Location and estimation of multiple outliers in weighted total least squares

•A total outlier was defined that simplifies the problem of testing multiple outliers.•A full search algorithm is developed that locates the total outliers in EIV models.•F-test is used as the general termination criterion for the full search.•A new algorithm was proposed to estimate the unknown parameters and total outliers. Although the weighted total least squares (WTLS) adjustment is a rigorous method for estimating parameters in errors-in-variables (EIV) models, its solution is unreliable if the design matrix and/or observations contain multiple outliers. Existing methods are not capable of fully eliminating the influence of multiple outliers on the parameters. First, we reformulate an EIV model as a correction model by taking the outliers of the design matrix and observations into account, and we introduce the concept of total outliers to simplify the problem of detecting multiple outliers in EIV models. Then, based on the effect of the outliers on the estimated posteriori variance, we develop a full search algorithm to form a location matrix that can describe the location of the total outliers. Next, we derive a set of formulae to numerically estimate the unknown model parameters and total outliers simultaneously. Finally, the results of three numerical experiments show that the proposed method can effectively eliminate the influence of the outliers and obtain reliable parameters.