Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squ...Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.展开更多
基金The research was supported by the National Natural Science Foundation of China(41204003)Scientific Research Foundation of ECIT(DHBK201113)Scientific Research Foundation of Jiangxi Province Key Laboratory for Digital Land(DLLJ201207)
文摘Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.
