随机Dirichlet问题解的调和展开

针对重力学随机Dirichlet问题,通过适当地对边界检验函数的分解,并在随机边界样本空间中提取确定性部分的对偶基,本文将随机Dirichlet问题的一般解展开为一随机系数的调和级数形式。     

A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.     

基于Oracle Spatial的多元重力场信息数据库的设计与应用

随着地球重力场信息多元化的发展及其应用领域越来越广,科学高效的管理和应用重力场信息数据就显得尤为重要。文中介绍了基于Oracle Spatial技术设计与构建的重力场信息数据库的结构框架,分析了存储数据信息的种类、属性及特点,研究了数据的存储方式。在多元化重力场数据与基础地图数据统一管理的基础上,初步实现了多元化重力场信息的存储、查询、计算、绘图及显示等功能。     

地壳运动速度场插值方法研究

分析了构建速度场的统计模型和函数模型法,提出利用两种模型逼近原始观测速度的综合逼近法,以减少剩余误差。计算和比较了各种方法,结果显示,综合法优于单独利用统计模型和函数模型法。     

Modeling errors in upward continuation for INS gravity compensation

Accurate upward continuation of gravity anomalies supports future precision, free-inertial navigation systems, since the latter cannot by themselves sense the gravitational field and thus require appropriate gravity compensation. This compensation is in the form of horizontal gravity components. An analysis of the model errors in upward continuation using derivatives of the standard Pizzetti integral solution (spherical approximation) shows that discretization of the data and truncation of the integral are the major sources of error in the predicted horizontal components of the gravity disturbance. The irregular shape of the data boundary, even the relatively rough topography of a simulated mountainous region, has only secondary effect, except when the data resolution is very high (small discretization error). Other errors due to spherical approximation are even less important. The analysis excluded all measurement errors in the gravity anomaly data in order to quantify just the model errors. Based on a consistent gravity field/topographic surface simulation, upward continuation errors in the derivatives of the Pizzetti integral to mean altitudes of about 3,000 and 1,500 m above the mean surface ranged from less than 1 mGal (standard deviation) to less than 2 mGal (standard deviation), respectively, in the case of 2 arcmin data resolution. Least-squares collocation performs better than this, but may require significantly greater computational resources.     

UKF在基于地磁场的自主导航中的应用

本文研究了基于地磁场的自王导航,建立了以卫星轨道动力学方程为基础的系统状态方程,并详细推导了以地磁场矢量为观测量时的观测方程;为了解决系统的非线性问题把常用来解决非线性问题的UKF引入到基于地磁场的自主导航系统中;最后,用Matlab对基于地磁场的自主导航系统进行了仿真,仿真结果表明UKF有很好的收敛性和稳定性.     

空间大地测量技术实测台站速度场精度分析

利用国际上3个著名的数据分析处理中心CSR、JPL和GSFC给出的3种空间大地测量技术实测的台站运动速度场数据,解算不同空间技术速度场之间的转换参数,即速度场之间的系统差。在扣除两两技术之间速度场的系统差后,用速度场残差计算了空间技术速度场之间的不符值加权中误差作为衡量不同空间技术实测台站速度场的外部检核指标,即外符精度。计算结果表明,VLBI和GPS实测台站地心速度已经达到1 mm/a的精度;SLR实测台站地心速度已经达到2 mm/a的精度。     

多类重力场模型的精度分析

分析国际公布的EGM2008、GECO和EIGEN-6C4等超高阶重力场模型及GOCO03S、GOCONSGCF2DIRR5和GOCONSGCF2TIMR5等低阶重力场模型的内符合精度。利用实测的GNSS/水准数据对各模型进行外符合精度的检核。分析6个模型在不同阶次组合的精度,进而选取可靠的截断阶次确定组合重力场模型。计算结果表明:EGM2008、GECO、EIGEN-6C4及DIRR5四个重力场模型的阶方差均保持在mm级,而GOCO03S在191阶之后的精度达到dm级,TIMR5模型在228阶之后的精度达到dm级;6个重力场模型中,EIGEN-6C4模型的累计阶方差最小;EGM2008、GECO模型的互差阶方差在高频部分呈现差异,而在超高阶部分两种模型的互差阶方差符合性好;与EGM2008模型相比,其组合重力场模型高程异常精度最优可达0.063 m,精度提升幅度为15%,与GECO模型相比,其组合重力场模型高程异常精度最优可达0.060 m,精度提升幅度为23%,与EIGEN-6C4模型相比,其对应的组合重力场模型高程异常精度最优可达0.064 m,精度提升幅度为18%,因此,组合重力场模型能提高重力场模型高程异常的精度。     

基于大视场光学测量设备的多星观测和解算天文经纬度研究

本文提出了一种新的基于大视场光学测量设备和GPS测量点位天文坐标的方法,即测量多个星体方位角相对于主光轴方位角的增量,然后通过非线性最小二乘法解算出点位的天文坐标。采用该方法不仅可以避免讨论大气蒙气差的修正问题,而且能够满足高精度天文坐标的测量要求。     

基于2.5维面的气象数据可视化技术——以风场数据显示为例

根据2.5维面的设计思想及曲面可视化的方法,结合部分气象数据信息具有相同的经纬度范围和海拔高度的特点,构造了基于温度和可降水量的2.5维面,并重点提出在2.5维面上进行风场流线可视化的方法。实践证明,应用2.5维面分析气象数据在一定程度上平衡了运算量和可视化结果之间的矛盾,对地理环境气象数据的分析和比较有帮助作用。