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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 pub-id-type="doi">10.17285/0869-7035.2017.25.4.035-059</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-328</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>Модели стохастических погрешностей инерциальных датчиков смартфонов, учитывающие динамику движения</article-title><trans-title-group xml:lang="en"><trans-title>Stochastic Error Modeling of Smartphone Inertial Sensors for Navigation in Varying Dynamic Conditions</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>Ради</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Radi</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ради Ахмед. Аспирант</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>Нассар</surname><given-names>С.</given-names></name><name name-style="western" xml:lang="en"><surname>Nassar</surname><given-names>S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Нассар Самех. Научный сотрудник </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>Эль-Шейми</surname><given-names>Н.</given-names></name><name name-style="western" xml:lang="en"><surname>El-Sheimy</surname><given-names>N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Эль-Шейми Насер. 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>Университет Калгари, факультет инженерной геоматики</institution><country>Канада</country></aff><aff xml:lang="en"><institution>Department of Geomatics Engineering, University of Calgary</institution><country>Canada</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>26</day><month>11</month><year>2025</year></pub-date><volume>25</volume><issue>4</issue><fpage>35</fpage><lpage>59</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ради А., Нассар С., Эль-Шейми Н., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ради А., Нассар С., Эль-Шейми Н.</copyright-holder><copyright-holder xml:lang="en">Radi A., Nassar S., El-Sheimy N.</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/328">https://www.gyroscopy.ru/jour/article/view/328</self-uri><abstract><p>Проведено исследование стохастических погрешностей инерциальных датчиков на основе технологии микроэлектромеханических систем (МЭМС) в статических и динамических условиях. В качестве образцов использовались датчики инерциальных измерительных модулей (ИИМ) двух моделей смартфонов. Оценка характеристик стохастических погрешностей производилась двумя методами: методом вариации Аллана (ВА) и обобщенным методом моментов вейвлетов (ОММВ). Параметры модели, определенные в динамических условиях в лаборатории, сопоставляются с параметрами, полученными на неподвижном основании. В используемых для идентификации моделей реализациях исключены аномальные данные на основе доверительного интервала (ДИ). Предложен новый алгоритм инерциально-спутниковой навигационной системы ИНС/GPS, адаптивный к динамике движения. Представлен анализ эффективности использования различных стохастических моделей на основе ВА и ОММВ с применением смоделированных данных инерциально-спутниковой навигационной системы при пропадании сигналов GPS. Анализ выполнен с помощью предложенного алгоритма. Точность определения местоположения, полученная с помощью адаптивного алгоритма комплексирования ИНС/GPS, превосходит точность, достигнутую при использовании стандартного алгоритма комплексирования ИНС/GPS на основе статической модели погрешностей. Кроме того, модели стохастической погрешности, полученные на основе ОММВ, показывают лучшие результаты, чем модели на основе ВА.</p></abstract><trans-abstract xml:lang="en"><p>This paper aims at investigating and analyzing the behavior of Micro Electromechanical Systems (MEMS) inertial sensors stochastic errors in both static and varying dynamic conditions using two MEMS-based Inertial Measurement Units (IMUs) of two different smartphones. The corresponding stochastic error processes were estimated using two different methods, the Allan Variance (AV) and the Generalized Method of Wavelets Moments (GMWM). The developed model parameters related to laboratory dynamic environment are compared to those obtained under static conditions. A contamination test was applied to all data sets to distinguish between clean and corrupted ones using a Confidence Interval (CI) investigation approach. A detailed analysis is presented to define the link between the error model parameters and the augmented dynamics of the tested smartphone platform. The paper proposes a new dynamically dependent integrated navigation algorithm which is capable of switching between different stochastic error parameters values according to the platform dynamics to eliminate dynamics-dependent effects. Finally, the performance of different stochastic models based on AV and GMWM were analyzed using simulated Inertial Navigation System (INS)/ Global Positioning System (GPS) data with induced GPS signal outages through the new proposed dynamically dependent algorithm.</p><p>The results showed that the obtained position accuracy is improved when using dynamic-dependent stochastic error models, through the adaptive integrated algorithm, instead of the commonly used static one, through the non-adaptive integrated one. The results also show that the stochastic error models from GMWM-based model structure offer better performance than those estimated from the AV-based model.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Стохастическая погрешность</kwd><kwd>калибровка инерциальных датчиков</kwd><kwd>инерциальный измерительный модуль</kwd><kwd>вариация Аллана</kwd><kwd>обобщенный метод моментов вейвлетов</kwd><kwd>комплексирование ИНС/GPS.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Stochastic error modeling</kwd><kwd>inertial sensors calibration</kwd><kwd>IMUs</kwd><kwd>Allan variance (AV)</kwd><kwd>generalized method of wavelet moments (GMWM)</kwd><kwd>dynamically dependent adaptive INS/GPS algorithm.</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">Jensen, A.B., GNSS satellite orbits, Technical University of Denmark, 2010.</mixed-citation><mixed-citation xml:lang="en">Jensen, A.B., GNSS satellite orbits, Technical University of Denmark, 2010.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">El-Sheimy, N., Lecture note 623 – Inertial techniques and INS/DGPS integration, Department of Geomatics Engineering, University of Calgary, 2014.</mixed-citation><mixed-citation xml:lang="en">El-Sheimy, N., Lecture note 623 – Inertial techniques and INS/DGPS integration, Department of Geomatics Engineering, University of Calgary, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Nassar, S., Syed, Z., Niu, X., and El-Sheimy, N., Improving MEMS IMU/GPS systems for accurate land-based navigation applications, ION NTM, 2006, pp. 523–529.</mixed-citation><mixed-citation xml:lang="en">Nassar, S., Syed, Z., Niu, X., and El-Sheimy, N., Improving MEMS IMU/GPS systems for accurate land-based navigation applications, ION NTM, 2006, pp. 523–529.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Woodman, O.J., An introduction to inertial navigation, University of Cambridge, Computer Laboratory, Tech. Rep. UCAMCL-TR-696, 2007, vol. 14, p. 15.</mixed-citation><mixed-citation xml:lang="en">Woodman, O.J., An introduction to inertial navigation, University of Cambridge, Computer Laboratory, Tech. Rep. UCAMCL-TR-696, 2007, vol. 14, p. 15.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Niu, X., Nasser, S., Goodall, C., and El-Sheimy, N., A universal approach for processing any MEMS inertial sensor configuration for land-vehicle navigation, The Journal of Navigation, 2007, vol. 60, no. 2, pp. 233–245.</mixed-citation><mixed-citation xml:lang="en">Niu, X., Nasser, S., Goodall, C., and El-Sheimy, N., A universal approach for processing any MEMS inertial sensor configuration for land-vehicle navigation, The Journal of Navigation, 2007, vol. 60, no. 2, pp. 233–245.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Nassar, S., Improving the inertial navigation system (INS) error model for INS and INS/DGPS applications, National Library of Canada, 2005.</mixed-citation><mixed-citation xml:lang="en">Nassar, S., Improving the inertial navigation system (INS) error model for INS and INS/DGPS applications, National Library of Canada, 2005.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Li, Y., Georgy, J., Niu, X., Li, Q., and El-Sheimy, N., Autonomous calibration of MEMS gyros in consumer portable devices, IEEE Sensors Journal, 2015, vol. 15, no. 7, pp. 4062–4072.</mixed-citation><mixed-citation xml:lang="en">Li, Y., Georgy, J., Niu, X., Li, Q., and El-Sheimy, N., Autonomous calibration of MEMS gyros in consumer portable devices, IEEE Sensors Journal, 2015, vol. 15, no. 7, pp. 4062–4072.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Niu, X., Gao, Z., Zhang, R., Chen, Z., and Dong, J., Micro-machined attitude measurement unit with application in satellite TV antenna stabilization, Symposium Gyro Technology 2002, Stuttgart, Germany, 2002, p. 2002.</mixed-citation><mixed-citation xml:lang="en">Niu, X., Gao, Z., Zhang, R., Chen, Z., and Dong, J., Micro-machined attitude measurement unit with application in satellite TV antenna stabilization, Symposium Gyro Technology 2002, Stuttgart, Germany, 2002, p. 2002.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Li, Y., Lan, H., Zhuang, Y., Zhang, P., Niu, X., and El-Sheimy, N., Real-time attitude tracking of mobile devices, Indoor Positioning and Indoor Navigation (IPIN), 2015 International Conference on, 2015, pp. 1–7.</mixed-citation><mixed-citation xml:lang="en">Li, Y., Lan, H., Zhuang, Y., Zhang, P., Niu, X., and El-Sheimy, N., Real-time attitude tracking of mobile devices, Indoor Positioning and Indoor Navigation (IPIN), 2015 International Conference on, 2015, pp. 1–7.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</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, 2008, vol. 57, no. 1, 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, 2008, vol. 57, no. 1, pp. 140–149.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Evans, J.R. et al., Method for calculating self-noise spectra and operating ranges for seismographic inertial sensors and recorders, Seismological Research Letters, 2010, vol. 81, no. 4, pp. 640–646.</mixed-citation><mixed-citation xml:lang="en">Evans, J.R. et al., Method for calculating self-noise spectra and operating ranges for seismographic inertial sensors and recorders, Seismological Research Letters, 2010, vol. 81, no. 4, pp. 640–646.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Petkov, P., and Slavov, T., Stochastic modeling of MEMS inertial sensors, Cybernetics and Information Technologies, 2010, vol. 10, no. 2, pp. 31–40.</mixed-citation><mixed-citation xml:lang="en">Petkov, P., and Slavov, T., Stochastic modeling of MEMS inertial sensors, Cybernetics and Information Technologies, 2010, vol. 10, no. 2, pp. 31–40.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Magill, D., Optimal adaptive estimation of sampled stochastic processes, IEEE Transactions on Automatic Control, 1965, vol. 10, no. 4, pp. 434–439.</mixed-citation><mixed-citation xml:lang="en">Magill, D., Optimal adaptive estimation of sampled stochastic processes, IEEE Transactions on Automatic Control, 1965, vol. 10, no. 4, pp. 434–439.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Dmitriev, S., Koshaev, D., and Stepanov, O., Multichannel filtration and its application in removing ambiguity when positioning objects by using the GPS, Journal of Computer and Systems Sciences International, 1997, vol. 36, no. 1, pp. 57–62.</mixed-citation><mixed-citation xml:lang="en">Dmitriev, S., Koshaev, D., and Stepanov, O., Multichannel filtration and its application in removing ambiguity when positioning objects by using the GPS, Journal of Computer and Systems Sciences International, 1997, vol. 36, no. 1, pp. 57–62.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Li, X.R. and Jilkov, V.P., Survey of maneuvering target tracking. Part V. Multiple-model methods, IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, no. 4, pp. 1255–1321.</mixed-citation><mixed-citation xml:lang="en">Li, X.R. and Jilkov, V.P., Survey of maneuvering target tracking. Part V. Multiple-model methods, IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, no. 4, pp. 1255–1321.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Allan, D.W., Statistics of atomic frequency standards, Proceedings of the IEEE, vol. 54, no. 2, pp. 221–230, 1966.</mixed-citation><mixed-citation xml:lang="en">Allan, D.W., Statistics of atomic frequency standards, Proceedings of the IEEE, vol. 54, no. 2, pp. 221–230, 1966.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, X., Li, Y., Mumford, P., and Rizos, C., Allan variance analysis on error characters of MEMS inertial sensors for an FPGA-based GPS/INS system, Proceedings of the International Symposium on GPS/GNNS, 2008, pp. 127–133.</mixed-citation><mixed-citation xml:lang="en">Zhang, X., Li, Y., Mumford, P., and Rizos, C., Allan variance analysis on error characters of MEMS inertial sensors for an FPGA-based GPS/INS system, Proceedings of the International Symposium on GPS/GNNS, 2008, pp. 127–133.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Marinov, M. and Petrov, Z., Allan variance analysis on error characters of low-cost MEMS accelerometer MMA8451Q, International conference of scientific paper AFASES, 2014.</mixed-citation><mixed-citation xml:lang="en">Marinov, M. and Petrov, Z., Allan variance analysis on error characters of low-cost MEMS accelerometer MMA8451Q, International conference of scientific paper AFASES, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Li, J.and Fang, J., Not fully overlapping Allan variance and total variance for inertial sensor stochastic error analysis, IEEE Transactions on Instrumentation and Measurement, 2013, vol. 62, no. 10, pp. 2659–2672.</mixed-citation><mixed-citation xml:lang="en">Li, J.and Fang, J., Not fully overlapping Allan variance and total variance for inertial sensor stochastic error analysis, IEEE Transactions on Instrumentation and Measurement, 2013, vol. 62, no. 10, pp. 2659–2672.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Hussen, A. and Jleta, I., Low cost inertial sensors modeling using Allan variance, World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering, 2015, vol. 9, no. 5, pp. 1237–1242.</mixed-citation><mixed-citation xml:lang="en">Hussen, A. and Jleta, I., Low cost inertial sensors modeling using Allan variance, World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering, 2015, vol. 9, no. 5, pp. 1237–1242.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Guerrier, S., Skaloud, J., Stebler, Y., and Victoria-Feser, M.-P., Wavelet-variance-based estimation for composite stochastic processes, Journal of the American Statistical Association, 2013, vol. 108, no. 503, pp. 1021–1030.</mixed-citation><mixed-citation xml:lang="en">Guerrier, S., Skaloud, J., Stebler, Y., and Victoria-Feser, M.-P., Wavelet-variance-based estimation for composite stochastic processes, Journal of the American Statistical Association, 2013, vol. 108, no. 503, pp. 1021–1030.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Balamuta, J., Molinari, R., Guerrier, S., and Yang, W., The gmwm R package: a comprehensive tool for time series analysis from state-space models to robustness, arXiv preprint arXiv:1607.04543, 2016.</mixed-citation><mixed-citation xml:lang="en">Balamuta, J., Molinari, R., Guerrier, S., and Yang, W., The gmwm R package: a comprehensive tool for time series analysis from state-space models to robustness, arXiv preprint arXiv:1607.04543, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Balamuta, J., Guerrier, S., Molinari, R., and Yang, W., A computationally efficient framework for automatic inertial sensor calibration, arXiv preprint arXiv:1603.05297, 2016.</mixed-citation><mixed-citation xml:lang="en">Balamuta, J., Guerrier, S., Molinari, R., and Yang, W., A computationally efficient framework for automatic inertial sensor calibration, arXiv preprint arXiv:1603.05297, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Guerrier, S., Molinari, R., and Stebler, Y., Wavelet-based improvements for inertial sensor error modeling, IEEE Transactions on Instrumentation and Measurement, vol. 65, no. 12, pp. 2693–2700, 2016.</mixed-citation><mixed-citation xml:lang="en">Guerrier, S., Molinari, R., and Stebler, Y., Wavelet-based improvements for inertial sensor error modeling, IEEE Transactions on Instrumentation and Measurement, vol. 65, no. 12, pp. 2693–2700, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Yuksel, Y., El-Sheimy, N., and Noureldin, A., Error modeling and characterization of environmental effects for low cost inertial MEMS units, Position Location and Navigation Symposium (PLANS), 2010 IEEE/ION, 2010, pp. 598–612: IEEE.</mixed-citation><mixed-citation xml:lang="en">Yuksel, Y., El-Sheimy, N., and Noureldin, A., Error modeling and characterization of environmental effects for low cost inertial MEMS units, Position Location and Navigation Symposium (PLANS), 2010 IEEE/ION, 2010, pp. 598–612: IEEE.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Aggarwal, P., Syed, Z., Niu, X., and El-Sheimy, N., Cost-effective testing and calibration of low cost MEMS sensors for integrated positioning, navigation and mapping systems, Proceedings of XXIII FIG Congress, Munich, Germany, 2006, vol. 813.</mixed-citation><mixed-citation xml:lang="en">Aggarwal, P., Syed, Z., Niu, X., and El-Sheimy, N., Cost-effective testing and calibration of low cost MEMS sensors for integrated positioning, navigation and mapping systems, Proceedings of XXIII FIG Congress, Munich, Germany, 2006, vol. 813.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">El-Diasty, M., El-Rabbany, A., and Pagiatakis, S., Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error, Measurement Science and Technology, 2007, vol. 18, no. 11, p. 3321.</mixed-citation><mixed-citation xml:lang="en">El-Diasty, M., El-Rabbany, A., and Pagiatakis, S., Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error, Measurement Science and Technology, 2007, vol. 18, no. 11, p. 3321.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Wis, M. and Colomina, I., Dynamic dependency of inertial sensor errors and its application to INS/GNSS navigation, Proc. NAVITEC Congr., 2010. pp. 1–7.</mixed-citation><mixed-citation xml:lang="en">Wis, M. and Colomina, I., Dynamic dependency of inertial sensor errors and its application to INS/GNSS navigation, Proc. NAVITEC Congr., 2010. pp. 1–7.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Stebler, Y., Guerrier, S., Skaloud, J., Molinari, R., and Victoria-Feser, M.-P., Study of MEMS-based inertial sensors operating in dynamic conditions, IEEE/ION Position, Location and Navigation Symposium-PLANS 2014, 2014, pp. 1227–1231: IEEE.</mixed-citation><mixed-citation xml:lang="en">Stebler, Y., Guerrier, S., Skaloud, J., Molinari, R., and Victoria-Feser, M.-P., Study of MEMS-based inertial sensors operating in dynamic conditions, IEEE/ION Position, Location and Navigation Symposium-PLANS 2014, 2014, pp. 1227–1231: IEEE.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Radi, A., Elsheimy, N., and Li, Y., Temperature variation effects on the stochastic performance of smartphone sensors using Allan variance and generalized method of wavelet moments, ed. Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 1242–1255.</mixed-citation><mixed-citation xml:lang="en">Radi, A., Elsheimy, N., and Li, Y., Temperature variation effects on the stochastic performance of smartphone sensors using Allan variance and generalized method of wavelet moments, ed. Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 1242–1255.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Shin, E.and El-Sheimy, N., Aided inertial navigation system (AINS™) toolbox for MatLab® software, INS/GPS integration software, Mobile Multi-Sensors System (MMSS) research group, the University of Calgary http://mms. geomatics. ucalgary. ca/Research/Tech% 20transfer/INS_toolbox. htm, 2004.</mixed-citation><mixed-citation xml:lang="en">Shin, E.and El-Sheimy, N., Aided inertial navigation system (AINS™) toolbox for MatLab® software, INS/GPS integration software, Mobile Multi-Sensors System (MMSS) research group, the University of Calgary http://mms. geomatics. ucalgary. ca/Research/Tech% 20transfer/INS_toolbox. htm, 2004.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Hayal, G., Static calibration of the tactical grade inertial measurement units, The Ohio State University, 2010.</mixed-citation><mixed-citation xml:lang="en">Hayal, G., Static calibration of the tactical grade inertial measurement units, The Ohio State University, 2010.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Savage, P.G., Analytical modeling of sensor quantization in strapdown inertial navigation error equations, Journal of Guidance, Control, and Dynamics, 2002, vol. 25, no. 5, pp. 833–842.</mixed-citation><mixed-citation xml:lang="en">Savage, P.G., Analytical modeling of sensor quantization in strapdown inertial navigation error equations, Journal of Guidance, Control, and Dynamics, 2002, vol. 25, no. 5, pp. 833–842.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">IEEE Standard Specification format guide and test procedure for linear, single-axis, Nongyroscopic Accelerometers, IEEE, 1999.</mixed-citation><mixed-citation xml:lang="en">IEEE Standard Specification format guide and test procedure for linear, single-axis, Nongyroscopic Accelerometers, IEEE, 1999.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Abdel-Hamid, W., Accuracy enhancement of integrated MEMS-IMU/GPS systems for land vehicular navigation applications. Library and Archives Canada, 2006.</mixed-citation><mixed-citation xml:lang="en">Abdel-Hamid, W., Accuracy enhancement of integrated MEMS-IMU/GPS systems for land vehicular navigation applications. Library and Archives Canada, 2006.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Guerrier, S., Molinari, R., and Stebler, Y., Theoretical limitations of Allan variance-based regression for time series model estimation, IEEE Signal Processing Letters, 2016, vol. 23, no. 5, pp. 597–601.</mixed-citation><mixed-citation xml:lang="en">Guerrier, S., Molinari, R., and Stebler, Y., Theoretical limitations of Allan variance-based regression for time series model estimation, IEEE Signal Processing Letters, 2016, vol. 23, no. 5, pp. 597–601.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Niu, X. et al., Using Allan variance to analyze the error characteristics of GNSS positioning, GPS solutions, 2014, vol. 18, no. 2, pp. 231–242.</mixed-citation><mixed-citation xml:lang="en">Niu, X. et al., Using Allan variance to analyze the error characteristics of GNSS positioning, GPS solutions, 2014, vol. 18, no. 2, pp. 231–242.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Hou, H., Modeling inertial sensors errors using Allan variance. Library and Archives Canada, 2005.</mixed-citation><mixed-citation xml:lang="en">Hou, H., Modeling inertial sensors errors using Allan variance. Library and Archives Canada, 2005.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Vaccaro, R.J. and Zaki, A.S., Statistical modeling of rate gyros, IEEE Transactions on Instrumentation and Measurement, 2012, vol. 61, no. 3, pp. 673–684.</mixed-citation><mixed-citation xml:lang="en">Vaccaro, R.J. and Zaki, A.S., Statistical modeling of rate gyros, IEEE Transactions on Instrumentation and Measurement, 2012, vol. 61, no. 3, pp. 673–684.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Percival, D.B. and Guttorp P., Long-memory processes, the Allan variance and wavelets, Wavelets in geophysics, 1994, vol. 4, pp. 325–344.</mixed-citation><mixed-citation xml:lang="en">Percival, D.B. and Guttorp P., Long-memory processes, the Allan variance and wavelets, Wavelets in geophysics, 1994, vol. 4, pp. 325–344.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Percival, D. B. and Walden, A.T., Wavelet methods for time series analysis. Cambridge university press, 2006.</mixed-citation><mixed-citation xml:lang="en">Percival, D. B. and Walden, A.T., Wavelet methods for time series analysis. Cambridge university press, 2006.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M.-P., A framework for inertial sensor calibration using complex stochastic error models, Position Location and Navigation Symposium (PLANS), 2012 IEEE/ION, 2012, pp. 849–861: IEEE.</mixed-citation><mixed-citation xml:lang="en">Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M.-P., A framework for inertial sensor calibration using complex stochastic error models, Position Location and Navigation Symposium (PLANS), 2012 IEEE/ION, 2012, pp. 849–861: IEEE.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Guerrier, S. and Molinari, R., Wavelet variance for random fields: an m-estimation framework, arXiv preprint arXiv:1607.05858, 2016.</mixed-citation><mixed-citation xml:lang="en">Guerrier, S. and Molinari, R., Wavelet variance for random fields: an m-estimation framework, arXiv preprint arXiv:1607.05858, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Guerrier, S., Molinari, R., and Skaloud, J., Automatic identification and calibration of stochastic parameters in inertial sensors, Navigation, 2015, vol. 62, no. 4, pp. 265–272.</mixed-citation><mixed-citation xml:lang="en">Guerrier, S., Molinari, R., and Skaloud, J., Automatic identification and calibration of stochastic parameters in inertial sensors, Navigation, 2015, vol. 62, no. 4, pp. 265–272.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M.-P., Generalized method of wavelet moments for inertial navigation filter design, IEEE Transactions on Aerospace and Electronic Systems, 2014, vol. 50, no. 3, pp. 2269–2283.</mixed-citation><mixed-citation xml:lang="en">Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M.-P., Generalized method of wavelet moments for inertial navigation filter design, IEEE Transactions on Aerospace and Electronic Systems, 2014, vol. 50, no. 3, pp. 2269–2283.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">Ifixit, A., Apple iPhone 5s.</mixed-citation><mixed-citation xml:lang="en">Ifixit, A., Apple iPhone 5s.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Kane, T.R. and Levinson, D.A., Dynamics, theory and applications. McGraw Hill, 1985.</mixed-citation><mixed-citation xml:lang="en">Kane, T.R. and Levinson, D.A., Dynamics, theory and applications. McGraw Hill, 1985.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">Ding, W., Wang, J., Li, Y., Mumford, P., and Rizos, C., Time synchronization error and calibration in integrated GPS/INS systems, ETRI journal, 2008, vol. 30, no. 1, pp. 59–67.</mixed-citation><mixed-citation xml:lang="en">Ding, W., Wang, J., Li, Y., Mumford, P., and Rizos, C., Time synchronization error and calibration in integrated GPS/INS systems, ETRI journal, 2008, vol. 30, no. 1, pp. 59–67.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">Stebler, Y., Guerrier, S., and Skaloud, J., An approach for observing and modeling errors in MEMS-based inertial sensors under vehicle dynamic, IEEE Transactions on Instrumentation and Measurement, 2015, vol. 64, no. 11, pp. 2926–2936.</mixed-citation><mixed-citation xml:lang="en">Stebler, Y., Guerrier, S., and Skaloud, J., An approach for observing and modeling errors in MEMS-based inertial sensors under vehicle dynamic, IEEE Transactions on Instrumentation and Measurement, 2015, vol. 64, no. 11, pp. 2926–2936.</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>
