Msplit Estimation Approach to Modeling Vertical Terrain Displacement from TLS Data Disturbed by Outliers

Terrestrial laser scanning (TLS) is a modern measurement technique that provides a point cloud in a relatively short time. TLS data are usually processed using different methods in order to obtain the final result (infrastructure or terrain models). M-split estimation is a modern method successfully applied for such a purpose. This paper addresses the possible application of the method in processing TLS data from two different epochs to model a vertical displacement of terrain resulting, for example, from landslides or mining damages. M-split estimation can be performed in two variants (the squared or absolute method) and two scenarios (two point clouds or one combined point cloud). One should understand that point clouds usually contain outliers of different origins. Therefore, this paper considers the contamination of TLS data by positive or/and negative outliers. The results based on simulated data prove that absolute M-split estimation provides better results and overperforms conventional estimation methods (least-squares or robust M-estimation). In practice, the processing of point clouds separately seems to be a better option. This paper proved that M-split estimation is a compelling alternative to conventional methods, as it can be applied to process TLS data disturbed by outliers of different types.