SVD-based model for mine quasi-geoid establishment

Abstract

Existing rank-defect free network adjustment is to some extent adaptable for singular problems with additional conditions but not responsible for abnormal adjustment including singular and ill-conditioned situations in the establishment of mine quasi-geoid. To avoid additional conditions, a new singular value decomposition (SVD)-based pseudoinverse solution is introduced, which needs only two steps for calculation. The coefficient matrix was transformed into bidiagonal matrix with full orthogonal decomposition, and the accomplishment was carried out by iterative algorithm of implicit symmetric QR decomposition. To evaluate the effects and stability, we compared the result using least squares for full rank including ill-conditioned and singular with that using SVD. Meanwhile, both inside precision and outside precision were used to assess the efficiency of these methods. Based on analyzing two situations with or without coordinates constants, the three methods have the same effect if there is no any constant; however, if there are some constants, only the SVD method can have a right result.