RESEARCH ON PERTURBATION ANALYSIS OF THE TOTAL LEAST SQUARES
Wang Leyang1,2）
1）Faculty of Geomatics, East China Institute of Technology, Nanchang 330013;2）Jiangxi Province Key Laboratory for Digital Land,Fuzhou 344000
Abstract On the basis of the condition number definition of coefficient matrix and from the viewpoint of numerical analysis, the perturbation analysis equations of least squares (LS) and data least squares (DLS) are deduced, in following cases when the perturbation is only contained in the observation data, the perturbations are contained in the observation data and coefficient matrix, and the perturbation is only contained in the coefficient matrix. On the basis of the closedform expression of the total least squares (TLS) solution and with the tool of the singular value decomposition (SVD), the perturbation analysis equation of TLS is deduced. Through the analysis, the perturbation analysis equation of TLS is the unified form of the perturbation analysis equation of LS and DLS.
Key words ：
total least squares (TLS)
least squares (LS)
data least squares (DLS)
perturbation analysis
condition number
Received: 01 January 1900
Corresponding Authors:
Wang Leyang
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