Performance of M_split estimates in the context of vertical displacement analysis

Abstract

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.

Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

“…Both types of iterative processes require a proper choice of starting points [43], and they should both be stopped for such a j = k for which [29,34]. Previous papers [34,35,43] showed that differences in the SMS and AMS estimations' objective functions also result in slightly different general properties. As was shown, both methods' weight functions differ from each other, which leads to the necessity of two different iterative processes.…”

“…Applications of M split estimation concerned so far not only processing of TLS data (presented in [1,15,22,31]) but also deformation analyses [29,30,[32][33][34][35][36], direct identification of gross errors [37], linear regression analyses [30,34], robust coordinate transformation [38], S-transformation [39] and marine navigation [40]. Most of these applications applied only the squared M split estimation (SMS), of which the objective functions stem from the assumption that observation errors are normally distributed.…”

“…Such a variant is called the absolute M split estimation (AMS) [34,43], and it has not been used in laser scanning data analysis so far. Due to that fact, it seems interesting to apply this method in such a context, especially since some previous papers proved that AMS estimation is generally less sensitive to outliers than SMS estimation [34,35]. Thus, the paper's main objective is to analyze both variants of M split estimation in the context of the determination of terrain and terrain details profiles based on TLS data.…”

Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

“…The next application of the Msplit method was as an estimation method in the context of the analysis of the vertical displacement of geodetic points [24] or for detecting circular objects in a point cloud [25].…”

Systematic bias of selected estimates applied in vertical displacement analysis

“…Whereas AMS estimation gives correct results (all biases close to 0) only for negative values of ∆H A or when ∆H A > 40 mm. It is caused by a coincidence of some ∆H A with value of ∆H B = 20 mm and with the gross error (Wyszkowska and Duchnowski, 2020). On the other hand, the biases of ∆Ĥ A and ∆Ĥ B for AMS estimation are of small magnitude.…”