The problem of outlying observations is very well-known in the surveying data processing. Outliers might have several sources, different magnitudes, and shares within the whole observation set. It means that it is not possible to propose one universal method to deal with such observations. There are two general approaches in such a context: data cleaning or robust estimation. For example, the robust M-estimation has found many practical applications. However, there are other options, such as R-estimation or the absolute M split estimation. The latter method was created to be less sensitive to outliers than the squared M split estimation (the basic variant of Msplit estimation). From the theoretical point of view, the absolute M split estimation cannot be classified as a robust method; however, it was proved that it could be used in such a context under certain conditions. The paper presents the primary comparison between that method and a conventional robust M-estimation. The results show that the absolute M split estimation predominates over the classical methods, especially when the percentage of outliers is high. Thus, that method might be used to process LiDAR data, including mismeasured points. Processing synthetic data from terrestrial laser scanning or airborne laser scanning confirms that the absolute M split / estimation can deal with outliers sufficiently.