绝对精度自动匹配的图斑椭球面积解算方法

A Calculation Method for Area of Polygons on the Earth Spherop with Automatic Matching of Absolute Precision

针对传统模拟积分法的图斑椭球面积误差模型构造复杂及绝对精度无法自动匹配问题,以梯形图幅面积理论计算公式为关联纽带,采用纬线等分割补的手段构建了梯形图块面积的通用计算公式。在分析梯形图块面积替代误差数值分布规律的基础上,通过纬度积分步长变量的引入建立了严密的面积替代误差数列模型;阐明了纬度积分步长变量调控下面积替代误差数列的极限收敛特性,设计了面积替代误差的超限判定准则;构建了面积误差限定条件下纬度积分步长的自动调控模型,提出了一种绝对精度自动匹配的图斑椭球面积解算方法。实验结果表明:该算法可实现任意图斑椭球面积的精确量算,且绝对精度控制在给定误差阈值之内。

Aiming at the complex construction of the spheroid polygon area error model of the traditional simulation integral method and the inability to automatically match the absolute precision,the general calculation formula of the trapezoidal block area is constructed by means of equal split supplement with parallels.On the basis of analyzing the law of area replacement error numerical distribution of trapezoidal block area,a strict area replacement error sequence model is established by the introduction of the latitude integral step variable,the limit convergence characteristic of area replacement error sequence under the latitude integral step variable regulation is expounded,an overrun determination criterion for the area replacement error is designed,the automatic control model of latitude integral step under area error limit conditions is constructed,and a calculation method for area of polygons on the earth spherop with automatic matching of absolute precision is proposed.The experimental results show that the algorithm can realize the precise calculation of any spheroid polygon area,and the absolute precision is controlled within the given error threshold.