This paper concerns two types of Msplit estimation: squared Msplit estimation (SMS), which assumes normality of observation errors and absolute Msplit estimation (AMS), which applies {\text{L}_{1}} norm criterion. The main objective of the paper is to assess the accuracy of such estimators in vertical displacement analysis by applying Monte Carlo simulations. Another issue is to compare the accuracy of both estimators with the accuracy of the least squares estimation (LS). The paper shows that the accuracy of both Msplit estimates is like the accuracy of LS estimates. However, if some nonrandom errors occur, then accuracy of AMS estimates might be better than the accuracy of the rest of the estimates considered here. It stems from the fact that AMS estimates are robust against disturbances which have a small magnitude. It is also worth noting that the accuracy of both Msplit estimates might depend on the magnitude of the displacement.
This paper presents an application of an Msplit estimation in the determination of terrain profiles from terrestrial laser scanning (TLS) data. We consider the squared Msplit estimation as well as the absolute Msplit estimation. Both variants have never been used to determine terrain profiles from TLS data (the absolute Msplit estimation has never been applied in any TLS data processing). The profiles are computed by applying polynomials of a different degree, determining which coefficients are estimated using the method in question. For comparison purposes, the profiles are also determined by applying a conventional least squares estimation. The analyses are based on simulated as well as real TLS data. The actual objects have been chosen to contain terrain details (or obstacles), which provide some measurements which are not referred to as terrain surface; here, they are regarded as outliers. The empirical tests prove that the proposed approach is efficient and can provide good terrain profiles even if there are outliers in an observation set. The best results are obtained when the absolute Msplit estimation is applied. One can suggest that this method can be used in a vertical displacement analysis in mining damages or ground disasters.
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