<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">10.17285/0869-7035.00109</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-113</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>Сокращение времени сходимости РРР-решений при использовании ограничений на скорость движения</article-title><trans-title-group xml:lang="en"><trans-title>Rapid Re-convergence of Real-time Dynamic Precise Point Positioning by Adding Velocity Constraints</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5459-536X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ван</surname><given-names>C</given-names></name><name name-style="western" xml:lang="en"><surname>Wang</surname><given-names>X.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ван Синсин, магистр</p><p>Шицзячуан</p></bio><bio xml:lang="en"><p>Shijiazhuang</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>Шэн</surname><given-names>Ч.</given-names></name><name name-style="western" xml:lang="en"><surname>Sheng</surname><given-names>C.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шэн Чуаньчжэнь, доктор технических наук </p><p>Шицзячуан </p></bio><bio xml:lang="en"><p>Shijiazhuang</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/0000-0002-7274-3888</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Юй</surname><given-names>Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Yu</surname><given-names>B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Юй Баого, доктор технических наук </p><p>Шицзячуан </p></bio><bio xml:lang="en"><p>Shijiazhuang</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>Чжан</surname><given-names>Ц.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhang</surname><given-names>Z.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжан Цзытэн, магистр </p><p>Шицзячуан </p></bio><bio xml:lang="en"><p>Shijiazhuang</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>Чжан</surname><given-names>Ц.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhang</surname><given-names>J.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжан Цзинкуй, магистр </p><p>Шицзячуан </p></bio><bio xml:lang="en"><p>Shijiazhuang</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>И</surname><given-names>Ц.-У.</given-names></name><name name-style="western" xml:lang="en"><surname>Yi</surname><given-names>Q.</given-names></name></name-alternatives><bio xml:lang="ru"><p>И Цин-У, магистр </p><p>Шицзячуан </p></bio><bio xml:lang="en"><p>Shijiazhuang</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Главная государственная лаборатория по спутниковым навигационным системам и оборудованию; 54-й Научно-исследовательский институт Корпорации электронных технологий</institution><country>Китай</country></aff><aff xml:lang="en"><institution>State Key Laboratory of Satellite Navigation System and Equipment Technology; The 54th Research Institute of China Electronics Technology Group Corporation</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Главная государственная лаборатория по спутниковым навигационным системам&#13;
и оборудованию; 54-й Научно-исследовательский институт Корпорации электронных технологий</institution><country>Китай</country></aff><aff xml:lang="en"><institution>State Key Laboratory of Satellite Navigation System and Equipment Technology; The 54th Research Institute of China Electronics Technology Group Corporation</institution><country>China</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>4</issue><fpage>152</fpage><lpage>168</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ван C., Шэн Ч., Юй Б., Чжан Ц., Чжан Ц., И Ц., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ван C., Шэн Ч., Юй Б., Чжан Ц., Чжан Ц., И Ц.</copyright-holder><copyright-holder xml:lang="en">Wang X., Sheng C., Yu B., Zhang Z., Zhang J., Yi Q.</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/113">https://www.gyroscopy.ru/jour/article/view/113</self-uri><abstract><p>В сложных условиях навигации, например в городе и в геологически опасных районах, может происходить блокировка сигналов ГНСС, а длительный период сходимости решения навигационной задачи способен значительно ограничивать применение динамического высокоточного абсолютного позиционирования (precise point positioning – PPP) в режиме реального времени. C учетом того что в течение периодов сходимости скорость определяется точнее, чем местоположение, мы предлагаем метод быстрого определения местоположения в реальном времени за счет учета различного рода ограничений по скорости в динамическом PPP-позиционировании. В зависимости от состояний и условий движения адаптивно используются различные данные о скорости. Например, модель с нулевой скоростью применяется в неподвижном положении, измерения доплеровской скорости – при временной блокировке большинства видимых спутников, данные о скорости от других датчиков – при частой блокировке спутникового сигнала. Поскольку неточная динамическая модель способна влиять на результаты динамического позиционирования, ограничение по скорости может постепенно ослабляться при возобновлении приема сигналов ГНСС и постепенного сокращения неопределенности. Результаты статических и кинематических экспериментов демонстрируют, что при значительном снижении количества видимых спутников из-за блокировки сигналов применение нового метода определения местоположения может оперативно ускорить сходимость решения навигационной задачи при PPP-позиционировании, обеспечить высокую точность и непрерывность динамического позиционирования в реальном времени.</p></abstract><trans-abstract xml:lang="en"><p>In challenging environments like urban vehicle navigation and geological hazards, the GNSS signals are easily blocked, and the long re-convergence time seriously limits many applications of real-time dynamic precise point positioning. Considering that the velocity accuracy is better than the position during re-convergence epochs, we proposed a real-time rapid-positioning method by introducing velocity constraints into the dynamic PPP. According to the different motion states and environments, different velocity constraints are used adaptively. For example, the zero-velocity constraint model is used in the stationary state; the Doppler-velocity constraint model is used when the most visible satellites are temporarily blocked; the other-sensors-velocity constraint model is used when the satellite signal is blocked frequently. Considering that the inaccurate dynamic model will affect the dynamic positioning results, the velocity constraint can be gradually relaxed after the GNSS signals are reacquired and the ambiguity gradually converges. Based on static and kinematic experiments with GPS data, the results show that when the number of visible satellites is greatly dropped due to signal blocking, the new positioning method can significantly speed up the re-convergence of precise point positioning, maintain high accuracy and improve the continuity of real-time dynamic positioning in a short time.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>сходимость решения</kwd><kwd>динамическое PPP-позиционирование</kwd><kwd>ограничения по скорости</kwd><kwd>режим реального времени</kwd><kwd>блокировка сигналов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>reconvergence</kwd><kwd>dynamic precise point positioning</kwd><kwd>velocity constraints</kwd><kwd>real-time</kwd><kwd>signal blocking</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при поддержке Китайской национальной программы ключевых научно-исследовательских и конструкторских работ (проект «Исследование ключевых технологий по высокопрецизионному позиционированию и дистанционной связи для спасательной платформы при геологических катастрофах» №2019YFC1511504).</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">Hein, G.W., Status, perspectives and trends of satellite navigation, Satellite Navigation, 2020, 1(1), 22.</mixed-citation><mixed-citation xml:lang="en">Hein, G.W., Status, perspectives and trends of satellite navigation, Satellite Navigation, 2020, 1(1), 22.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Geng, J., Chang, H., Guo, J., et al., Three multi-frequency and multi-system GNSS high-precision point positioning methods and their performance in complex urban environment [J], Acta Geodaetica et Cartographica Sinica, 2020, 49, (1): 1–13, doi:10.11947/j.AGCS.2020.20190106.</mixed-citation><mixed-citation xml:lang="en">Geng, J., Chang, H., Guo, J., et al., Three multi-frequency and multi-system GNSS high-precision point positioning methods and their performance in complex urban environment [J], Acta Geodaetica et Cartographica Sinica, 2020, 49, (1): 1–13, doi:10.11947/j.AGCS.2020.20190106.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Tang, X., Jin, S., et al., Prior Position- and ZWD-Constrained PPP for Instantaneous Convergence in Real-Time Kinematic Application, 2021.</mixed-citation><mixed-citation xml:lang="en">Tang, X., Jin, S., et al., Prior Position- and ZWD-Constrained PPP for Instantaneous Convergence in Real-Time Kinematic Application, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang, X., Li, X., Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing, GPS Solut, 2012,16, 315–327, https://doi.org/10.1007/s10291-011-0233-9.</mixed-citation><mixed-citation xml:lang="en">Zhang, X., Li, X., Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing, GPS Solut, 2012,16, 315–327, https://doi.org/10.1007/s10291-011-0233-9.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Banville, S., Langley, R.B., Instantaneous Cycle-Slip Correction for Real-Time PPP Applications, NAVIGATION: Journal of The Institute of Navigation, Winter 2010-2011, vol. 57, no. 4, pp. 325–334.</mixed-citation><mixed-citation xml:lang="en">Banville, S., Langley, R.B., Instantaneous Cycle-Slip Correction for Real-Time PPP Applications, NAVIGATION: Journal of The Institute of Navigation, Winter 2010-2011, vol. 57, no. 4, pp. 325–334.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Ding, W., Ou, J., Instantaneous re-initialization of real time kinematic PPP by adding doppler observation, Journal of Astronautics, 2013, doi:10.3873/j.issn.1000-1328.2013.06.008.</mixed-citation><mixed-citation xml:lang="en">Ding, W., Ou, J., Instantaneous re-initialization of real time kinematic PPP by adding doppler observation, Journal of Astronautics, 2013, doi:10.3873/j.issn.1000-1328.2013.06.008.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Geng, J., Meng, X., Dodson, A.H. et al., Rapid re-convergences to ambiguity-fixed solutions in precise point positioning, J. Geod., 2010, 84, 705–714, https://doi.org/10.1007/s00190-010-0404-4.</mixed-citation><mixed-citation xml:lang="en">Geng, J., Meng, X., Dodson, A.H. et al., Rapid re-convergences to ambiguity-fixed solutions in precise point positioning, J. Geod., 2010, 84, 705–714, https://doi.org/10.1007/s00190-010-0404-4.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Kuang, C., Jin, L., Higher-order ionospheric error correction for precise point positioning, Geomatics and Information Science of Wuhan University, 2013, 38(8), 888–891+924.</mixed-citation><mixed-citation xml:lang="en">Kuang, C., Jin, L., Higher-order ionospheric error correction for precise point positioning, Geomatics and Information Science of Wuhan University, 2013, 38(8), 888–891+924.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Song, C., Hao, J., Zhang, H., A method to accelerate PPP re-convergence with prior troposphere delay constraint, Journal of Geomatics Science and Technology, 2015.</mixed-citation><mixed-citation xml:lang="en">Song, C., Hao, J., Zhang, H., A method to accelerate PPP re-convergence with prior troposphere delay constraint, Journal of Geomatics Science and Technology, 2015.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Zheng, Y., Liu, J., Song, W., and Sun, H., PPP rapid convergence algorithm based on regional enhanced information, Journal of Geodesy and Geodynamics, 2012.</mixed-citation><mixed-citation xml:lang="en">Zheng, Y., Liu, J., Song, W., and Sun, H., PPP rapid convergence algorithm based on regional enhanced information, Journal of Geodesy and Geodynamics, 2012.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Wang, A., Zhang, Y., Chen, J. et al., Improving the (re-)convergence of multi-GNSS real-time precise point positioning through regional between-satellite single-differenced ionospheric augmentation, GPS Solutions, 2022, 26(2), 1–16.</mixed-citation><mixed-citation xml:lang="en">Wang, A., Zhang, Y., Chen, J. et al., Improving the (re-)convergence of multi-GNSS real-time precise point positioning through regional between-satellite single-differenced ionospheric augmentation, GPS Solutions, 2022, 26(2), 1–16.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Cui, B., Wang, J., Li, P., et al., Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution, GPS Solutions, 2022, 26, 56, https://doi.org/10.1007/s10291-022-01243-1.</mixed-citation><mixed-citation xml:lang="en">Cui, B., Wang, J., Li, P., et al., Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution, GPS Solutions, 2022, 26, 56, https://doi.org/10.1007/s10291-022-01243-1.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Tu, R., Fast determination of displacement by PPP velocity estimation, Geophysical Journal International, 2014 (3), 603.</mixed-citation><mixed-citation xml:lang="en">Tu, R., Fast determination of displacement by PPP velocity estimation, Geophysical Journal International, 2014 (3), 603.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Su, K., Jin, S., Ge, Y., Rapid displacement determination with a stand-alone multi-GNSS receiver: GPS, Beidou, GLONASS, and Galileo, GPS Solutions, 2019, 23, 54, https://doi.org/10.1007/s10291-019-0840-4.</mixed-citation><mixed-citation xml:lang="en">Su, K., Jin, S., Ge, Y., Rapid displacement determination with a stand-alone multi-GNSS receiver: GPS, Beidou, GLONASS, and Galileo, GPS Solutions, 2019, 23, 54, https://doi.org/10.1007/s10291-019-0840-4.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Zumberge, J., Heflin, M., Jefferson, D., Watkins, M.M., Webb, F.H., Precise point positioning for the efficient and robust analysis of GPS data from large networks, Journal of Geophysical Research: Solid Earth, 1997, vol. 102, no. B3, pp. 5005–5017.</mixed-citation><mixed-citation xml:lang="en">Zumberge, J., Heflin, M., Jefferson, D., Watkins, M.M., Webb, F.H., Precise point positioning for the efficient and robust analysis of GPS data from large networks, Journal of Geophysical Research: Solid Earth, 1997, vol. 102, no. B3, pp. 5005–5017.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Kouba, J., and Héroux, P., Precise point positioning using IGS orbit and clock products, GPS Solutions, 2001, vol. 5, no. 2, pp. 12–28.</mixed-citation><mixed-citation xml:lang="en">Kouba, J., and Héroux, P., Precise point positioning using IGS orbit and clock products, GPS Solutions, 2001, vol. 5, no. 2, pp. 12–28.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Gao, Y., Lahaye, F., Heroux, P., Modeling and estimation of C1–P1 bias in GPS receivers, Journal of Geodesy, 2001, vol. 74, no. 9, pp. 621–626.</mixed-citation><mixed-citation xml:lang="en">Gao, Y., Lahaye, F., Heroux, P., Modeling and estimation of C1–P1 bias in GPS receivers, Journal of Geodesy, 2001, vol. 74, no. 9, pp. 621–626.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Abdel-Salam, M., Precise point positioning using undifferenced code and carrier phase observations, PhD Thesis, 2005, University of Calgary, Calgary, AB, Canada.</mixed-citation><mixed-citation xml:lang="en">Abdel-Salam, M., Precise point positioning using undifferenced code and carrier phase observations, PhD Thesis, 2005, University of Calgary, Calgary, AB, Canada.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J., Global Positioning System. Theory and Practice, Springer Vienna, Springer-Verlag/Wien 2001, 382 p., https://doi.org/10.1007/978-3-7091-6199-9.</mixed-citation><mixed-citation xml:lang="en">Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J., Global Positioning System. Theory and Practice, Springer Vienna, Springer-Verlag/Wien 2001, 382 p., https://doi.org/10.1007/978-3-7091-6199-9.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Kalman, R.E., A new approach to linear filtering and prediction problems, Journal of Basic Engineering Transactions, 1960, vol. 82, pp. 35–45.</mixed-citation><mixed-citation xml:lang="en">Kalman, R.E., A new approach to linear filtering and prediction problems, Journal of Basic Engineering Transactions, 1960, vol. 82, pp. 35–45.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Guo, F., Theory and Methodology of Quality Control and Quality Analysis for GPS Precise Point Positioning, Wuhan University Press, 2016.</mixed-citation><mixed-citation xml:lang="en">Guo, F., Theory and Methodology of Quality Control and Quality Analysis for GPS Precise Point Positioning, Wuhan University Press, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Wang, X., Comparison of GPS Velocity Obtained Using Three Different Estimation Models, Gyroscopy and Navigation, 2020, vol. 11, no. 2, pp. 138–148, doi: 10.1134/S2075108720020091.</mixed-citation><mixed-citation xml:lang="en">Wang, X., Comparison of GPS Velocity Obtained Using Three Different Estimation Models, Gyroscopy and Navigation, 2020, vol. 11, no. 2, pp. 138–148, doi: 10.1134/S2075108720020091.</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>
