Methodology Research And Simulation Analysis Of The Earth’s Gravity Field Determination Using Satellite Formation

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.