In deformation analyses, it is important to find a stable reference frame and therefore the stability of the possible reference points must be controlled. There are several methods to test such stability. The paper’s objective is to examine one of such methods, namely the method based on application of R-estimation, for its sensitivity to gross errors. The method in question applies three robust estimators, however, it is not robust itself. The robustness of the method depends on the number of unstable points (the fewer unstable points there are, the more robust is the proposed method). Such property makes it important to know how the estimates applied and the strategy itself respond to a gross error. The empirical influence functions (EIF) can provide necessary information and help to understand the response of the strategy for a gross error. The paper presents examples of EIFs of the estimates, their application in the strategy and describes how important and useful is such knowledge in practice.

M _split estimation is a novel method developed to process observation sets that include two (or more) observation aggregations. The main objective of the method is to estimate the location parameters of each aggregation without any preliminary assumption concerning the division of the observation set into respective subsets. Up to now, two different variants of M _split estimation have been derived. The first and basic variant is the squared M _split estimation, which can be derived from the assumption about the normal distribution of observations. The second variant is the absolute M _split estimation, which generally refers to the least absolute deviation method. The main objective of the paper is to compare both variants of M _split estimation by showing similarities and differences between the methods. The main dissimilarity stems from the different influence functions, making the absolute M _split estimation less sensitive to gross errors of moderate magnitude. The empirical analyses presented confirm that conclusion and show that the accuracy of the methods is similar, in general. The absolute M _split estimation is more accurate than the squared M _split estimation for less accurate observations. In contrast, the squared M _split estimation is more accurate when the number of observations in aggregations differs much. Concerning all advantages and disadvantages of M _split estimation variants, we recommend using the absolute M _split estimation in most geodetic applications.