Total least squares

Errors-in-Variables is a robust modeling technique in statistics, which assumes that every variable can have error or noise. Total least squares (TLS) is also referred to as Errors-in-Variables (EIV), in a broad sense, in the literature of computational mathematics and engineering. However, TLS in a strict sense implies the application of EIV or orthogonal regression to linear regression.

In linear regression, one field of statistics, the least squares (LS) has variant versions according to the error configuration such as Total least squares, Data least squares (DLS), Constrained or structured TLS and so on.

The solution of LS can be obtained using (pseudo-)inverse of system matrix. The other solutions of TLS or DLS have been shown to be closely connected to a set of singular vectors of (augmented) system matrix corresponding to the minimum singular value.

References

• S. V. Huffel and P. Lemmerling, Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications. Dordrecht, The Netherlands: Kluwer Academic Publishers, 2002.