Scaled weighted total least-squares adjustment for partial errors-in-variables model

Scaled total least squares fundamentals

The standard approaches to solving overdetermined linear systems Bx ≈ c construct minimal corrections to the vector c and/or the matrix B such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to c, while in data least squares (DLS) it is restricted to B. In scaled total least squares (STLS) [22], corrections to both c and B are allowed, and th...

Fourth Total Least Squares and Errors-in-Variables Modeling Workshop

Total least squares and errors-in-variables modeling

The main purpose of this special issue is to present an overview of the progress of a modeling technique which is known as total least squares (TLS) in computational mathematics and engineering, and as errors-in-variables (EIV) modeling or orthogonal regression in the statistical community. The TLS method is one of several linear parameter estimation techniques that has been devised to compensa...

An iterative solution of weighted total least-squares adjustment

Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute. Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares adjustment. In this cont...

Consistency of the structured total least squares estimator in a multivariate errors-in-variables model

The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given structural constraints. In the paper, an affine structure with additional assumptions is considered. In particular, Toeplitz and Hankel structured, noise free and unstructured blocks a...