引用本文: 朱圣源. 一等三角测量测站系统误差的数学模型[J]. 武汉大学学报 ( 信息科学版), 1980, 5(2): 40-45.
Zhu Shengyuan. Mathematical Model for Systematic Error in the First Order Triangulation Stations[J]. Geomatics and Information Science of Wuhan University, 1980, 5(2): 40-45.
 Citation: Zhu Shengyuan. Mathematical Model for Systematic Error in the First Order Triangulation Stations[J]. Geomatics and Information Science of Wuhan University, 1980, 5(2): 40-45.

## Mathematical Model for Systematic Error in the First Order Triangulation Stations

• 摘要: 按史赖伯测角法或全组合测角法,在测站平差后理应得到一组独立的方向观测值,但由于旁折光等系统误差的影响,使方向实际不独立。根据误差源的物理几何性质及根据数理统计原理,得出相邻方向间的相关系数为ρi,j=cos(i,j)/1+K,测角中误差为mα=0".55√1-1/1+Kcosα/1-1/2(1+K)。其中α为该角的大小,K为偶然误差与系统误差的均方值之比。对我国K为0.9左右。这一系统误差的存在,使测角中误差与角的大小有关,使大角中误差大,这也正是导线测角中误差大于三角网(锁)测角中误差的原因。这个系统误差也正是地面经典光学测角法精度难以进一步提高的主要原因。最后给出角度(及方向)的相关权矩阵模型。从模型知,以角度或方向作为独立量进行平差都是真实情况的近似。

Abstract: After a station adjustment according to the method of complete set of directions,a set of independent directions ought to be obtained.But because of lateral refraction and other kinds of systematic errors,directions in a station are really correlated.Using statistical theory and according to the charactoristics of error sources,we have obtained that the correlation coefficient between two directions is ρ=cos(i,j)/1+K,the rms of an angel is 0."55√1-1/1+Kcosα/1-1/2(1+K),here α is the value of the angle,and K is the ratio of random error and systimatic error.In China the average value of K is about 0.9.That is,the rms of an angle is dependent upon the value of the angle itself,larger angle having larger rms.In a traverse line,the angles all approximate to 180º,so their rms must be larger than those of a triangulation of the same class.Because of this kind of systematic error,the accuracy of the classical optical observation of traverse angles can hardly be improved.Lastly a model of correlated weight matrix is given,when we do the adjustment of an astro-geodetic network,we may take either angles or directions as independent elements,but they both have some degrees of approximation.

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