卫星重力测量低低卫卫跟踪模式解析误差分析研究

Satellite-to-satellite low-low tracking (SST-ll) has an advantage to obtain the time-variable gravity field information with high precision and a huge potential for accuracy gains as it adopts Laser Ranging system, so it is the main mode of the next generation gravity mission. As a result, it is significant to discuss the error analysis of SST-ll. The latest and incoming gravitational models with increasing accuracy and resolution make the computation more difficult since the computation becomes huge and serious numerical instabilities arise when degree/order of models gets higher. It is significant to establish an effective and stable method to analyze the relationship between parameters and scientific requirements and the effects of the measurement noise on accuracies of the recovery of gravity fields. A direct relationship between the power spectrum density (PSD) of SST-ll observations and the coefficients of the Earth’s gravity potential is established based on 2-D FFT, modulation theorem and orbit perturbation theory. Essentially, the aim of this study is to obtain the transfer function between them. The results of this research can directly determine the requirements of the accuracies of orbit determination, accelerometers and ranging system, analyze the matching relationship among these terms, and is useful to design and verify the parameters for the next generation gravity mission.

低低卫卫跟踪(SST-ll)具备高精度获取地球重力场时变信息的优势，而且随着激光测距等技术的发展，SST-ll恢复重力场精度的提升潜力大，将作为下一代重力卫星计划的主要测量模式，因此开展相应的误差分析研究有着重要科学意义和应用价值。随着解算模型分辨率的增加，急剧增长的计算量和数值不稳定性问题已成为制约误差分析研究的主要因素，建立高效、稳定的评估SST-ll恢复重力场精度的方法是开展下一代重力卫星计划研究的重要环节。本项目拟在重力场频谱分析的基础上，利用二维傅立叶变换性质、调制理论和轨道扰动理论建立测量噪声功率谱与重力位系数恢复精度的直接对应关系，即从信号理论的角度建立两者的传递函数。本项目的研究结果可以快速、直接地分析SST-ll中轨道参数和载荷噪声的影响，并回答定轨精度、加速度计和星间距测量精度的需求以及匹配关系，为下一代卫星重力测量计划的初期选取和确定相应载荷指标提供理论指导。

卫星重力测量技术被公认为是探测和研究全球重力场最有效且极具发展潜力的方法之一。任务前期的误差分析是建立科学目标与仪器参数联系的重要手段。传统的误差分析方法是根据卫星轨道扰动理论或者能量守恒理论建立相应的观测方程，然后根据最小二乘法求解方程组。最小二乘误差分析方法从数值的角度间接地进行评估参数的影响，难以直接评估某些单一参数的影响。利用信号与系统理论，本文建立了低低卫—卫跟踪测量噪声功率谱密度与位系数恢复精度的解析关系，这个关系给出了位系数恢复精度与测量噪声功率谱密度一一对应关系。