空域最小二乘法用于重力卫星误差分析
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摘要
重力测量卫星性能不仅与轨道参数、载荷误差、数据分辨率等因素密切相关,也与反演算法有关。传统的分析方法如动力学法、短弧法等用于误差分析,不可避免将算法误差引入分析结果,使得分析结论确定性不足。为解决这一问题,提出了空域最小二乘分析法,用空域格网重力扰动数据替代重力卫星载荷数据反演地球重力场,有效避免了算法误差对于分析结果的影响。分析结果表明,重力卫星在500 km轨道高度、一次数据覆盖条件下,测量重力场最高阶数约为240阶,载荷误差为1×10~(-10) m·s~(-2)⋅Hz~(-1/2)水平时,测量重力场最高阶数为136阶,其累积重力异常误差为2.7 mGal,累积大地水准面误差为14 cm。要达到最优测量能力,轨道倾角通常不小于89°。为减小地球引力高频信号对于地球重力场低阶位系数估计值的影响,估计位系数最高阶数需大于240阶。
The performance of satellite gravimetry is determined not only by orbital parameters, sensitivity of payloads, resolution of data, et al, but also by inaccuracy of the Earth gravity recovered methods. In past years, the performance analysis results were unavoidably affected by the mathematical model error from recovering methods such as dynamic method, short-arc integrated method, et al. To solve this problem, space-wise least square method is present. The effects of each items which affected the performance of satellite gravimetry are evaluated by this method. The results indicate that the highest degree of the earth gravity model recovered is 240 for the satellite with 500 km orbital height. Then if the error of payload is 1×10~(-10) m·s~(-2)·Hz~(-1/2), the degree of model recovered only approach to 136 with the accumulated gravity anomaly error 2.7 mGal and the accumulated geoid height error 14 cm. In order to achieve the best surveying performance, the orbital inclination should be greater than 89°. While, the max degree of the earth gravity model recovered should be greater than 240 so as to reduce the effect of high frequency gravity signal on low degree coefficients recovered. All these conclusions benefit to satellite designing and data processing.
The performance of satellite gravimetry is determined not only by orbital parameters, sensitivity of payloads, resolution of data, et al, but also by inaccuracy of the Earth gravity recovered methods. In past years, the performance analysis results were unavoidably affected by the mathematical model error from recovering methods such as dynamic method, short-arc integrated method, et al. To solve this problem, space-wise least square method is present. The effects of each items which affected the performance of satellite gravimetry are evaluated by this method. The results indicate that the highest degree of the earth gravity model recovered is 240 for the satellite with 500 km orbital height. Then if the error of payload is 1×10~(-10) m·s~(-2)·Hz~(-1/2), the degree of model recovered only approach to 136 with the accumulated gravity anomaly error 2.7 mGal and the accumulated geoid height error 14 cm. In order to achieve the best surveying performance, the orbital inclination should be greater than 89°. While, the max degree of the earth gravity model recovered should be greater than 240 so as to reduce the effect of high frequency gravity signal on low degree coefficients recovered. All these conclusions benefit to satellite designing and data processing.
引文
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[9] Xiao Yun, Liu Xiaogang, Guo Feixiao. Core Indexes Design for the Next Generation Satellite Gravimetry Mission [J]. Journal of Geodesy and Geodynamics, 2017,37(1):1-4 ( 肖云,刘晓刚,郭飞宵.新一代重力测量卫星核心指标分析[J]. 大地测量与地球动力学,2017,37(1):1-4)
[10] Kim J. Simulation Study of a Low-Low Satellite-to-Satellite Tracking Mission [D]. Austin: University of Texas, 2000
[11] Loomis B D. Simulation Study of a Follow-on Gra-vity Mission to GRACE [D]. Colorado: University of Colorado, 2009
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[16] Zhou Hao, Luo Zhicai, Zhong Bo,et al. MPI Parallel Algorithm in Satellite Gravity Field Inversion on the Basis of Least Square Method [J]. Acta Geodaetica et Cartographica Sinica, 2015,44(8):833-839(周浩,罗志才,钟波,等. 利用最小二乘直接法反演卫星重力场模型的MPI并行算法[J].测绘学报,2015,44(8):833-839)
[17] Lu Fei,You Wei,Fan Dongming,et al. Chinese Continental Water Storage and Ocean Water Mass Variations Analysis in Recent Ten Years Based on GRACE RL05 Data [J]. Acta Geodaetica et Cartographica Sinica, 2015,44(2):160-167(卢飞,游为,范东明,等.由GRACE RL05数据反演近10年中国大陆水储量及海水质量变化[J].测绘学报,2015,44(2):160-167)
[18] Luo Jia. A Crossover Approach to Calculate the Time-Variable of the Earth Gravity Field Low Degree Zonal Harmonic Terms Based on LEO Cluster[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 703-708(罗佳.利用LEO星群反演地球重力场低阶带谐项变化的交叠点法[J].测绘学报,2012, 41(5): 703-708)
[19] Chen Q, Shen Y, Zhang X, et al. Global Earth’s Gravity Field Solution with GRACE Orbit and Range Measurements Using Modified Short Arc Approach[J]. Acta Geodaetica et Geophysica, 2014, 50(2): 173-185
[20] Ilk K, Loecher A. The Use of Energy Balance Relations for Validation of Gravity Field Models and Orbit Determination Results [C]. The 36th IAG General Assembly, Prague, Czech, 2005
[2] Tapley B D, Bettadpur S, Watkins M, et al. The Gravity Recovery and Climate Experiment: Mission Overview and Early Results[J]. Geophysical Research Letters, 2004, 31(9): 9 607-9 610
[3] Drinkwater M R, Haagmans R, Muzi D, et al. The GOCE Gravity Mission: ESA’s First Core Earth Explorer[C]. The 3rd International GOCE User Workshop, Noordwijk, the Netherlands, 2006
[4] Pang Zhenxing, Ji Jianfeng, Xiao Yun, et al. Estemation of the Resolution of Earth’s Gravity Field for GRACE Follow on Using the Spectrum Method [J].Acta Geodaetica et Cartographica Sinica, 2012,41(3): 333-338(庞振兴,姬剑锋,肖云, 等.利用谱分析法估计GRACE Follow on地球重力场的空间分辨率[J].测绘学报,2012,41(3): 333-338)
[5] Jiang Weiping,Zhang Chuanyin,Li Jiancheng. Analysis and Determination of the Major Payload Indexes for Gravity Exploring Satellite [J]. Geomatics and Information Science of Wuhan University, 2003,28(S):104-109 (姜卫平,章传银,李建成.重力卫星主要有效载荷指标分析与确定[J].武汉大学学报·信息科学版, 2003,28(S): 104-109)
[6] Zhong Bo. Study on Determination of the Earth’s Gravity Field from Satellite Gravimetry Mission GOCE [D]. Wuhan:Wuhan University, 2010 (钟波.基于GOCE卫星重力测量技术确定地球重力场的研究[D].武汉:武汉大学, 2010)
[7] Zheng Wei, Xu Houze, Zhong Min, et al. Efficient and Rapid Estimation of the Accuracy of the Future GRACE Follow-on Earth’s Gravitational Field Using the Analytic Method [J]. Chinese Journal of Geophysics,2010,53(4): 796-806 ( 郑伟,许厚泽,钟敏, 等.利用解析法有效快速估计将来GRACE Follow-on地球重力场的精度[J].地球物理学报, 2010,53(4):796-806)
[8] Zheng Wei, Xu Houze, Zhong Min, et al. Demonstration on Different Matching Relationship of Accuracy Indexes of Key Payload in the Satellite-to-Satellite Tracking Mode[J]. Journal of Astronautics, 2011,32(3):697-705 ( 郑伟,许厚泽,钟敏, 等.卫星跟踪卫星测量模式中关键载荷精度指标不同匹配关系论证[J].宇航学报, 2011,32(3):697-705)
[9] Xiao Yun, Liu Xiaogang, Guo Feixiao. Core Indexes Design for the Next Generation Satellite Gravimetry Mission [J]. Journal of Geodesy and Geodynamics, 2017,37(1):1-4 ( 肖云,刘晓刚,郭飞宵.新一代重力测量卫星核心指标分析[J]. 大地测量与地球动力学,2017,37(1):1-4)
[10] Kim J. Simulation Study of a Low-Low Satellite-to-Satellite Tracking Mission [D]. Austin: University of Texas, 2000
[11] Loomis B D. Simulation Study of a Follow-on Gra-vity Mission to GRACE [D]. Colorado: University of Colorado, 2009
[12] Flechtner F,Morton P,Watkins M,et al. Status of the GRACE Follow-on Mission[J]. EGU General Assembly, 2013, 141:117-121
[13] Oberdorfer H, Müller J. GOCE Closed-Loop Simulation [J]. Journal of Geodynamics, 2002,33(1):53-63
[14] Wan Xiaoyun, Yu Jinhai. Influence of Polar Gaps on Gravity Field Recovery Using GOCE Data[J]. Acta Geodaetica et Cartographica Sinica,2013,42(3):317-322(万晓云,于锦海. 基地空白对GOCE引力场恢复的影响[J].测绘学报,2013,42(3):317-322)
[15] Zou Xiancai, Li Jiancheng, Wang Haihong, et al. Application of Parallel Computing with OpenMP in Data Processing for Satellite Gravity[J]. Acta Geodaetica et Cartographica Sinica, 2010,39(6):636-641(邹贤才,李建成,汪海洪,等. OpenMP并行计算在卫星重力数据处理中的应用[J].测绘学报,2010,39(6):636-641)
[16] Zhou Hao, Luo Zhicai, Zhong Bo,et al. MPI Parallel Algorithm in Satellite Gravity Field Inversion on the Basis of Least Square Method [J]. Acta Geodaetica et Cartographica Sinica, 2015,44(8):833-839(周浩,罗志才,钟波,等. 利用最小二乘直接法反演卫星重力场模型的MPI并行算法[J].测绘学报,2015,44(8):833-839)
[17] Lu Fei,You Wei,Fan Dongming,et al. Chinese Continental Water Storage and Ocean Water Mass Variations Analysis in Recent Ten Years Based on GRACE RL05 Data [J]. Acta Geodaetica et Cartographica Sinica, 2015,44(2):160-167(卢飞,游为,范东明,等.由GRACE RL05数据反演近10年中国大陆水储量及海水质量变化[J].测绘学报,2015,44(2):160-167)
[18] Luo Jia. A Crossover Approach to Calculate the Time-Variable of the Earth Gravity Field Low Degree Zonal Harmonic Terms Based on LEO Cluster[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 703-708(罗佳.利用LEO星群反演地球重力场低阶带谐项变化的交叠点法[J].测绘学报,2012, 41(5): 703-708)
[19] Chen Q, Shen Y, Zhang X, et al. Global Earth’s Gravity Field Solution with GRACE Orbit and Range Measurements Using Modified Short Arc Approach[J]. Acta Geodaetica et Geophysica, 2014, 50(2): 173-185
[20] Ilk K, Loecher A. The Use of Energy Balance Relations for Validation of Gravity Field Models and Orbit Determination Results [C]. The 36th IAG General Assembly, Prague, Czech, 2005