This paper presents an estimation method allowing direct and robust outlier assessment of parameter shifts in functional models of geodetic observations. The systems adopted in the discussion refer to functional models used in geodetic network deformation analysis. The proposed method is a robustness-oriented development of Shift-Msplit estimation. The problem of robustness is solved using an additional random variable with realizations that are outliers. The paper shows that the application of this variable also facilitates the selection of the appropriate number of competitive models in Msplit(q) estimation. Two numerical examples explain the manner of Shift-Msplit∗ estimation performance and indicate the basic properties of the determined estimates.

The article presents the issue of determining a proper number of competitive functional models in the square M_split(q) estimation. It is assumed in the theoretical fundamentals of the method of parameter estimation in a split functional model that the observation vector may constitute an unrecognised and unassigned mixture of realisations of several random variables. As such, the observation vector may contain the realisations of a greater number of random variables than the adopted of the competitive functional models. Too small number of competitive functional models may leads to breakdown of M_split(q) estimation. In the theoretical part of the paper, a modified Baarda’s test was proposed to detect too small a number of competitive functional models. The idea of the proposed approach is about detection of the observations that should not be assigned to a specific functional model. The efficacy of the proposed strategy was illustrated by two numerical examples.