Iteratively reweighted total least squares: a robust estimation in errors-in-variables models

In this contribution, the iteratively reweighted total least squares (IRTLS) method is introduced as a robust estimation in errors-in-variables (EIV) models. The method is a follow-up to the iteratively reweighted least squares (IRLS) that is applied to the Gauss-Markov and/or Gauss-Helmert models, when the observations are corrupted by gross errors (outliers). In a relatively new class of models, namely EIV models, IRLS or other known robust estimation methods introduced in geodetic literature cannot be directly applied. This is because the vector of observations or the coefficient matrix of the EIV model may be falsified by gross errors. The IRTLS can then be a good alternative as a robust estimation method in the EIV models. This method is based on the algorithm of weighted total least squares problem according to the traditional Lagrange approach to optimise the target function of this problem. Also a new weight function is introduced for IRTLS approach in order to obtain better results. A simulation study and an empirical example give insight into the robustness and the efficiency of the procedure proposed.