卫星重力加速度计标校方法研究
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摘要
重力卫星搭载的加速度计用于测量非保守力。加速度计的偏差和标度因数在空间随环境变化而缓慢变化,需要实施外部标定,以方便正确应用于数据处理。很多文献研究了动力学标定法、定轨标定方法、能量标定法等,在快速性、高精度性等方面有待提高。本文提出了加速度标定方法,建立数学模型,用于重力卫星的加速度计标定。结果表明,该方法是一种有效的标定方法,在目前的数据条件下,其标校达到10-8—10-9 m/s2水平,标校效果X方向参数最优,Z轴次之,Y轴最差。加速度标校法受到先验地球重力场模型的影响,需要采用迭代方法,逐步逼近真实的加速度计参数。如果提高GNSS轨高产品采样率,可提高总加速度计算精度,从而提高加速度计的定标精度。加速度标定方法是一种有效、快速、精度较高的标定方法,提供精确的标定参数,可以在重力卫星数据处理中使用。
Satellite gravimetry is a technique of surveying the earth's gravity and geoid and their changing signal. The data are used in geodesy science, environment monitoring, seismic, hydrology, and ocean science.An accelerometer is a core payload in the satellite-to-satellite tracking model or satellite gravity gradiometry and is used to sense nongravity forces. An accelerometer cannot survey a non-conservative force absolutely for its bias, drift, scale, and second-order terms. Parameters change with the environment, status, and time. Thus, the accelerometer should be calibrated and validated. The accelerometer STAR is loaded on the Challenging Mini-Satellite Payload for Geophysical Research and Application(CHAMP)satellite and has an accuracy of 10~(-8)—10~(-9) m/s~2. The SuperStar accelerometer is loaded on the Gravity Recovery And Climate Experiment(GRACE) satellite, and its accuracy is improved to 10~(-9)—10~(-10) m/s~2. The GRADIO accelerometer is loaded on the Gravity field and steadystate Ocean Circulation Explorer(GOCE) satellite, and its accuracy is 10~(-11)—10~(-12) m/s~2. With the improving accuracy, additional requirements are needed to calibrate the accelerometer. In terms of data type, the three calibration methods are as follows: The first method is direct calibration, where non-gravity force model data are used to compare the output of the accelerometer. The second is the dynamic method, where GNSS data are used to determine the satellite orbit and the accelerometer bias parameters together. The third is the integrated method, where all data are used to determine the total coefficients of the gravity model and the bias of the accelerometer. In addition, the energy domain, the cross point, and the gravity upcontinue methods are used to calibrate the accelerometer. The energy domain method is based on persistence energy. The dissipative energy is deduced by the satellite position and velocity. Then, the parameters of the accelerometer are evaluated from the dissipative energy. Its accuracy is not better because the dissipative energy cannot be calculated precisely given the error of the satellite position and velocity. The cross point method is based on the hypothesis that the force of satellite, which crosses a point twice, is equivalent. Evidently, it is an inaccurate method. The gravity up-continue method is used to calibrate the gravity gradiometer. All these methods have been used to calibrate the accelerometer on CHAMP and GRACE. Results indicate that the dynamic and integrated methods are appropriate for external calibration. A new calibration method called the acceleration domain method is proposed. The calibration method is discussed, and the mathematic model is deduced. The acceleration domain method is used to calibrate the GRACE accelerometer. Results indicate that the total calibration accuracy is 10~(-8)—10~(-9) m/s~2. The best calibration is that of the X-axis parameters, followed by the Z-axis parameters, and then the Y-axis. The acceleration domain method effectively determines the accelerometer parameters. The calibration method is affected by the prior earth gravity model. Thus, iterative procedures should be applied. The accuracy of total acceleration, which is calculated from GNSS data, is related to the position sample rate. Thus, if the GNSS data rate is increased, then the calibration accuracy is improved. If the GNSS data rate is 1 s, and the calibration accuracy is 10~(-9)—10~(-10) m/s~2, then the accuracy is improved 8–10 times.
Satellite gravimetry is a technique of surveying the earth's gravity and geoid and their changing signal. The data are used in geodesy science, environment monitoring, seismic, hydrology, and ocean science.An accelerometer is a core payload in the satellite-to-satellite tracking model or satellite gravity gradiometry and is used to sense nongravity forces. An accelerometer cannot survey a non-conservative force absolutely for its bias, drift, scale, and second-order terms. Parameters change with the environment, status, and time. Thus, the accelerometer should be calibrated and validated. The accelerometer STAR is loaded on the Challenging Mini-Satellite Payload for Geophysical Research and Application(CHAMP)satellite and has an accuracy of 10~(-8)—10~(-9) m/s~2. The SuperStar accelerometer is loaded on the Gravity Recovery And Climate Experiment(GRACE) satellite, and its accuracy is improved to 10~(-9)—10~(-10) m/s~2. The GRADIO accelerometer is loaded on the Gravity field and steadystate Ocean Circulation Explorer(GOCE) satellite, and its accuracy is 10~(-11)—10~(-12) m/s~2. With the improving accuracy, additional requirements are needed to calibrate the accelerometer. In terms of data type, the three calibration methods are as follows: The first method is direct calibration, where non-gravity force model data are used to compare the output of the accelerometer. The second is the dynamic method, where GNSS data are used to determine the satellite orbit and the accelerometer bias parameters together. The third is the integrated method, where all data are used to determine the total coefficients of the gravity model and the bias of the accelerometer. In addition, the energy domain, the cross point, and the gravity upcontinue methods are used to calibrate the accelerometer. The energy domain method is based on persistence energy. The dissipative energy is deduced by the satellite position and velocity. Then, the parameters of the accelerometer are evaluated from the dissipative energy. Its accuracy is not better because the dissipative energy cannot be calculated precisely given the error of the satellite position and velocity. The cross point method is based on the hypothesis that the force of satellite, which crosses a point twice, is equivalent. Evidently, it is an inaccurate method. The gravity up-continue method is used to calibrate the gravity gradiometer. All these methods have been used to calibrate the accelerometer on CHAMP and GRACE. Results indicate that the dynamic and integrated methods are appropriate for external calibration. A new calibration method called the acceleration domain method is proposed. The calibration method is discussed, and the mathematic model is deduced. The acceleration domain method is used to calibrate the GRACE accelerometer. Results indicate that the total calibration accuracy is 10~(-8)—10~(-9) m/s~2. The best calibration is that of the X-axis parameters, followed by the Z-axis parameters, and then the Y-axis. The acceleration domain method effectively determines the accelerometer parameters. The calibration method is affected by the prior earth gravity model. Thus, iterative procedures should be applied. The accuracy of total acceleration, which is calculated from GNSS data, is related to the position sample rate. Thus, if the GNSS data rate is increased, then the calibration accuracy is improved. If the GNSS data rate is 1 s, and the calibration accuracy is 10~(-9)—10~(-10) m/s~2, then the accuracy is improved 8–10 times.
引文
Dai S W,Wan L and Xu S H.2014.Accelerometer calibration method based on Iterative calculation.Ship Electronic Engineering,34(1):63-65,95(戴邵武,万龙,徐胜红.2014.基于迭代计算的加速度计标定方法.舰船电子工程,34(1):63-65,95)[DOI:10.3969/j.issn1672-9730.2014.01.018]
Drinkwater M R,Haagmans R,Muzi D,Popescu A,Floberghagen R,Kern M and Fehringer M.2007.The GOCE gravity mission:ESA’s first core Earth explorer.Proceedings of the 3rd International GOCE User Workshop.Frascati,Italy:European Space Agency
Perosanz F,Biancale R,Lemoine J M,Vales N,Loyer S and Bruinsma S.2005.Evaluation of the CHAMP accelerometer on two years of mission//Reigber C,Lühr H,Schwintzer P and Wickert J,eds.Earth Observation with CHAMP,Results from Three Years in Orbit.Berlin Heidelberg:Springer:77-82[DOI:10.1007/3-540-26800-6_12]
Qian X W and Cai T J.2016.Calibration method for gravity gradiometer of rotating accelerometer.Journal of Chinese Inertial Technology,24(4):427-430,436(钱学武,蔡体菁.2016.旋转加速度计重力梯度仪标定方法.中国惯性技术学报,24(4):427-430,436)[DOI:10.13695/j.cnki.12-1222/o3.2016.04.002]
Reigber C,Balmino G,Schwintzer P,Biancale R,Bode A,Lemoine JM,K?nig R,Loyer S,Neumayer H,Marty J C,Barthelmes F,Perosanz F and Zhu S Y.2002.A high-quality global gravity field model from CHAMP GPS tracking data and accelerometry(EI-GEN-1s).Geophysical Research Letters,29(14):37-1-37-4[DOI:10.1029/2002GL015064]
Tapley B D,Bettadpur S,Watkins M and Reigber C.2004.The gravity recovery and climate experiment:mission overview and early results.Geophysical Research Letters,31(9):L09607[DOI:10.1029/2004GL019920]
Xin N,Qiu L D,Zhang L H and Liu N J.2016.On-orbit calibration algorithm of electrostatic accelerometer for gravity measurement satellite.Spacecraft Engineering,25(1):25-30(辛宁,邱乐德,张立华,刘乃金.2016.一种重力测量卫星静电加速度计在轨标定算法.航天器工程,25(1):25-30)[DOI:10.3969/j.issn.1673-8748.2016.01.004]
Xiong Y Q,Wang H B,Xu X L and Zhao C Y.2011.The calibration research for GRACE accelerometer.Scientia Sinica(Physica,Mechanica and Astronomica),41(11):1319-1327(熊永清,汪宏波,许晓丽,赵长印.2011.GRACE加速仪资料定标研究.中国科学(物理学力学天文学),41(11):1319-1327)[DOI:10.1360/132010-1234]
Xu T H and Yang Y X.2005.Spectral analysis on time series of calibration parameters of CHAMP accelerometer.Chinese Journal of Space Science,25(2):143-148(徐天河,杨元喜.2005.CHAMP卫星加速度计标校参数序列的谱分析.空间科学学报,25(2):143-148)[DOI:10.3969/j.issn.0254-6124.2005.02.011]
Xu X Y,Li J C,Wang Z T and Zou X C.2008.Calibration of GRACEaccelerometer using reference gravity field model based on energy balance approach.Geomatics and Information Science of Wuhan University,33(1):72-75(徐新禹,李建成,王正涛,邹贤才.2008.利用参考重力场模型基于能量法确定GRACE加速度计校准参数.武汉大学学报(信息科学版),33(1):72-75)
Zhang X F and Shen Y Z.2007.Calibration of CHAMP accelerometer data with dynamical method.Geomatics and Information Science of Wuhan University,32(2):176-179(张兴福,沈云中.2007.利用动力学法标校CHAMP卫星加速度计数据.武汉大学学报(信息科学版),32(2):176-179)[DOI:10.3321/j.issn:1671-8860.2007.02.021]
Zhou Z B,Bai Y Z,Zhu Z and Zhang X M.2009.In-orbit calibration methods of accelerometer parameters on satellite-borne gravimetry.Chinese Space Science and Technology,29(6):74-80(周泽兵,白彦峥,祝竺,张晓敏.2009.卫星重力测量中加速度计在轨参数校准方法研究.中国空间科学技术,29(6):74-80)[DOI:b10.3321/j.issn:1000-758X.2009.06.012]
Zhu Z,Zhang X M and Zhou Z B.2010.In-orbit verification for accelerometers using rotating spacecraft method.Journal of Astronautics,31(5):1362-1367(祝竺,张晓敏,周泽兵.2010.利用旋转卫星法开展加速度计在轨检验研究.宇航学报,31(5):1362-1367)[DOI:10.3873/j.issn.1000-1328.2010.05.018]
Zou X C,Li J C,Luo J and Xu X Y.2007.Calibration of onboard accelerometer by dynamic method.Geomatics and Information Science of Wuhan University,32(12):1152-1155(邹贤才,李建成,罗佳,徐新禹.2007.星载加速度计的动力法校准.武汉大学学报(信息科学版),32(12):1152-1155)[DOI:10.3969/j.issn.1671-8860.2007.12.016]
Zou X C,Li J C Zhong L P and Xu X Y.2015.Calibration of the accelerometers Onboard GRACE with the dynamic method.Geomatics and Information Science of Wuhan University,40(3):357-360(邹贤才,李建成,衷路萍,徐新禹.2015.动力法校准GRACE星载加速度计.武汉大学学报(信息科学版),40(3):357-360)[DOI:10.13203/j.whugis20130269]
Drinkwater M R,Haagmans R,Muzi D,Popescu A,Floberghagen R,Kern M and Fehringer M.2007.The GOCE gravity mission:ESA’s first core Earth explorer.Proceedings of the 3rd International GOCE User Workshop.Frascati,Italy:European Space Agency
Perosanz F,Biancale R,Lemoine J M,Vales N,Loyer S and Bruinsma S.2005.Evaluation of the CHAMP accelerometer on two years of mission//Reigber C,Lühr H,Schwintzer P and Wickert J,eds.Earth Observation with CHAMP,Results from Three Years in Orbit.Berlin Heidelberg:Springer:77-82[DOI:10.1007/3-540-26800-6_12]
Qian X W and Cai T J.2016.Calibration method for gravity gradiometer of rotating accelerometer.Journal of Chinese Inertial Technology,24(4):427-430,436(钱学武,蔡体菁.2016.旋转加速度计重力梯度仪标定方法.中国惯性技术学报,24(4):427-430,436)[DOI:10.13695/j.cnki.12-1222/o3.2016.04.002]
Reigber C,Balmino G,Schwintzer P,Biancale R,Bode A,Lemoine JM,K?nig R,Loyer S,Neumayer H,Marty J C,Barthelmes F,Perosanz F and Zhu S Y.2002.A high-quality global gravity field model from CHAMP GPS tracking data and accelerometry(EI-GEN-1s).Geophysical Research Letters,29(14):37-1-37-4[DOI:10.1029/2002GL015064]
Tapley B D,Bettadpur S,Watkins M and Reigber C.2004.The gravity recovery and climate experiment:mission overview and early results.Geophysical Research Letters,31(9):L09607[DOI:10.1029/2004GL019920]
Xin N,Qiu L D,Zhang L H and Liu N J.2016.On-orbit calibration algorithm of electrostatic accelerometer for gravity measurement satellite.Spacecraft Engineering,25(1):25-30(辛宁,邱乐德,张立华,刘乃金.2016.一种重力测量卫星静电加速度计在轨标定算法.航天器工程,25(1):25-30)[DOI:10.3969/j.issn.1673-8748.2016.01.004]
Xiong Y Q,Wang H B,Xu X L and Zhao C Y.2011.The calibration research for GRACE accelerometer.Scientia Sinica(Physica,Mechanica and Astronomica),41(11):1319-1327(熊永清,汪宏波,许晓丽,赵长印.2011.GRACE加速仪资料定标研究.中国科学(物理学力学天文学),41(11):1319-1327)[DOI:10.1360/132010-1234]
Xu T H and Yang Y X.2005.Spectral analysis on time series of calibration parameters of CHAMP accelerometer.Chinese Journal of Space Science,25(2):143-148(徐天河,杨元喜.2005.CHAMP卫星加速度计标校参数序列的谱分析.空间科学学报,25(2):143-148)[DOI:10.3969/j.issn.0254-6124.2005.02.011]
Xu X Y,Li J C,Wang Z T and Zou X C.2008.Calibration of GRACEaccelerometer using reference gravity field model based on energy balance approach.Geomatics and Information Science of Wuhan University,33(1):72-75(徐新禹,李建成,王正涛,邹贤才.2008.利用参考重力场模型基于能量法确定GRACE加速度计校准参数.武汉大学学报(信息科学版),33(1):72-75)
Zhang X F and Shen Y Z.2007.Calibration of CHAMP accelerometer data with dynamical method.Geomatics and Information Science of Wuhan University,32(2):176-179(张兴福,沈云中.2007.利用动力学法标校CHAMP卫星加速度计数据.武汉大学学报(信息科学版),32(2):176-179)[DOI:10.3321/j.issn:1671-8860.2007.02.021]
Zhou Z B,Bai Y Z,Zhu Z and Zhang X M.2009.In-orbit calibration methods of accelerometer parameters on satellite-borne gravimetry.Chinese Space Science and Technology,29(6):74-80(周泽兵,白彦峥,祝竺,张晓敏.2009.卫星重力测量中加速度计在轨参数校准方法研究.中国空间科学技术,29(6):74-80)[DOI:b10.3321/j.issn:1000-758X.2009.06.012]
Zhu Z,Zhang X M and Zhou Z B.2010.In-orbit verification for accelerometers using rotating spacecraft method.Journal of Astronautics,31(5):1362-1367(祝竺,张晓敏,周泽兵.2010.利用旋转卫星法开展加速度计在轨检验研究.宇航学报,31(5):1362-1367)[DOI:10.3873/j.issn.1000-1328.2010.05.018]
Zou X C,Li J C,Luo J and Xu X Y.2007.Calibration of onboard accelerometer by dynamic method.Geomatics and Information Science of Wuhan University,32(12):1152-1155(邹贤才,李建成,罗佳,徐新禹.2007.星载加速度计的动力法校准.武汉大学学报(信息科学版),32(12):1152-1155)[DOI:10.3969/j.issn.1671-8860.2007.12.016]
Zou X C,Li J C Zhong L P and Xu X Y.2015.Calibration of the accelerometers Onboard GRACE with the dynamic method.Geomatics and Information Science of Wuhan University,40(3):357-360(邹贤才,李建成,衷路萍,徐新禹.2015.动力法校准GRACE星载加速度计.武汉大学学报(信息科学版),40(3):357-360)[DOI:10.13203/j.whugis20130269]