Analytical Error Analysis For Satellite Gravity Field Determination

Satellite gravimetry is recognized as one of the most effective and potential technique for exploring and researching the Earth’s gravity field with a global coverage. In the beginning of the21st century, dedicated gravity field missions like CHAMP, GRACE and GOCE were successfully launched. Based on the high spatial resolution and accuracy gravity field information retrieved from the missions, we can have a further understanding of the mass transport, mass anomalies, mass distribution in the Earth system, the fine structure of the Earth, and so on. Currently, the corresponding methods of error analysis, which determine science requirements and mission parameters, are mainly based on least-squares (LS) theory, and basically divided into two types:the time-wise approach and the space-wise approach. The solution to the equations based on LS has the optimum statistical properties, but both the time-wise and space-wise approaches address the effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of view. It is difficult to directly estimate the effect of the parameters, and the latest and incoming gravitational models with increasing accuracy and resolution makes the computation more difficult since the computation become huge and serious numerical instabilities arise when degree/order of models gets higher.For the reasons mentioned above, it is important to develop a direct and efficient procedure of error analysis for satellite gravity field determination. Direct relationship between the power spectrum density of satellite gravimetry observations and the coefficients of the Earth’s gravity potential is established based on definitions of the instrument’s power spectrum density and the Earth’s gravity field potential, and then the effect of measurement accuracy, the altitude of the satellite, and the operation duration on recovering of the Earth’s gravity field is analyzed by using this method which is based on the assumption that the measurement errors are white. Furthermore, the relationship between the spatial frequencies and the temporal frequencies is concluded based on2-D Fourier methods,2-D sample theorem and modulation theory. Thus, it is possible to quantify the effect of color noise in missions. From the results in this study, it is indicated that the low frequency noise degrades the gravity field recovery in all degrees and the signals of gravity information at low frequencies are also filtered out when filters are employed, so the colored noise must be processed carefully.The analytical relationship between the measurement error PSD of SST-hl and the coefficient of the Earth gravity potential is established by using a method based on the principles of SST-hl, the linear perturbations theory and control theory. Then we analysis the effects of GPS and accelerometer measurement errors on the accuracy of the Earth gravity field recovery, which is limited by the accuracy of GPS.In addition, the lunar satellite gravity gradiometry is also proposed and discussed for improving the Moon’s gravity field model. This mode not only is effective in recovering the medium and short wavelength gravity field information, but also can reduce the effect of non-gravitational forces in order to improve the recovery accuracy. The mission scenario with a high accuracy of14mGal and the geoid with an accuracy of20.5cm at a spatial resolution of7km is recommended, which is under the conditions of orbit height of20km and gradiometer accuracy level of30mE/Hz1/2.The method established in this study is effective and direct compared with the others based on the least square approach, and is very useful to design and verify the parameters for the Earth gravity recovery missions.