Locally robust Msplit estimation

Abstract Processing measurement data is an essential part of surveying engineering. One can list several methods in such a context: least squares estimation, M-estimation, R-estimation, etc. Some methods were developed by surveyors, e.g., the Danish method, IGG scheme, or M split estimation. The last method is, in fact, a class of estimation procedures dedicated to different problems. As a new approach to processing data, M split estimation is still being developed and improved. That paper concerns the local robustness of M split estimation and introduces a new M split estimation variant that is less sensitive to local outliers. Such a property seems important, especially in big data processing, such as observations from Light Detection and Ranging systems. The new variant modifies the squared M split estimation (SMS estimation) by implementing the adapted Tukey weight function, hence its acronym SMSTL estimation. The basic theoretical and empirical analyses, which were performed for the univariate model using, among others, the appropriate measures of robustness, confirmed the expected property of the method. The further tests, based on simulated as well as real data, show that the new method might overperform other M split estimation variants and classical methods for the chosen types of observation sets.