M_split and Mp estimations are new methods of assessing the parameters of functional models of geodetic observations. The first method assumes that each observation can be assigned to either of some functional models which differ from each other in competitive parameters. While the latter method is based on the assumption that distributions of measurement errors differ from the normal one in asymmetry and excess kurtosis. The theoretical properties indicate that both methods are also robust against outliers. However, the sense of robustness is a little wider than in the case of M-estimation. In M_split estimation the outliers are treated as variables with competitive functional models (in relation to models of “good” observations) while robustness of Mp estimation depends on the mentioned parameters of probabilistic models of observations. This paper shows that on one hand robustness is an interesting property of the methods in question, but on the other hand it broadens possible application of such estimation methods.

DOI: https://doi.org/10.3846/enviro.2017.185