Gabriel Weiss’s scientific contributions

Deformation analyzes are important for long-term monitoring of areas, where, in the first place, it is necessary to take into account human safety and environmental protection for the purpose of sustainable development of human society. The quality of the results of deformation analysis will also be affected by the quality of establishment of the geodetic network. When a new Local Geodetic Network (LGN) is established, for example, during deformation monitoring (landslides, open-pit mining, excavations, etc.) for the purpose of environmental protection, its determination can be influenced by some mistakes: a) geometric quantities measured can be contaminated by blunders, b) compatibilities of some "old" points in the area of LGN can be incorrect, c) appropriate coordinates of some new points may be defective. The case c), using two methods - Least Squares (LSM) unconstrained adjustment; - iteratively reweighted LSM of Robust Estimation, is analyzed in the paper. The main objective of this paper is to compare the adjustment of the geodetic network by the Gauss-Markov model based on GMM with full rank and robust LSM adjustment. The main adjustment steps with important numerical results are presented for both methods. The method how to detect the presence of the used wrong approximate coordinates of new network points is addressed, and the detection approaches are given for both adjustment procedures. The results of both adjustment procedures summarized in the Discussion indicate that the combination of these procedures is the most suitable way of detecting errors in a geodetic network.

In the issue of height compatibility of different types of vertical controls (levelling, trigonometric, GPS, etc.), only levelling point fields, respectively, networks, that are so far dominant not only for the vertical expression of points relative to the geoid, or quasigeoid, but also in terms of the technology and accuracy of height determination, will be considered.

Every survey control point (horizontal and vertical) has a physical mark and assigned numerical data (coordinates and heights) from certain reference systems, which should be related to a survey mark of this point. So far as those determining attributes are in stochastic planimetric or altimetric identity, the point can be considered as compatible, otherwise if specified attributes of point are mutually in geometrical significantly different positions, it is an incompatible point.

The verification of the compatibility of points of spatial networks forms a very important component of completion and extension of networks by new points required for accurate geodetic activities. Therefore, it is necessary to have a quality geodetic control. A quality geodetic control can be achieved not only by new and quality measurement of new points, but also fine connecting points of which a new geodetic control is being established must be available.

By using the GNSS technology (GPS, GLONASS, …), spatial positions of points in 3D coordinate systems (WGS-84, ETRS-89, …) are determined. As required by their geodetic use, they may or may not be transformed into national planimetric or/and vertical coordinate systems. Afterward, also the quality (or stability) of determined points is assessed separately in them.

The compatibility of height points HL, i.e., a geometric height identity of horizontal tangent plane of height survey mark (Fig. 4. 1) with height data h from a certain vertical datum S(h) defined relative to the geoid or quasigeoid by the relevant level surface of the field of gravity (tangential to the survey mark), is just as important for the correct and reliable performance of altimetric measurements and determination of heights of new points as requirements for positional compatibility of geodetic controls.

The verification of compatibility of points in planimetric geodetic controls that are part of national, regional network structures, or individual local, purpose-built networks represents a very important component of all processes of complementing and expansion of networks by new points that are necessary for different geodetic activities, requiring reliable geodetic bases, i.e., points.

This work deals with the issue of geodetic network structures, i.e. methods of verifying the condition of existing geodetic controls in terms of their compatibility and thereby their applicability. The presented work addresses these problems only for geodetic controls on a local scale. This is a common surveying issue in a number of countries, especially where there are concerns about the quality of the structure and homogeneity of national spatial and triangulation networks. There is a need for verification, not only for the use of terrestrial methods of determination of points but also for other surveying technology, since all technology operates with a certain threshold accuracy and using physical marks located on an unstable earth surface as survey control points. Issues of the compatibility of points whose coordinates are defined as functions of time by specific equations with respect to basal positions of points at certain epochs (points in systems ITRS, ETRS and others) are not considered.

Consider the position of points defined by coordinates C = [X, Y] in a specific planimetric system S(XY), which are properly monumented on the earth surface or objects. It is obvious that each point, as stated in Chap. 2, must be identified and defined by the following two fundamental components in terms of its functionality.