一种新的病态问题奇异值修正方法

针对测量平差中的病态最小二乘问题，提出了统一的奇异值修正公式，以此为基础提出一种新的奇异值修正法.所提方法克服了现有方法需要确定奇异值截断阈值或者修正阈值的缺陷，基本没有增加额外的计算量，计算简单快捷精度高. 另外，所提方法普适性强，对方程组系数矩阵的维数和是否满秩没有特殊的要求，可以适用于多种类型平差方程组的求解. 以两个病态方程为例对所提方法进行了数值验证，并将计算结果与最小二乘解和奇异值截断解进行了比较，结果表明，所提方法可以获得精度更高的计算结果. 

Singular value correction method for ill conditioned least squares problem in survey adjustment

To solve the ill conditioned least squares problem in survey adjustment, a new singular value correction method is proposed in this paper based on a unified singular value correction formula. The proposed method overcomes the shortcomings of the existing methods, which need to determine the threshold value of singular value truncation or modification. The proposed method is simple and fast in calculation with high accuracy, and does not increase the amount of the computation cost. In addition, the proposed method has strong universality and no special requirements for the dimension and rank of the coefficient matrix of the system of equations. It can be applied to the solution of any type of linear system of equations. Two ill conditioned equations are taken as examples to verify the proposed method. The results are compared with the least square solution and the singular value truncation solution. It has been shown that the proposed method is simple and easy to use, and can obtain more accurate results than the singular value truncation method.