Mathematical Model for Systematic Error in the First Order Triangulation Stations

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.