利用卫星编队探测地球重力场的方法研究与仿真分析
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摘要
本世纪初重力测量卫星CHAMP、GRACE和GOCE的成功发射,昭示着人类迎来了一个前所未有的卫星重力探测时代。尤其是GRACE任务,提供了月时间尺度的时变重力场信息,为研究物质迁移、全球变化、自然灾害等提供了新的重要途径。目前CHAMP任务已经结束,GRACE任务将在三年之内结束,GOCE卫星已经完成其重力场探测的使命。为保证时变重力场探测的连续性,进一步提高静态重力场的探测精度,研究和发展新一代卫星重力任务已经迫在眉睫。利用卫星编队来确定地球重力场可以提高重力卫星任务的时空分辨率,并在一定程度上削弱GRACE任务存在的混频和重力场精度各向异性等问题的影响,已成为国内外相关学者研究的热点问题。本文在此背景下,系统研究了利用各种卫星编队来反演地球重力场的理论方法；通过仿真实验深入探讨了各种卫星编队和卫星星座对不同阶次重力场反演的影响,比较分析了它们解决现有问题的能力；并探索了利用卫星编队来解决混频问题的可行性,可为重力卫星任务的设计与分析提供参考技术依据。
本文的主要研究工作和成果包括：
(1)深入地研究了卫星编队飞行的原理与方法,分析并给出了适应于重力任务的各种卫星编队和卫星星座构形。
提出并实现了利用线性化的C-w方程及其解析解来设计适应于重力任务的卫星编队的方法。本文在圆参考轨道、线性化相对运动、除二体引力外无其它摄动和编队中各卫星具有相同轨道周期这几个假设条件下,推导出描述编队卫星相对运动的C1ohessy-Wiltshire方程及其解析解。通过不同初始相对运动状态设计,给出几种可用于重力任务的卫星编队构形：GRACE-type、Pendulum-type、Cartwheel-type和GRACE-Pendulum-type;分析了卫星编队和卫星星座的主要区别,并以两组GRACE-type卫星编队为基础设计了三种卫星星座模式(ΔM、ΔΩ、Δi)。
(2)基于动力法全面分析了重力卫星关键轨道参数和观测值误差对重力场反演的影响,并进行仿真验算,进而给出了重力卫星轨道关键参数设计的依据。
提出重力卫星轨道高度的选择应以长重复周期和满足卫星寿命为主要参考,选择290km以上并且重复周期较长的高度是重力卫星的最佳合理高度；而轨道倾角则以长重复周期和极空白的影响为依据,尽量选择近极轨的倾角。在轨道参数选定的前提下,对GRACE-type编队中不同类型观测量的误差特性进行了全方位仿真分析,重点分析了定轨误差和星间测距误差对重力场反演精度的影响。结果表明,定轨精度对于重力场低阶项贡献较大,星间测距数据则对重力场中高阶贡献较大；在当前定轨精度2-3cm下,重力场解算的精度主要取决于低低跟踪数据,其精度越高,重力场反演精度也越高；但当星间距离变率精度达到纳米级而轨道误差不变时,定轨精度在一定程度上会影响重力场反演精度,尤其是低阶项部分。
(3)仿真分析了各种卫星编队构形探测地球重力场的能力,结果表明单一的星间观测量是造成重力场条纹误差的关键因素,而联合多方向的观测量有利于去条纹和提高重力场解算精度。
针对GRACE-type、Pendulum-type、Cartwheel-type和GRACE-Pendulum-type这四种卫星编队,比较分析了它们30天数据所反演的不同阶次(n=60、90、120阶)地球重力场的结果。只有沿轨方向观测量的GRACE-type的误差全球分布图显示出明显的南北方向条纹误差,而法向观测量占优Pendulum-type编队则表现出东西方向的条纹误差,这在一定程度上验证了条纹误差是由于轨道设计所造成的固有问题,单一的星间观测量的强相关性导致了重力场各向异性的敏感度。无论解算阶次高低,GRACE-Pendulum-type编队(均衡的沿轨方向+法向观测量)和Cartwheel-type编队(均衡的沿轨方向+径向观测量)的重力场反演精度都较高,与GRACE-type编队相比,对于重力场解算精度的提高可达9%-65%,并明显的消除了条纹误差。这说明均衡的多方向的观测量有利于去条纹和提高重力场解算精度。
(4)首次分析了东西径向Cartwheel和南北径向Cartwheel编队在重力场反演精度上的差异,并提出南北径向Cartwheel编队是适合高阶重力场解算的最优编队构形。
当n=60时,两种Cartwheel编队对于重力场反演的精度相当。但随着解算阶次的增高,发现东西径向编队的重力场反演精度降低,高阶扇谐和田谐系数误差急剧增大,提出地球扁率的影响是导致这种编队在重力场高阶部分的误差增大的主要因素。而南北径向的Cartwheel编队对于高阶重力场反演十分敏感,无论解算阶次高低,都能得到精度较高且各向同性的重力场解算结果。当n=120时,与GRACE-type相比,这种由两颗卫星构成的卫星编队对于重力场解算精度的提高可达50%,已经接近由三颗卫星构成的GRACE-Pendulum-type编队结果,是适合于高阶重力场解算的最优编队构形。
(5)给出了沿轨方向、法向和径向星间观测量对带谐、扇谐和田谐重力场球谐系数的敏感程度,从一个新的角度(即利用不同方向观测量)为设计特定应用需求的重力卫星任务提供了参考。
各卫星编队都包含着不同方向的星间观测量,从它们反演的重力场系数的误差谱图可知,星间沿轨方向观测量和东西径向观测量对高阶扇谐和近扇谐系数反演能力最差,而法向观测量会影响带谐项系数的反演精度,南北径向观测量和均衡的多方向联合的观测量能得到最好的接近各向同性敏感度的全阶次重力场系数分布。
(6)分析了各种卫星星座探测地球重力场的能力,发现采用不同倾角组合(极轨+低倾角)的卫星星座能得到较好的重力场解算结果,并给出低倾角卫星的倾角最优选择范围。
由两组GRACE-type的卫星编队构成的各种卫星星座基于15天观测数据仿真计算了地球重力场,发现可在较短的任务周期中得到较高的重力场解算精度。尤其是采用不同倾角的卫星星座,与30天GRACE-type编队结果相比,对重力场解算的精度提高可达34%。从仿真结果来看,低倾角卫星应选择在70°-75°之间,才能获得全球一致的高精度结果,同时要顾及选择能得到与近极轨卫星重复周期一致的倾角度数。
(7)提出在目前时变信号模型误差的影响下,利用卫星编队并通过动力法确定重力场并不能有效降低混频误差。
分析了海洋潮汐这种时变信号模型误差造成的混频现象对地球重力场反演精度的影响。结果表明,当考虑真实时变信号模型误差时,即使提高了星间观测精度,利用Pendulum-type(?)Cartwheel-type编队也不能消除混频影响。其中,Pendulum-type(?)GRACE-type卫星编队的重力场解算精度相当,而Cartwheel-type编队则显示出较大的误差,这是由于径向观测量对重力场的高频信号更为敏感,包含了更多的海潮模型误差的高频信号。
The launch of gravity satellites CHAMP, GRACE, GOCE at the beginning of this century illustrated an unprecedented era of gravity satellite exploration. The GRACE mission, in particular, provides time-variable gravity field in monthly scale, and serves as a new important tool to investigate mass transformation, global changing, natural disaster and so on. Till now, the CHAMP mission has already finished, the GRACE mission will finish in three years, and the GOCE mission has already finished its mission of gravity field exploration. To keep continuity of gravity field mission and improve exploration precision of static gravity field, it is urgent to develop a new generation of gravity field satellite mission. Using satellite formation technology to determine earth gravity field has been hot issues, since this method could improve spatial-temporal resolution, reduce aliasing effects in GRACE mission and eliminate anisotropy. Under this background, gravity field inverse theories using different types of satellite formation are systematically studied. Through simulation experiments, effects of different types of satellite formation on the gravity field with different orders are analyzed. Then comparative analyses are carried out on their capabilities of solving current problems. The feasibility of solving the problem of aliasing using satellite formation is also studied in the dissertation, which could provide technical reference basis for orbit design of future gravity satellite mission.
Contents and contributions of this dissertation paper mainly include:
(1) Principles and methods of satellite formation are studied. Satellite formation and constellation adaptable to the gravity mission are analyzed and put forward.
Under the assumptions of circular orbit, linear relative motion, only two-body gravitation without any other perturbation, together with identical orbital period, Clohessy-Wiltshire equation and its analytical solution describing relative motions of satellite formation are deduced. By setting different initial relative motion status, the following satellite formation configurations which might be used for gravity field mission: GRACE-type, Pendulum-type, Cartwheel-type and GRACE-Pendulum-type are put forward. Main differences between satellite formation and constellation are given. Then three types of satellite constellation configuration (ΔM, ΔΩ, Δi) are designed based on the condition of containing two types of GRACE-type satellite formation.
(2) Based on the dynamic method, effects of key orbital parameters and observation error on gravity field reflection precision are analyzed and verified through simulation experiments. Then references of gravity satellite orbit key parameters are proposed.
The gravity satellite altitude should refer to long repeated period and satellite lifetime. Altitude of at least290km and that of longer repeated period is suggested. The gravity satellite inclination should refer to long repeated period and consider the effect of polar gap. Inclination of near polar orbit is suggested. In the premise of setting orbital elements, comprehensive simulation analysis of various type of observation error characteristics in GRACE-type is performed, especially the effects of orbital error and inter-satellite ranging error in gravity field inverse. Results show that orbital determination precision contributes on gravity field with low-order, while the inter-satellite ranging precision contributes on the gravity field with middle-to-high order. When orbital precision stays at2～3cm level, resolution accuracy of gravity field depends on inter-satellite ranging data, that is, the higher precision of inter-satellite ranging data, the higher inverse precision of gravity field. However, orbital determination precision impact low order part of gravity field when inter-satellite ranging-rate reaches nano-meter level with invariable orbital error.
(3) Capability of gravity field exploration of various satellite formation is analyzed through simulation experiments. The key factor causing gravity field stripes due to single inter-satellite observation is proposed. Conclusions are drawn that de-striping and resolution improvement of gravity field can be achieved by multi-direction observations.
Inversed30-day gravity field with different orders (n=60,90,120) from four formations:GRACE-type, Pendulum-type, Cartwheel-type and GRACE-Pendulum-type are analyzed. From the global error distribution curves, the north-south stripes error appears obviously in GRACE-type configuration which has only along-track observation, while the east-west stripes error appears obviously in Pendulum-type configuration of which the cross-track observation is the main factor. It proves the theory that stripes error is the inherent problem caused by orbit design partly, and single inter-satellite observation results in gravity anisotropy sensitivity. Despite of orders, GRACE-Pendulum-type configuration (balanced along-track+cross-track observation) and Cartwheel-type configuration (balanced along-track+radial observation) can get better gravity field inversion result, whose solution precision is about9%-65%higher than the one from GRACE-type configuration, and the stripes error is removed significantly. It is concluded that balanced multi-direction observation is useful for de-striping and improving gravity field solution precision.
(4) Difference of gravity field inversion precision between east-west along-track Cartwheel configuration and north-south along-track Cartwheel configuration is analyzed for the first time. The latter one is the optimal formation configuration for high-order gravity field solution.
Inversed gravity field is comparative in precision for both Cartwheel formation when n=60. With the order increasing, the precision of east-west radial formation decreases, while the high-order sectorial harmonic and tesseral harmonic coefficient error increases dramatically. The influence of earth oblateness is regarded as the main factor causing high-order error increment of the gravity field under this type of formation. While the north-south Cartwheel formation is beneficial to the inversion of gravity field with high-order, the gravity field solution result of higher precision with isotropy can be obtained under all orders. When the order reaches120, the gravity field solution precision of this type of satellite formation consisting of two satellites is50%better than the result from GRACE-type formation, and close to the result of GRACE-Pendulum-type formation consists of three satellites. It is the optimal formation configuration for high-order gravity field solution.
(5) Response of along-track, cross-track and radial inter-satellite observations to zonal harmonics, sectorial harmonic and tesseral harmonic coefficients are given, which provides a brand new angle for specified application of gravity field.
All types of satellite formation containing inter-satellite observations from various directions, from the error spectrum of inversed gravity field coefficients, satellite-satellite along-track observation and east-west radial observation has the worst inverse result to high-order sectorial harmonic and near-sectorial harmonic coefficient, while cross-track observation can impact the inverse precision of zonal harmonic coefficient. The north-south radial observation and balanced multi-direction combined observations shall be the best way to get the gravity field coefficient close to the isotropy sensitivity.
(6) Capability of gravity field exploration with various satellite constellation is analyzed. Combination of different inclinations (polar+low inclination) constellation can obtain better gravity field solution result. The optimal ranges of inclination is also suggested.
Gravity fields are simulated with15-day observations based on various satellite constellations, and better precision of gravity field can be achieved in short period. In particular, the resolution precision improves by34%with various inclinations of satellite constellation compared with30-day GRACE-type formation results. Simulation results suggest that lower inclined satellite between70°～75°can get globally consistent results with high-precision. Meanwhile, those inclination should agree with repeated period of the near polar orbit satellite.
(7) Under the influence of time-varying signal model error, aliasing error cannot be solved effectively through satellite formation and gravity field determination from dynamic method.
The effect of aliasing caused by time-varying signal of ocean tide on gravity field inverse precision is analyzed. Results show that when real time-variable signal is considered, aliasing effect cannot be eliminated through Pendulum-type and Cartwheel-type satellite formation even if the inter-satellite observations precision is improved. Resolution of Pendulum-type and GRACE-type satellite formation is comparable, while that of Cartwheel-type shows large error. Possible explanation is that the radial observation is much sensitive to high-frequency signal, which contains more high-frequency signals of ocean tide model errors.
本文的主要研究工作和成果包括：
(1)深入地研究了卫星编队飞行的原理与方法,分析并给出了适应于重力任务的各种卫星编队和卫星星座构形。
提出并实现了利用线性化的C-w方程及其解析解来设计适应于重力任务的卫星编队的方法。本文在圆参考轨道、线性化相对运动、除二体引力外无其它摄动和编队中各卫星具有相同轨道周期这几个假设条件下,推导出描述编队卫星相对运动的C1ohessy-Wiltshire方程及其解析解。通过不同初始相对运动状态设计,给出几种可用于重力任务的卫星编队构形：GRACE-type、Pendulum-type、Cartwheel-type和GRACE-Pendulum-type;分析了卫星编队和卫星星座的主要区别,并以两组GRACE-type卫星编队为基础设计了三种卫星星座模式(ΔM、ΔΩ、Δi)。
(2)基于动力法全面分析了重力卫星关键轨道参数和观测值误差对重力场反演的影响,并进行仿真验算,进而给出了重力卫星轨道关键参数设计的依据。
提出重力卫星轨道高度的选择应以长重复周期和满足卫星寿命为主要参考,选择290km以上并且重复周期较长的高度是重力卫星的最佳合理高度；而轨道倾角则以长重复周期和极空白的影响为依据,尽量选择近极轨的倾角。在轨道参数选定的前提下,对GRACE-type编队中不同类型观测量的误差特性进行了全方位仿真分析,重点分析了定轨误差和星间测距误差对重力场反演精度的影响。结果表明,定轨精度对于重力场低阶项贡献较大,星间测距数据则对重力场中高阶贡献较大；在当前定轨精度2-3cm下,重力场解算的精度主要取决于低低跟踪数据,其精度越高,重力场反演精度也越高；但当星间距离变率精度达到纳米级而轨道误差不变时,定轨精度在一定程度上会影响重力场反演精度,尤其是低阶项部分。
(3)仿真分析了各种卫星编队构形探测地球重力场的能力,结果表明单一的星间观测量是造成重力场条纹误差的关键因素,而联合多方向的观测量有利于去条纹和提高重力场解算精度。
针对GRACE-type、Pendulum-type、Cartwheel-type和GRACE-Pendulum-type这四种卫星编队,比较分析了它们30天数据所反演的不同阶次(n=60、90、120阶)地球重力场的结果。只有沿轨方向观测量的GRACE-type的误差全球分布图显示出明显的南北方向条纹误差,而法向观测量占优Pendulum-type编队则表现出东西方向的条纹误差,这在一定程度上验证了条纹误差是由于轨道设计所造成的固有问题,单一的星间观测量的强相关性导致了重力场各向异性的敏感度。无论解算阶次高低,GRACE-Pendulum-type编队(均衡的沿轨方向+法向观测量)和Cartwheel-type编队(均衡的沿轨方向+径向观测量)的重力场反演精度都较高,与GRACE-type编队相比,对于重力场解算精度的提高可达9%-65%,并明显的消除了条纹误差。这说明均衡的多方向的观测量有利于去条纹和提高重力场解算精度。
(4)首次分析了东西径向Cartwheel和南北径向Cartwheel编队在重力场反演精度上的差异,并提出南北径向Cartwheel编队是适合高阶重力场解算的最优编队构形。
当n=60时,两种Cartwheel编队对于重力场反演的精度相当。但随着解算阶次的增高,发现东西径向编队的重力场反演精度降低,高阶扇谐和田谐系数误差急剧增大,提出地球扁率的影响是导致这种编队在重力场高阶部分的误差增大的主要因素。而南北径向的Cartwheel编队对于高阶重力场反演十分敏感,无论解算阶次高低,都能得到精度较高且各向同性的重力场解算结果。当n=120时,与GRACE-type相比,这种由两颗卫星构成的卫星编队对于重力场解算精度的提高可达50%,已经接近由三颗卫星构成的GRACE-Pendulum-type编队结果,是适合于高阶重力场解算的最优编队构形。
(5)给出了沿轨方向、法向和径向星间观测量对带谐、扇谐和田谐重力场球谐系数的敏感程度,从一个新的角度(即利用不同方向观测量)为设计特定应用需求的重力卫星任务提供了参考。
各卫星编队都包含着不同方向的星间观测量,从它们反演的重力场系数的误差谱图可知,星间沿轨方向观测量和东西径向观测量对高阶扇谐和近扇谐系数反演能力最差,而法向观测量会影响带谐项系数的反演精度,南北径向观测量和均衡的多方向联合的观测量能得到最好的接近各向同性敏感度的全阶次重力场系数分布。
(6)分析了各种卫星星座探测地球重力场的能力,发现采用不同倾角组合(极轨+低倾角)的卫星星座能得到较好的重力场解算结果,并给出低倾角卫星的倾角最优选择范围。
由两组GRACE-type的卫星编队构成的各种卫星星座基于15天观测数据仿真计算了地球重力场,发现可在较短的任务周期中得到较高的重力场解算精度。尤其是采用不同倾角的卫星星座,与30天GRACE-type编队结果相比,对重力场解算的精度提高可达34%。从仿真结果来看,低倾角卫星应选择在70°-75°之间,才能获得全球一致的高精度结果,同时要顾及选择能得到与近极轨卫星重复周期一致的倾角度数。
(7)提出在目前时变信号模型误差的影响下,利用卫星编队并通过动力法确定重力场并不能有效降低混频误差。
分析了海洋潮汐这种时变信号模型误差造成的混频现象对地球重力场反演精度的影响。结果表明,当考虑真实时变信号模型误差时,即使提高了星间观测精度,利用Pendulum-type(?)Cartwheel-type编队也不能消除混频影响。其中,Pendulum-type(?)GRACE-type卫星编队的重力场解算精度相当,而Cartwheel-type编队则显示出较大的误差,这是由于径向观测量对重力场的高频信号更为敏感,包含了更多的海潮模型误差的高频信号。
The launch of gravity satellites CHAMP, GRACE, GOCE at the beginning of this century illustrated an unprecedented era of gravity satellite exploration. The GRACE mission, in particular, provides time-variable gravity field in monthly scale, and serves as a new important tool to investigate mass transformation, global changing, natural disaster and so on. Till now, the CHAMP mission has already finished, the GRACE mission will finish in three years, and the GOCE mission has already finished its mission of gravity field exploration. To keep continuity of gravity field mission and improve exploration precision of static gravity field, it is urgent to develop a new generation of gravity field satellite mission. Using satellite formation technology to determine earth gravity field has been hot issues, since this method could improve spatial-temporal resolution, reduce aliasing effects in GRACE mission and eliminate anisotropy. Under this background, gravity field inverse theories using different types of satellite formation are systematically studied. Through simulation experiments, effects of different types of satellite formation on the gravity field with different orders are analyzed. Then comparative analyses are carried out on their capabilities of solving current problems. The feasibility of solving the problem of aliasing using satellite formation is also studied in the dissertation, which could provide technical reference basis for orbit design of future gravity satellite mission.
Contents and contributions of this dissertation paper mainly include:
(1) Principles and methods of satellite formation are studied. Satellite formation and constellation adaptable to the gravity mission are analyzed and put forward.
Under the assumptions of circular orbit, linear relative motion, only two-body gravitation without any other perturbation, together with identical orbital period, Clohessy-Wiltshire equation and its analytical solution describing relative motions of satellite formation are deduced. By setting different initial relative motion status, the following satellite formation configurations which might be used for gravity field mission: GRACE-type, Pendulum-type, Cartwheel-type and GRACE-Pendulum-type are put forward. Main differences between satellite formation and constellation are given. Then three types of satellite constellation configuration (ΔM, ΔΩ, Δi) are designed based on the condition of containing two types of GRACE-type satellite formation.
(2) Based on the dynamic method, effects of key orbital parameters and observation error on gravity field reflection precision are analyzed and verified through simulation experiments. Then references of gravity satellite orbit key parameters are proposed.
The gravity satellite altitude should refer to long repeated period and satellite lifetime. Altitude of at least290km and that of longer repeated period is suggested. The gravity satellite inclination should refer to long repeated period and consider the effect of polar gap. Inclination of near polar orbit is suggested. In the premise of setting orbital elements, comprehensive simulation analysis of various type of observation error characteristics in GRACE-type is performed, especially the effects of orbital error and inter-satellite ranging error in gravity field inverse. Results show that orbital determination precision contributes on gravity field with low-order, while the inter-satellite ranging precision contributes on the gravity field with middle-to-high order. When orbital precision stays at2～3cm level, resolution accuracy of gravity field depends on inter-satellite ranging data, that is, the higher precision of inter-satellite ranging data, the higher inverse precision of gravity field. However, orbital determination precision impact low order part of gravity field when inter-satellite ranging-rate reaches nano-meter level with invariable orbital error.
(3) Capability of gravity field exploration of various satellite formation is analyzed through simulation experiments. The key factor causing gravity field stripes due to single inter-satellite observation is proposed. Conclusions are drawn that de-striping and resolution improvement of gravity field can be achieved by multi-direction observations.
Inversed30-day gravity field with different orders (n=60,90,120) from four formations:GRACE-type, Pendulum-type, Cartwheel-type and GRACE-Pendulum-type are analyzed. From the global error distribution curves, the north-south stripes error appears obviously in GRACE-type configuration which has only along-track observation, while the east-west stripes error appears obviously in Pendulum-type configuration of which the cross-track observation is the main factor. It proves the theory that stripes error is the inherent problem caused by orbit design partly, and single inter-satellite observation results in gravity anisotropy sensitivity. Despite of orders, GRACE-Pendulum-type configuration (balanced along-track+cross-track observation) and Cartwheel-type configuration (balanced along-track+radial observation) can get better gravity field inversion result, whose solution precision is about9%-65%higher than the one from GRACE-type configuration, and the stripes error is removed significantly. It is concluded that balanced multi-direction observation is useful for de-striping and improving gravity field solution precision.
(4) Difference of gravity field inversion precision between east-west along-track Cartwheel configuration and north-south along-track Cartwheel configuration is analyzed for the first time. The latter one is the optimal formation configuration for high-order gravity field solution.
Inversed gravity field is comparative in precision for both Cartwheel formation when n=60. With the order increasing, the precision of east-west radial formation decreases, while the high-order sectorial harmonic and tesseral harmonic coefficient error increases dramatically. The influence of earth oblateness is regarded as the main factor causing high-order error increment of the gravity field under this type of formation. While the north-south Cartwheel formation is beneficial to the inversion of gravity field with high-order, the gravity field solution result of higher precision with isotropy can be obtained under all orders. When the order reaches120, the gravity field solution precision of this type of satellite formation consisting of two satellites is50%better than the result from GRACE-type formation, and close to the result of GRACE-Pendulum-type formation consists of three satellites. It is the optimal formation configuration for high-order gravity field solution.
(5) Response of along-track, cross-track and radial inter-satellite observations to zonal harmonics, sectorial harmonic and tesseral harmonic coefficients are given, which provides a brand new angle for specified application of gravity field.
All types of satellite formation containing inter-satellite observations from various directions, from the error spectrum of inversed gravity field coefficients, satellite-satellite along-track observation and east-west radial observation has the worst inverse result to high-order sectorial harmonic and near-sectorial harmonic coefficient, while cross-track observation can impact the inverse precision of zonal harmonic coefficient. The north-south radial observation and balanced multi-direction combined observations shall be the best way to get the gravity field coefficient close to the isotropy sensitivity.
(6) Capability of gravity field exploration with various satellite constellation is analyzed. Combination of different inclinations (polar+low inclination) constellation can obtain better gravity field solution result. The optimal ranges of inclination is also suggested.
Gravity fields are simulated with15-day observations based on various satellite constellations, and better precision of gravity field can be achieved in short period. In particular, the resolution precision improves by34%with various inclinations of satellite constellation compared with30-day GRACE-type formation results. Simulation results suggest that lower inclined satellite between70°～75°can get globally consistent results with high-precision. Meanwhile, those inclination should agree with repeated period of the near polar orbit satellite.
(7) Under the influence of time-varying signal model error, aliasing error cannot be solved effectively through satellite formation and gravity field determination from dynamic method.
The effect of aliasing caused by time-varying signal of ocean tide on gravity field inverse precision is analyzed. Results show that when real time-variable signal is considered, aliasing effect cannot be eliminated through Pendulum-type and Cartwheel-type satellite formation even if the inter-satellite observations precision is improved. Resolution of Pendulum-type and GRACE-type satellite formation is comparable, while that of Cartwheel-type shows large error. Possible explanation is that the radial observation is much sensitive to high-frequency signal, which contains more high-frequency signals of ocean tide model errors.
引文
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