《GJB2000中国大地测量系统》中的韦森特公式计算误差及其应用改进

The Compute Error and Application Improvement of Vicente Formula in GJB China Geodetic System 2000

文章首先提出一种准确计算地球椭球面上两点间弧长的方法,并且验证了该方法的正确性;进而利用此方法来核对国军标的韦森特公式计算弧长结果,发现跨越地球赤道的两点且接近韦森特公式适用边界时,计算弧长有不可容忍的误差。针对这种情况(国军标中韦森特公式的计算实例4),提出了分赤道南北两段按韦森特公式计算两段弧长之和,作为两点间的弧长,与准确算法相比,误差比原来减小了84.3%。所以这种应用改进方法非常有效,能够满足某些应用。

This paper first advances a method by which are length between two points is nicety calculated on the earth ellipsoid,and has validated the exactitude of the method.The paper has checked the result of arc length calculation by Vicente formula in GJB China geodetic system 2000 with the method.The paper has found that are length calculation by Vicente formula is with impatient error when two points spanned the equator and are adjacent to the applicable border of Vicente formula.The paper advances that arc length between two positions is calculated according to the south and north two segments of the equator with Vicente formula calculation,then sums the two arcs length,aiming at this case(calculation example 4 of Vicente formula in GJB China geodetic system 2000).Compared with exactitude method,the error is decreased by 84.3%.So the application improve-ment is effective and can satisfy some applications.