一种适用于星载GPS自主定轨的地球引力近似计算改进方法
|
摘要
提出了一种适用于星载GPS自主定轨的改进的地球引力近似函数方法(improved gravity acceleration approximation function, IGAAF)。对IGAAF方法的性能进行评估,结果表明:IGAAF方法的计算耗时小于45×45阶球谐模型;拟合系数容量仅为200～320 kB;引力加速度的截断误差(3D RMS)处于1×10~2～1×10~3 nm/s~2量级,小于每颗低轨卫星自主定轨所需的最优阶次球谐模型(GOCE:105×105,CHAMP:85×85,GRACE-A:65×65, ZY3/TerraSAR-X:55×55);将IGAAF方法应用于星载GPS自主定轨试验,相比于球谐模型,不会降低自主定轨精度。IGAAF方法在保证定轨精度的同时兼顾计算效率与系数容量的平衡,在星载GPS自主定轨的工程化应用中具有较强的实用价值。
We present an improved gravity acceleration approximation function(IGAAF) suitable for space-borne GPS real-time onboard orbit determination. The test of analyzing IGAAF's performances demonstrates that IGAAF maintains the truncation error in the magnitude of 1×10~2-1×10~3 nm/s~2 only with the computational burden less than a 45×45 spherical model and a 200-320 kB RAM requirement for fitting coefficients, and that its accuracy is slightly superior to the spherical models with optimal degree and order for autonomous orbit determination(105×105 model for GOCE, 85×85 for CHAMP, 65×65 for GRACE-A and 55×55 for ZY3 and TerraSAR-X). Compared to the spherical model, IGAAF does not decrease the orbit accuracies. The IGAAF method attains a good trade-off between computational efficiency and coefficient capacity without decreasing the orbit accuracy, so it is of strong engineering value for space-borne GPS autonomous orbit determination.
We present an improved gravity acceleration approximation function(IGAAF) suitable for space-borne GPS real-time onboard orbit determination. The test of analyzing IGAAF's performances demonstrates that IGAAF maintains the truncation error in the magnitude of 1×10~2-1×10~3 nm/s~2 only with the computational burden less than a 45×45 spherical model and a 200-320 kB RAM requirement for fitting coefficients, and that its accuracy is slightly superior to the spherical models with optimal degree and order for autonomous orbit determination(105×105 model for GOCE, 85×85 for CHAMP, 65×65 for GRACE-A and 55×55 for ZY3 and TerraSAR-X). Compared to the spherical model, IGAAF does not decrease the orbit accuracies. The IGAAF method attains a good trade-off between computational efficiency and coefficient capacity without decreasing the orbit accuracy, so it is of strong engineering value for space-borne GPS autonomous orbit determination.
引文
[1] Gill E, Montenbruck O, Arichandran K, et al. High-Precision Onboard Orbit Determination for Small Satellites:The GPS-based XNS on X-SAT[C]. The 6th Symposium on Small Satellites Systems and Services, La Rochelle, France, 2004
[2] Montenbruck O, Markgraf M, Garia-Fernandez M, et al. GPS for Microsatellites-Status and Perspectives[C]. The 6th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany, 2007
[3] Florio S D, Gill E, D’amico S. Comparison of the Performance of Microprocessors for Spaced-Based Navigation Applications[C]. The 7th IAA Symposium on Small Satellites for Earth Observation, New York, USA, 2009
[4] Montenbruck O, Gill E. Satellite Orbits: Models, Methods and Applications [M]. Berlin: Springer, 2001
[5] Zheng Wei, Xu Houze, Zhong Min, et al. Progress and Present Status of Research on Earth’s Gravitational Field Models[J]. Journal of Geodesy and Geodynamics, 2010, 30(4): 83-91(郑伟,许厚泽,钟敏,等. 地球重力场模型研究进展和现状[J]. 大地测量与地球动力学, 2010, 30(4): 83-91)
[6] Hujsak R S. Gravity Acceleration Approximation Functions[J]. Advance in the Astronautical Scie-nces, 1996, 93(1): 335-349
[7] Goldstein D B. Real-Time, Autonomous Precise Satellite Orbit Determination Using the Global Positioning System[D]. Boulder: University of Colorado, 2000
[8] Wang Fuhong, Xu Qichao, Gong Xuewen, et al. Application of a Gravity Acceleration Approximation Function in the Precise Real-Time Orbit Determination Using Space-Borne GPS Measurements [J]. Geomatics and Information Science of Wuhan University, 2014, 39(1): 47-51(王甫红,徐其超,龚学文,等. GAAF在星载GPS实时定轨中的应用研究[J]. 武汉大学学报·信息科学版,2014, 39(1): 47-51)
[9] Beylkin G, Cramer R. Toward Multi-resolution Estimation and Efficient Representation of Gravitatio-nal Fields [J]. Celestial Mechanics and Dynamical Astronomy, 2002, 84(1): 87-104
[10] Jones B A, Born G H, Beylkin G. Comparisons of the Cubed Sphere Gravity Model with the Spherical Harmonics[J]. Journal of Guidance, Control and Dynamics, 2010, 33(2): 415-425
[11] Arora N, Russell R P. Fast, Efficient and Adaptive Interpolation of the Geopotential[C]. AAS/AIAA Astrodynamics Specialist Conference, New York, USA, 2011
[12] Pavlis N K, Holmes S A, Kenyon S C, et al. An Earth Gravitational Model to Degree 2160: EGM 2008[R]. EGU General Assembly, New York, USA, 2008
[13] Wang Fuhong, Gong Xuewen, Sang Jizhang, et al. A Novel Method for Precise Onboard Real-Time Orbit Determination with a Standalone GPS Receiver [J]. Sensors, 2015, 15(12): 30 403-30 418
[2] Montenbruck O, Markgraf M, Garia-Fernandez M, et al. GPS for Microsatellites-Status and Perspectives[C]. The 6th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany, 2007
[3] Florio S D, Gill E, D’amico S. Comparison of the Performance of Microprocessors for Spaced-Based Navigation Applications[C]. The 7th IAA Symposium on Small Satellites for Earth Observation, New York, USA, 2009
[4] Montenbruck O, Gill E. Satellite Orbits: Models, Methods and Applications [M]. Berlin: Springer, 2001
[5] Zheng Wei, Xu Houze, Zhong Min, et al. Progress and Present Status of Research on Earth’s Gravitational Field Models[J]. Journal of Geodesy and Geodynamics, 2010, 30(4): 83-91(郑伟,许厚泽,钟敏,等. 地球重力场模型研究进展和现状[J]. 大地测量与地球动力学, 2010, 30(4): 83-91)
[6] Hujsak R S. Gravity Acceleration Approximation Functions[J]. Advance in the Astronautical Scie-nces, 1996, 93(1): 335-349
[7] Goldstein D B. Real-Time, Autonomous Precise Satellite Orbit Determination Using the Global Positioning System[D]. Boulder: University of Colorado, 2000
[8] Wang Fuhong, Xu Qichao, Gong Xuewen, et al. Application of a Gravity Acceleration Approximation Function in the Precise Real-Time Orbit Determination Using Space-Borne GPS Measurements [J]. Geomatics and Information Science of Wuhan University, 2014, 39(1): 47-51(王甫红,徐其超,龚学文,等. GAAF在星载GPS实时定轨中的应用研究[J]. 武汉大学学报·信息科学版,2014, 39(1): 47-51)
[9] Beylkin G, Cramer R. Toward Multi-resolution Estimation and Efficient Representation of Gravitatio-nal Fields [J]. Celestial Mechanics and Dynamical Astronomy, 2002, 84(1): 87-104
[10] Jones B A, Born G H, Beylkin G. Comparisons of the Cubed Sphere Gravity Model with the Spherical Harmonics[J]. Journal of Guidance, Control and Dynamics, 2010, 33(2): 415-425
[11] Arora N, Russell R P. Fast, Efficient and Adaptive Interpolation of the Geopotential[C]. AAS/AIAA Astrodynamics Specialist Conference, New York, USA, 2011
[12] Pavlis N K, Holmes S A, Kenyon S C, et al. An Earth Gravitational Model to Degree 2160: EGM 2008[R]. EGU General Assembly, New York, USA, 2008
[13] Wang Fuhong, Gong Xuewen, Sang Jizhang, et al. A Novel Method for Precise Onboard Real-Time Orbit Determination with a Standalone GPS Receiver [J]. Sensors, 2015, 15(12): 30 403-30 418