 98 magnetic control points have been used to increase robustness about every kilometer, which is coordinated by GPS. Furthermore, odometer measurements have been employed as measurements in the EKF. The results show that using such a hybrid approach has improved the PIG positioning accuracy by about 81% compared with that of the Basic EKF. In addition, positioning accuracy in comparison with the latest methods like EKF/pipeline junctions (PLJ) has increased by 32%. Furthermore, the proposed method is 55% better than EKF/ PLJ in the algorithm runtime. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>ОФК</kwd><kwd>одометр</kwd><kwd>неголономные ограничения</kwd><kwd>ИИМ с микромеханическими чувствительными элементами</kwd><kwd>БИНС</kwd></kwd-group><kwd-group xml:lang="en"><kwd>EKF</kwd><kwd>odometer</kwd><kwd>navigation constraint</kwd><kwd>MEMS IMU</kwd><kwd>CPF</kwd><kwd>PLJ</kwd><kwd>SINS</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Данные для проведения этого исследования были предоставлены первым иранским предприятием по производству внутритрубных снарядов Segal Processing Engineering Company. Оператором и собственником магистрального трубопро- вода, на котором проводились исследования, является Иранская газотранспортная компания (Iranian Gas Transmission Company, IGTC)</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">Guan, L., Cong, X., Sun, Y., Gao, Y., Iqbal, U., and Noureldin, A., Enhanced MEMS SINS aided pipeline surveying system by pipeline junction detection in small diameter pipeline, IFAC-PapersOnLine, 2017, vol. 50, no. 1, pp. 3560–3565.</mixed-citation><mixed-citation xml:lang="en">Guan, L., Cong, X., Sun, Y., Gao, Y., Iqbal, U., and Noureldin, A., Enhanced MEMS SINS aided pipeline surveying system by pipeline junction detection in small diameter pipeline, IFAC-PapersOnLine, 2017, vol. 50, no. 1, pp. 3560–3565.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Murray, I. and Dawson, J., Evaluating pipeline integrity using ILI mapping data, Proc. 9th Pipeline Technology Conference 2014, Berlin, Germany, 2014.</mixed-citation><mixed-citation xml:lang="en">Murray, I. and Dawson, J., Evaluating pipeline integrity using ILI mapping data, Proc. 9th Pipeline Technology Conference 2014, Berlin, Germany, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Guan, l., Gao, Y., Osman, A., Iqbal, U. and Noureldin, A., Analysis of rolling motion effect on SINS error modeling in PIG, Proc. 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), 2016, pp. 681–686.</mixed-citation><mixed-citation xml:lang="en">Guan, l., Gao, Y., Osman, A., Iqbal, U. and Noureldin, A., Analysis of rolling motion effect on SINS error modeling in PIG, Proc. 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), 2016, pp. 681–686.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Li, R., Cai, M., Shi, Y., Feng, Q. and Chen, P., Technologies and application of pipeline centerline and bending strain of In-line inspection based on inertial navigation, Transactions of the Institute of Measurement and Control, 2018, vol. 40, pp. 1554–1567.</mixed-citation><mixed-citation xml:lang="en">Li, R., Cai, M., Shi, Y., Feng, Q. and Chen, P., Technologies and application of pipeline centerline and bending strain of In-line inspection based on inertial navigation, Transactions of the Institute of Measurement and Control, 2018, vol. 40, pp. 1554–1567.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Santana, D.D.S., Maruyama, N. and Furukawa, C.M., Estimation of trajectories of pipeline PIGs using inertial measurements and non linear sensor fusion, Proc. 9th IEEE/IAS International Conference on Industry Applications – INDUSCON, 2010, pp. 1–6.</mixed-citation><mixed-citation xml:lang="en">Santana, D.D.S., Maruyama, N. and Furukawa, C.M., Estimation of trajectories of pipeline PIGs using inertial measurements and non linear sensor fusion, Proc. 9th IEEE/IAS International Conference on Industry Applications – INDUSCON, 2010, pp. 1–6.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Arribas, J., Moragrega, A., Fernández-Prades, C. and Closas, P., Low-cost GNSS/INS/Odometric sensor fusion platform for ground intelligent transportation systems, Proc. 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, 2017, pp. 436–455.</mixed-citation><mixed-citation xml:lang="en">Arribas, J., Moragrega, A., Fernández-Prades, C. and Closas, P., Low-cost GNSS/INS/Odometric sensor fusion platform for ground intelligent transportation systems, Proc. 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, 2017, pp. 436–455.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Jin, S. and Ping, Y., Research on the describing of trajectory for subsea pipeline based on inertial navigation system, Proc. IEEE Power Engineering and Automation Conference, 2011, pp. 463–468.</mixed-citation><mixed-citation xml:lang="en">Jin, S. and Ping, Y., Research on the describing of trajectory for subsea pipeline based on inertial navigation system, Proc. IEEE Power Engineering and Automation Conference, 2011, pp. 463–468.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Yadav, S.M., Shastri, S.K., Chakravarthi, G.B., Kumar, V., Rao, A.D. and Agrawal, V.K., A fast, parallel algorithm for fully overlapped Allan variance and total variance for analysis and modeling of noise in inertial sensors, IEEE Sensors Letters, 2018, vol. 2, pp. 1–4.</mixed-citation><mixed-citation xml:lang="en">Yadav, S.M., Shastri, S.K., Chakravarthi, G.B., Kumar, V., Rao, A.D. and Agrawal, V.K., A fast, parallel algorithm for fully overlapped Allan variance and total variance for analysis and modeling of noise in inertial sensors, IEEE Sensors Letters, 2018, vol. 2, pp. 1–4.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">El-Sheimy, N., Hou, H. and Niu, X., Analysis and modeling of inertial sensors using Allan variance, IEEE Transactions on Instrumentation and Measurement, 2007, vol. 57, pp. 140–149.</mixed-citation><mixed-citation xml:lang="en">El-Sheimy, N., Hou, H. and Niu, X., Analysis and modeling of inertial sensors using Allan variance, IEEE Transactions on Instrumentation and Measurement, 2007, vol. 57, pp. 140–149.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ghafil, H.N. and Jármai, K., Spatial representations, Optimization for Robot Modelling with MATLAB, Springer, 2020, pp. 55–68.</mixed-citation><mixed-citation xml:lang="en">Ghafil, H.N. and Jármai, K., Spatial representations, Optimization for Robot Modelling with MATLAB, Springer, 2020, pp. 55–68.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Hou, H., Modeling inertial sensors errors using Allan variance, Master of Science Thesis, University of Calgary, Department of Geomatics Engineering, Calgary, 2004.</mixed-citation><mixed-citation xml:lang="en">Hou, H., Modeling inertial sensors errors using Allan variance, Master of Science Thesis, University of Calgary, Department of Geomatics Engineering, Calgary, 2004.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Barreda Pupo, L., Characterization of errors and noises in MEMS inertial sensors using Allan variance method, Master of Science Thesis, Universitat Politècnica de Catalunya, Barcelona, 2016.</mixed-citation><mixed-citation xml:lang="en">Barreda Pupo, L., Characterization of errors and noises in MEMS inertial sensors using Allan variance method, Master of Science Thesis, Universitat Politècnica de Catalunya, Barcelona, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Sahli, H., MEMS-based aided inertial navigation system for small diameter pipelines, PhD Thesis, University of Calgary, 2016.</mixed-citation><mixed-citation xml:lang="en">Sahli, H., MEMS-based aided inertial navigation system for small diameter pipelines, PhD Thesis, University of Calgary, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Sahli, H. and El-Sheimy, N., A novel method to enhance pipeline trajectory reconstruction using pipeline junctions, Sensors, 2016, vol. 16, no. 4, pp. 567.</mixed-citation><mixed-citation xml:lang="en">Sahli, H. and El-Sheimy, N., A novel method to enhance pipeline trajectory reconstruction using pipeline junctions, Sensors, 2016, vol. 16, no. 4, pp. 567.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">El-Sheimy, N., Sahli, H. and Moussa, A., Methods and systems to enhance pipeline trajectory reconstruction using pipeline junctions, Patent of the US, no. US 2017/0138524 A1, 2017.</mixed-citation><mixed-citation xml:lang="en">El-Sheimy, N., Sahli, H. and Moussa, A., Methods and systems to enhance pipeline trajectory reconstruction using pipeline junctions, Patent of the US, no. US 2017/0138524 A1, 2017.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Guan, L., Xu, X., Gao, Y., Liu, F., Rong, H., Wang, M. et al., Micro-Inertial-Aided High-Precision Positioning Method for Small-Diameter PIG Navigation, IntechOpen, 2018.</mixed-citation><mixed-citation xml:lang="en">Guan, L., Xu, X., Gao, Y., Liu, F., Rong, H., Wang, M. et al., Micro-Inertial-Aided High-Precision Positioning Method for Small-Diameter PIG Navigation, IntechOpen, 2018.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, M., Li, K., Hu, B. and Meng, C., Comparison of Kalman filters for inertial integrated navigation, Sensors, 2019, vol. 19, no. 6, p. 1426.</mixed-citation><mixed-citation xml:lang="en">Zhang, M., Li, K., Hu, B. and Meng, C., Comparison of Kalman filters for inertial integrated navigation, Sensors, 2019, vol. 19, no. 6, p. 1426.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Ji, M., Liu, J., Xu, X., Guo, Y. and Lu, Z., Improved pedestrian positioning with inertial sensor based on adaptive gradient descent and double-constrained extended Kalman filter, Complexity, 2020, vol. 2020, ID 4361812.</mixed-citation><mixed-citation xml:lang="en">Ji, M., Liu, J., Xu, X., Guo, Y. and Lu, Z., Improved pedestrian positioning with inertial sensor based on adaptive gradient descent and double-constrained extended Kalman filter, Complexity, 2020, vol. 2020, ID 4361812.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">IEEE Standard 952-1997: Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros, IEEE Standards Board, 1998.</mixed-citation><mixed-citation xml:lang="en">IEEE Standard 952-1997: Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros, IEEE Standards Board, 1998.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Gonzalez, R., Giribet, J. and Patino, H., An approach to benchmarking of loosely coupled low-cost navigation systems, Mathematical and Computer Modelling of Dynamical Systems, 2015, vol. 21, no. 3, pp. 272–287.</mixed-citation><mixed-citation xml:lang="en">Gonzalez, R., Giribet, J. and Patino, H., An approach to benchmarking of loosely coupled low-cost navigation systems, Mathematical and Computer Modelling of Dynamical Systems, 2015, vol. 21, no. 3, pp. 272–287.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Noureldin, A., Karamat, T.B. and Georgy, J., Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer Science &amp; Business Media, 2012.</mixed-citation><mixed-citation xml:lang="en">Noureldin, A., Karamat, T.B. and Georgy, J., Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer Science &amp; Business Media, 2012.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Titterton, D.H. and Weston, J.L., Strapdown Inertial Navigation Technology, 2nd Edition, Stevenage: Institution of Electrical Engineers, The American Institute of Aeronautics and Astronautics, 2004.</mixed-citation><mixed-citation xml:lang="en">Titterton, D.H. and Weston, J.L., Strapdown Inertial Navigation Technology, 2nd Edition, Stevenage: Institution of Electrical Engineers, The American Institute of Aeronautics and Astronautics, 2004.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House, 2013.</mixed-citation><mixed-citation xml:lang="en">Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House, 2013.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Vavilova, N., Golovan, A., Kozlov, A., Nikitin, I., Panyov and A., Parusnikov, N., A navigation system of a pipeline inspection system for oil and gas pipelines: the results of the development and testing, Proc. 22nd St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg: Concern CSRI Elektropribor, 2015.</mixed-citation><mixed-citation xml:lang="en">Vavilova, N., Golovan, A., Kozlov, A., Nikitin, I., Panyov and A., Parusnikov, N., A navigation system of a pipeline inspection system for oil and gas pipelines: the results of the development and testing, Proc. 22nd St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg: Concern CSRI Elektropribor, 2015.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">www.segaltech.com.</mixed-citation><mixed-citation xml:lang="en">www.segaltech.com.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">www.nigtc.ir.</mixed-citation><mixed-citation xml:lang="en">www.nigtc.ir.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
