The DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) was presented in Kamiński (2009). The method has been developed for the determination of displacements and strains of engineering objects in unstable reference systems, as well as for examining the stability of reference points. The DiSTFAG (Gross errors) method presented in the paper is the extension of the DiSTFA method making it robust to gross errors. Theoretical considerations have been supplemented with an example of a practical application on a simulated 3D surveying network.

The problem of determining displacements of objects is an important and current issue, in particular in terms of operational safety. This is a requirement that covers geodetic, periodic control measurements in order to determine horizontal and vertical displacements. The paper is focused on the analysis of vertical displacements. Geodetic measurements and their interpretation allow to reduce the risk of possible structural catastrophes. The major research topic of the majority of available papers is displacement determination of individual controlled points, in a situation where there are identified as fixed reference points. There are cases making identification of such points difficult or impossible to use in displacement analysis. This paper addresses a rare case of determining vertical displacements in unstable reference systems. Due to the fact that most of the existing and known literature methods do not always bring satisfactory results, the paper propose a new method of vertical displacement determination in the absence of reference points in the local coordinate system. Practical considerations on simulated data show that the presented method performs the task correctly.

The paper presents the results of research on the DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) for the determination of displacement and strains of a surface determined in unstable reference systems. Additionally, covariance matrices were introduced to assess the accuracy of estimation results. The theoretical discussion includes an example of its application in a simulated, three-dimensional geodetic network. The obtained results encourage further, more detailed analysis of real geodetic networks.