加权整体最小二乘在GPS高程拟合中的应用

Weighted Total Least Squares Theory with Applications in GPS Elevation Fitting

对于L=BX的工程问题,因为系数矩阵B和观测向量L的元素都是实测数据,并且有时候是不等精度获得的,存在或大或小的误差,因此在这些地方运用加权整体最小二乘求解是更加适用的。本文给出了加权整体最小二乘的解法,最后结合实例进行计算,得出利用加权整体最小二乘方法所得到的检核数据的残差最小的结论,验证了该理论的可行性,可以在工程应用中进行推广。

For the engineering problems of L = BX,the elements of coefficient matrix B and the observation vector L were measured data,and sometimes they were unequal precision obtained,exsisting error or big or small,so in these areas using the weighted total least squares solution was more suitable. This paper gave a method of weighted total least squares,finally calculated with examples,came to conclusion that the residuals of checking data by using the weighted total least squares method was least,verified the feasibility of theory,could be applied in engineering application.