2012•Geodesy and GeodynamicsOpen access

Properties of the total least squares estimation

Leyang Wang

Abstract

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.

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Key concepts: Total least squares, Non-linear least squares, Generalized least squares, Least-squares function approximation, Mathematics, Least trimmed squares, Iteratively reweighted least squares, Statistics