ISSN 0253-2778

CN 34-1054/N

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Localized atmospheric density prediction method based on NARX neural network

  • 1.

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

  • 2.

    State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2017.12.007
  • Received Date: 15 March 2017
  • Rev Recd Date: 02 June 2017
  • Publish Date: 30 December 2017
    Abstract

  • Abstract

    Errors of orbit determination and prediction for low earth orbit (LEO) satellites mainly arise from the lack of accuracy in existing atmospheric density models. The lack of observation methods and insufficient understanding of physical mechanism of the upper atmosphere have brought difficulties to the modelling of atmospheric density. Two line element (TLE) was used to calibrate the MSIS atmospheric model, aiming at getting a localized density model along the orbit. Then a predictor was built based on the nonlinear autoregressive neural network with exogenous inputs (NARX). It uses calibrated MISIS model and a set of proxies of solar and geomagnetic activities to predict localized density values along the future orbit of a satellite. This model was applied for different types of satellite orbits and tested for different prediction windows. Comparison with the predictor based on the MSIS model shows a decrease in the mean error of the proposed model, which throws new light on improving the accuracy of LEO satellites’ short-time prediction.

    Abstract

    Errors of orbit determination and prediction for low earth orbit (LEO) satellites mainly arise from the lack of accuracy in existing atmospheric density models. The lack of observation methods and insufficient understanding of physical mechanism of the upper atmosphere have brought difficulties to the modelling of atmospheric density. Two line element (TLE) was used to calibrate the MSIS atmospheric model, aiming at getting a localized density model along the orbit. Then a predictor was built based on the nonlinear autoregressive neural network with exogenous inputs (NARX). It uses calibrated MISIS model and a set of proxies of solar and geomagnetic activities to predict localized density values along the future orbit of a satellite. This model was applied for different types of satellite orbits and tested for different prediction windows. Comparison with the predictor based on the MSIS model shows a decrease in the mean error of the proposed model, which throws new light on improving the accuracy of LEO satellites’ short-time prediction.
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    • References(22)
  • [1]
    VALLADO D A. Fundamentals of Astrodynamics and Applications [M]. New York, USA: Springer-Verlag, 2010:242-233.
    [2]
    BOWMAN B, TOBISKA W K, MARCOS F, et al. A new empirical thermospheric density model JB2008 using new solar and geomagnetic indices [C] // Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, USA: AIAA, 2008.
    [3]
    HEDIN A E. MSIS-86 thermospheric model [J]. Journal of Geophysical Research Space Physics, 1987, 92(A5): 4649-4662.
    [4]
    PICONE J M, HEDIN A E, DROB D P, et al. NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues [J]. Journal of Geophysical Research Space Physics, 2002, 107(A12): SIA 15-1-SIA 15-16.
    [5]
    PARDINI C, ANSELMO L. Comparison and accuracy assessment of semi-empirical atmosphere models through the orbital decay of spherical satellites [J]. Journal of the Astronautical Sciences, 2001, 49(2): 255-268.
    [6]
    SUTTON E K, NEREM R S, FORBES J M. Density and winds in the thermosphere deduced from accelerometer data [J]. Journal of Spacecraft & Rockets, 2007, 44(6): 1210-1219.
    [7]
    PICONE J M, EMMERT J T, LEAN J L. Thermospheric densities derived from spacecraft orbits: Accurate processing of two-line element sets [J]. Journal of Geophysical Research Atmospheres, 2005, 110(A3): 103-115.
    [8]
    EMMERT J T. A long-term data set of globally averaged thermospheric total mass density [J]. Journal of Geophysical Research Space Physics, 2009, 114(A6): 61-69.
    [9]
    DOORNBOS E, KLINKRAD H, VISSER P N. Use of two-line element data for thermosphere neutral density model calibration [J]. Advances in Space Research, 2008, 41(7): 1115-1122.
    [10]
    任廷领, 苗娟, 刘四清, 等. 利用卫星两行轨道根数反演热层密度 [J]. 空间科学学报, 2014, 34(4): 426-433.
    REN Tingling, MIAO Juan, LIU Siqing, et al. Research on thermospheric densities derived from two-line element sets[J]. Chinese Journal of Space Science , 2014, 34(4): 426-433.
    [11]
    苗娟, 任廷领, 龚建村, 等. 基于星载高精度GPS观测数据的大气密度反演 [J]. 地球物理学报, 2016, 59(10): 3566-3572.
    MIAO Juan ,REN Tingling,GONG Jiancun, et al. Thermospheric density derived from onboard GPS observation data[J]. Chinese Journal of Geophysics, 2016, 59(10): 3566-3572.
    [12]
    陈旭杏, 胡雄, 肖存英, 等. 基于卫星数据和NRLMSISE-00模型的低轨道大气密度预报修正方法 [J]. 地球物理学报, 2013, 56(10): 3246-3254.
    CHEN Xuxing, HU Xiong, XIAO Cunying, et al. Correction method of the low earth orbital neutral density prediction based on the satellites data and NRLMSISE-00 model[J].Chinese Journal of Geophysics, 2013, 56(10): 3246-3254.
    [13]
    BOWMAN B R. True satellite ballistic coefficient determination for HASDM [C] // Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, USA: AIAA, 2002.
    [14]
    STASTNY N, LIN C, LOVELL A, et al. Localized density/drag prediction for improved onboard orbit propagation[C]// Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2009:7-9.
    [15]
    PREZ D, WOHLBERG B, LOVELL T A, et al. Orbit-centered atmospheric density prediction using artificial neural networks [J]. Acta Astronautica, 2014, 98(5): 9-23.
    [16]
    LIN T, HORNE B G, TIO P, et al. Learning long-term dependencies in NARX recurrent neural networks [J]. IEEE Transactions on Neural Networks, 1996, 7(6): 1329-1338.
    [17]
    MENEZES J, MARIA P, BARRETO G A. Long-term time series prediction with the NARX network: An empirical evaluation [J]. Neurocomputing, 2008, 71: 3335-3343.
    [18]
    HOOTS F R, ROEHRICH R L. Spacetrack report #3: Models for propagation of the NORAD element sets [J]. Spacetrack Report, 1998:46-47.
    [19]
    KING H D. Satellite Orbits in an Atmosphere: Theory and Applications [M]. Princeton, USA: Princeton University Press, 1987:87-90.
    [20]
    ALZAHRANI A, KIMBALL J W, DAGLI C. Predicting solar irradiance using time series neural networks [J]. Procedia Computer Science, 2014, 36: 623-628.
    [21]
    CAI L, MA S Y, CAI H T, et al. Prediction of SYH-H Index by NARX neural network from IMF and solar wind data [J]. Science in China Series E: Technological Sciences, 2009, 52(10): 2877-2885.
    [22]
    翁利斌, 方涵先, 季春华, 等. 基于卫星加速度数据反演的热层大气密度与NRLMSIS-00模式结果的比较研究 [J]. 空间科学学报, 2012, 32(5): 713-719.
    WENG Libin, FANG Hanxian, JI Chunhua, et al. Comparison between the CHAMP/STAR derived thermospheric density and the NRLMSISE-00 model[J]. Chinese Journal of Space Science, 2012,32(5):713-719.
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    [1]
    VALLADO D A. Fundamentals of Astrodynamics and Applications [M]. New York, USA: Springer-Verlag, 2010:242-233.
    [2]
    BOWMAN B, TOBISKA W K, MARCOS F, et al. A new empirical thermospheric density model JB2008 using new solar and geomagnetic indices [C] // Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, USA: AIAA, 2008.
    [3]
    HEDIN A E. MSIS-86 thermospheric model [J]. Journal of Geophysical Research Space Physics, 1987, 92(A5): 4649-4662.
    [4]
    PICONE J M, HEDIN A E, DROB D P, et al. NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues [J]. Journal of Geophysical Research Space Physics, 2002, 107(A12): SIA 15-1-SIA 15-16.
    [5]
    PARDINI C, ANSELMO L. Comparison and accuracy assessment of semi-empirical atmosphere models through the orbital decay of spherical satellites [J]. Journal of the Astronautical Sciences, 2001, 49(2): 255-268.
    [6]
    SUTTON E K, NEREM R S, FORBES J M. Density and winds in the thermosphere deduced from accelerometer data [J]. Journal of Spacecraft & Rockets, 2007, 44(6): 1210-1219.
    [7]
    PICONE J M, EMMERT J T, LEAN J L. Thermospheric densities derived from spacecraft orbits: Accurate processing of two-line element sets [J]. Journal of Geophysical Research Atmospheres, 2005, 110(A3): 103-115.
    [8]
    EMMERT J T. A long-term data set of globally averaged thermospheric total mass density [J]. Journal of Geophysical Research Space Physics, 2009, 114(A6): 61-69.
    [9]
    DOORNBOS E, KLINKRAD H, VISSER P N. Use of two-line element data for thermosphere neutral density model calibration [J]. Advances in Space Research, 2008, 41(7): 1115-1122.
    [10]
    任廷领, 苗娟, 刘四清, 等. 利用卫星两行轨道根数反演热层密度 [J]. 空间科学学报, 2014, 34(4): 426-433.
    REN Tingling, MIAO Juan, LIU Siqing, et al. Research on thermospheric densities derived from two-line element sets[J]. Chinese Journal of Space Science , 2014, 34(4): 426-433.
    [11]
    苗娟, 任廷领, 龚建村, 等. 基于星载高精度GPS观测数据的大气密度反演 [J]. 地球物理学报, 2016, 59(10): 3566-3572.
    MIAO Juan ,REN Tingling,GONG Jiancun, et al. Thermospheric density derived from onboard GPS observation data[J]. Chinese Journal of Geophysics, 2016, 59(10): 3566-3572.
    [12]
    陈旭杏, 胡雄, 肖存英, 等. 基于卫星数据和NRLMSISE-00模型的低轨道大气密度预报修正方法 [J]. 地球物理学报, 2013, 56(10): 3246-3254.
    CHEN Xuxing, HU Xiong, XIAO Cunying, et al. Correction method of the low earth orbital neutral density prediction based on the satellites data and NRLMSISE-00 model[J].Chinese Journal of Geophysics, 2013, 56(10): 3246-3254.
    [13]
    BOWMAN B R. True satellite ballistic coefficient determination for HASDM [C] // Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, USA: AIAA, 2002.
    [14]
    STASTNY N, LIN C, LOVELL A, et al. Localized density/drag prediction for improved onboard orbit propagation[C]// Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2009:7-9.
    [15]
    PREZ D, WOHLBERG B, LOVELL T A, et al. Orbit-centered atmospheric density prediction using artificial neural networks [J]. Acta Astronautica, 2014, 98(5): 9-23.
    [16]
    LIN T, HORNE B G, TIO P, et al. Learning long-term dependencies in NARX recurrent neural networks [J]. IEEE Transactions on Neural Networks, 1996, 7(6): 1329-1338.
    [17]
    MENEZES J, MARIA P, BARRETO G A. Long-term time series prediction with the NARX network: An empirical evaluation [J]. Neurocomputing, 2008, 71: 3335-3343.
    [18]
    HOOTS F R, ROEHRICH R L. Spacetrack report #3: Models for propagation of the NORAD element sets [J]. Spacetrack Report, 1998:46-47.
    [19]
    KING H D. Satellite Orbits in an Atmosphere: Theory and Applications [M]. Princeton, USA: Princeton University Press, 1987:87-90.
    [20]
    ALZAHRANI A, KIMBALL J W, DAGLI C. Predicting solar irradiance using time series neural networks [J]. Procedia Computer Science, 2014, 36: 623-628.
    [21]
    CAI L, MA S Y, CAI H T, et al. Prediction of SYH-H Index by NARX neural network from IMF and solar wind data [J]. Science in China Series E: Technological Sciences, 2009, 52(10): 2877-2885.
    [22]
    翁利斌, 方涵先, 季春华, 等. 基于卫星加速度数据反演的热层大气密度与NRLMSIS-00模式结果的比较研究 [J]. 空间科学学报, 2012, 32(5): 713-719.
    WENG Libin, FANG Hanxian, JI Chunhua, et al. Comparison between the CHAMP/STAR derived thermospheric density and the NRLMSISE-00 model[J]. Chinese Journal of Space Science, 2012,32(5):713-719.
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