Efficient weighted total least-squares solution for partial errors-in-variables model

Due to great computation burden of the original computational formula for partial errors-in-variables (EIV), an alternative formula for parameter estimation in the partial EIV model was proposed to promote computational efficiency. Unfortunately, more iteration is required for obtaining the weighted total least-squares (WTLS) solution of the partial EIV model with above two formulae. Consequently, those methods are not proper for larger data problem in terms of computational efficiency. To circumvent this difficulty, a new formula and the fast algorithm are proposed based on the Lagrange extreme value method. Through some numerical examples with coordinate transformation, it is illustrated that the new developed method is an effective strategy to conduct the WTLS adjustment for the partial EIV model. The computational efficiency is significantly improved at least 80%.