Gabriel Weiss

The Verification of Compatibility of Spatial Points

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.

The Verification of Compatibility of Planimetric Points

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.

The Verification of Compatibility of Height Points

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 Compatibility of 1D (Height) Points

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.

The Compatibility of Geodetic Control

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 Compatibility of 2D (Planimetric) Points

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.

The Compatibility of 3D Spatial Points

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.

Application of Robust Estimation Methods for the Analysis of Outlier Measurements / Aplikácia Robustných Odhadovacích Metód Pri Analýze Odľahlých Meraní

Abstract The basis of mathematical analysis of geodetic measurements is the method of least squares (LSM), whose bicentenary we celebrated in 2006. In geodetic practice, we quite often encounter the phenomenon when outlier measurements penetrate into the set of measured data as a result of e.g. the impact of physical environment. That fact led to modifications of LSM that have been increasingly published mainly in foreign literature in recent years. The mentioned alternative estimation methods are e.g. robust estimation methods and methods in linear programming. The aim of the present paper is to compare LSM with the robust estimation methods on an example of a regression line. Abstrakt Základom matematickej analýzy dát je metóda najmenších štvorcov (MNŠ), ktorej dvesté výročie sme si pripomenuli v roku 2006. V geodetickej praxi sa v dôsledku napr. vplyvu fyzikálneho prostredia pomerne často stretávame s javom, že do súboru meraných dát prenikajú odľahlé merania. Práve táto skutočnosť viedla k modifikáciám MNŠ ktoré sa v posledných rokoch čoraz častejšie publikujú predovšetkým v zahraničnej literatúre. Spomínanými alternatívnymi odhadovacími metódami, sú napr. robustné odhadovacie metódy a metódy lineárneho programovania. Náplňou predloženého príspevku je porovnanie MNŠ s robustnými odhadovacími metódami na príklade regresnej priamky.