通过对静止卫星在三轴椭球参数条件下地心坐标的标称投影公式推导过程,建立了经纬度到单位平面位置的可逆映射方程,其正反算公式精度可达10<'-20>;并对大地坐标的经纬度进行了类似的推导,但标识线垂直地表而不过地心的坐标定义导致正算公式中存在角度正切的四次方项,因此反算需要采用数值解法.两组解析表达式为查照表的建立提供了直接的数学依据,相对于迭代数值计算方法而言,解析方法更便于分析投影过程的误差和畸变.围绕FY2-C卫星地面系统工程中查照表的重建,兼顾卫星图像陆地位置与主要大陆轮廓数据的投影吻合,需要对单位平面的投影进行放大和平移,并提供多组可选择的放大因子,使得经纬度到图像点映射与查照表对应值整体误差较小.建议根据实际应用的坐标系统、卫星位置参数、地球参数选择不同的匹配参数.这种方法可以应用于图像点地理位置精度要求很高但计算不是特别频繁的数据处理算法中,如相对定标和定位,但在其他算法中除了精度以外查照表还是有作用的.

Presently the lookup table is adoptedwhen corresponding relation between the position of remote sensing images and the geographic coordinates, which are involved in ground system engineering ofgeostationary satellites. For the corresponding geographic coordinates of sub-pixelorcorresponding pointofnonstandard grid nodes, which are not in lookup table, bilinear interpolation have to be introduced so that the precision loses remarkably for the image location. By deducing the formulas of geostationary satellite normalized projection at the condition of three-axis ellipsoidalparameter, the reversible equation from longitude/latitude to position on unitplane is established, which provides the mathematical reliance for lookup table for satellite image engineering. And corresponding match parameter for FY2-C application is provided after comparing with the practicing data of lookup table. The same procedure is applied to the situation of geographic coordinate system, but the inverse problem needs numerical solutions. The inversemethod of geocenter coordinate system may be used as approximation when ellipsoidal parameter is close to sphere, while notapplicable for fine image processing. Thepossibility of the application in FY2-C engineering of this reversible formulas is also discussed, with the analysis of the errordistribution comparedwith practicaldata and the selection ofapplicable parameters forbest fitting actualdata.