A method of generalized inverse adjustment based on improved Gram-Schmidt orthogonalization

被引:0
作者
Luo, Sanming [1 ]
Bo, Wanju [1 ]
Huang, Quhong [2 ]
Wang, Xining [2 ]
机构
[1] First Crust Deformation Monitoring and Application Center, CEA, 7 Naihuo Road, Tianjin 300180, China
[2] First Geodetic Surveying Brigade, SBSM, 4 Cehui Road, Xi'an 710054, China
来源
Wuhan Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University | 2012年 / 37卷 / 02期
关键词
Covariance matrix - Defects - Inverse problems;
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摘要
Starting directly with coefficient matrix of condition equation or error equation, the least square solution by triangulation decomposition on coefficient matrix is carried on with improved Gram-Schmidt orthogonalization procedure. Then, the math formula and the calculation steps of solving generalized inverse matrix on improved Gram-Schmidt algorithm are deduced. The unknown solution vectors and the mathematical expression of the variance-covariance matrix are given through the generalized inverse expression. Two examples are used to verify its effect, and the results show that the modified Gram-Schmidt orthogonal method can process any matrix including rank defect array.
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页码:174 / 177
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