Assessing vertical terrain displacement from TLS data by applying Msplit estimation – theoretical analysis

Abstract

Terrestrial laser scanning (TLS) is a measurement technique that has become popular in the last decades. Measurement results, usually as a point cloud, contain many points measured. When the TLS technique is used to determine terrain surface (e.g., by determining terrain profiles), one should realize that some points measured do not concern the terrain surface itself, but trees, shrubs, or generally the vegetation cover. Considering terrain surface determination, they should be regarded as outliers. Some other observations can also be outliers of different origins; for example, they might be disturbed by gross errors. We should consider such observation types when the data are processed. Two leading solutions in such a context are data cleaning and the application of robust estimation methods. Robust M-estimation is the most popular for the latter approach. As an alternative, one can also consider the application of Msplit estimation, in which the functional model is split into two competing ones. Hence, the paper aims to analyze how Msplit estimation can assess vertical terrain displacement based on terrain profile determination from TLS data. We consider processing data in separate sets (two measurement epochs) or one combined set, a natural approach in Msplit estimation. The analyses based on simulated TLS data proved that the first solution seems better. Furthermore, the application of Msplit estimation can also provide more satisfactory results than the classical methods used in such a context.