Point displacements during classical measurements – a practical approach to pseudo epochs between measurements

Abstract

Various measurement techniques and data processing are applied to determine point displacements and deformation of geodetic networks or buildings. Considering classical measurements and analysis of the network deformation, we should realize that the measurements are not “immediate.” The question arises: what happens if a point (or some points) displaces between particular measurements within one epoch. In such a case, the observation set would consist of the observations before and after point displacement, and such hypothetical observation groups can be regarded as related to two (or more) pseudo epochs. The paper's main objective is to examine some estimation methods that would probably deal with such a problem, namely Msplit estimation (in two variants, the squared and the absolute Msplit estimation) and chosen robust methods, namely Huber’s method (example M-estimation) and the Hodges-Lehmann weighted estimation (basic R-estimation). The first approach can provide two (or more) variants of the network point coordinates (here, before and after point movements), providing information about two (or more) states of the network during measurements. In contrast, the robust methods can only decrease the influence of the outliers on the computed network point coordinates. Thus, estimation results would concern only one network state in such a case. The presented empirical analyses show that the better and more realistic results are obtained by applying Msplit estimation. Huber’s method can also provide acceptable results (describing the network state at the epoch beginning) only if the number of observations conducted after the point displacements is not too high.