RESEARCH ON PROPERTIES OF TOTAL LEAST SQUARES ESTIMATION
Wang Leyang 1,2)
1)Faculty of Geomatics, East China Institute of Technology, Nanchang 330013;2)Jiangxi Province Key Laboratory for Digital Land, Fuzhou 344000
Abstract Through theory derivation and proof, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation. When the coefficient matrix contains error,the least squares is biased.The total least squares estimation is unbiased. The condition number of the total least squares estimation is bigger than that of the least squares estimation, so the total least squares estimation is more easier to be affected by the data error than the least squares estimation. Through further derivation, the relation of solutions, residuals, unit weight variance estimations between the total least squares and the least squares are given.
Key words ：
total least squares (TLS)
least squares (LS)
singular value decomposition (SVD)
residual
unit weight variance
Received: 01 January 1900
Corresponding Authors:
Wang Leyang
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