## 1 Introduction  
Reference coordinate systems are the basis for most geodetic work. They are primarily used for mapping, but they are also used for delineating engineering work and maintaining land registers. Historically, leveling represented a more accurate method of measuring elevation; as a result, coordinate systems are generally divided into horizontal and vertical parts. The first coordinate systems originated from measuring horizontal angles in triangles, i.e., triangulation. In the territory of the Czech Republic, the first positional coordinate systems were created in the Austro-Hungarian empire in the 19 th century using triangulation for the second military mapping [1], for the mapping of the stable cadaster [2], and subsequently for the Central European degree measurement and third military mapping [3]. Based on the military triangulation for the third military mapping, the System of the Unified Trigonometric Cadastral Network (S-JTSK) reference system was created in the 1920s based on the Bessel reference ellipsoid. The measurement of horizontal angles at some of the triangulation stations was adopted from military triangulation, and, in particular, the scale and orientation of the network were adopted. The reference system S-JTSK is still in use today in the Czech Republic as a geodetic basis for the mapping of new cadastral maps [4], the conversion of older cadastral [5] and topographic maps [6; 7], the delineation and surveying of infrastructures (e.g., railways) [8], the connection of mine operations [9], the monitoring of the impact of mining on the surface [10], and other uses. The reference system S-JTSK uses [PERSON]'s cartographic projection [11] for planar coordinates. The Krovak projection comprises two conformal projections: In the first step, the geodetic coordinates based on the Bessel ellipsoid are conformally projected onto a sphere with a reduced diameter using the Gauss conformal projection of the ellipsoid to a sphere; in the second step, the coordinates on the sphere are projected to the mapping surface by a conformal conic projection in the general position, which is a special subtype of the Lambert conformal conic (LCC) projection. The Krovak projection was optimized for the territory of the Czechoslovak Republic in the period 1918-1938, i.e., the general position of the conic projection was optimally selected for the territory of the Czechoslovak Republic. The length scale of the Krovak projection takes values from \(-10\) cm/km on the tangential cartographic parallel in the center of the territory to \(+14\) cm/km on the edges of the territory of the Czechoslovak Republic [12]. With the advent of space geodesy methods--in particular, Global Navigation Satellite Systems (GNSS) technology, the Real-Time Kinematic (RTK) method of measurement [13], and virtual stations implemented by using the networks of permanent stations, i.e., CZEPOS [14]--surveyors have a tool at their disposal that enables rapid and efficient positioning with an accuracy that is sufficient for most applications, in addition to highly efficient delineation, the mapping of unforested and undeveloped areas and linear structures [13], and the monitoring of geodynamics on local [15] and regional scales [16; 17]. In contrast with other countries, where the advent of GNSS has resulted in a fundamental change in reference coordinate systems (e.g., Oman) [18] or in countries that are preparing for fundamental changes (e.g., Serbia) [19], in the Czech Republic, the binding reference coordinate system remains the S-JTSK. The use of GNSS is linked to networks of permanent GNSS stations that have coordinates in the European Terrestrial Reference Frame 2000 (ETRF2000). This factor makes it necessary to ensure the transformation of coordinates determined by the GNSS in the ETRF2000 reference frame into the S-JTSK system [20]. The transformation procedure is determined using the S-JTSK/05 working reference system with a modified Krovak projection [21].