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.