## 1 Introduction  
The requirement for the accuracy of the spatial position of the railway track is based on the Czech technical standard (CSN) 73 6360-2 (2013) [1], Article 6.4.1, which specifies, among other things, that \"the absolute lateral positional deviation of the track axis from its design position shall not be greater than \(\pm\)10 mm when accepting work in the rail with the placing of new material, \(\pm\)15 mm with the placing of used material, and when accepting other work shall not be greater than \(\pm\)20 mm, while the mutual deviation of the lateral distance between the track axis and the platform edge shall be maintained within \(<\)\(-\)0\({}_{+}\)20\(>\) mm from the design nominal position value\". The technical standards assume the invariance of the reference system, which is very difficult to ensure under operating conditions. Therefore, it is necessary to use proven precise measurement procedures that allow long-term repeatability and reproducibility of results. Real-time technologies of Global Navigation Satellite Systems (GNSS) are very effective for precise positioning, as they allow for higher accuracy in the positional component than conventional terrestrial methods, even at a length of 1 km. In addition, they are efficient and easy to use due to the high degree of automation of the measurement process. To achieve the required high sub-centimeter accuracy, a phase signal and two GNSS instruments (reference and rover) are required. Ideally, a network of permanent stations should be used if they are available in the area. Accuracy of less than 1 cm using only one GNSS device in real time is not yet realistic. For the real-time kinematic PPP method, although the algorithms are constantly improving, longer observation times of hours are required, e.g., 3 h, and the accuracies achieved are in the range of 2.5-5 cm in the horizontal component and around 10 cm in the elevation component [2; 3], which are insufficient for accurate measurements on railways. The use of low-cost solutions further reduces the accuracy to a few decimeters [4]. The horizon required for GNSS measurements is blocked by obstacles along the railway line. Obstacles that cause horizon blocking in non-urban areas are mainly nearby vegetation (trees, bushes), as well as construction objects and nearby buildings in urban areas. An innovative solution for precise absolute measurement of the center of the track based on the integration of GNSS, inertial navigation system (INS) and odometer is presented in [5]. The GNSS/INS/odometer system does not depend on a high-precision measurement network along the line, and, unlike conventional methods, it can operate in mobile measurement mode with measurement speeds ranging from 0.15 km/h to 5 km/h. Test results on the Zhengzhou\(-\)Xuzhou high-speed railway line showed that the measurement errors were less than 6 mm in the horizontal direction and 11 mm in the vertical direction, and the measurement system is capable of maintaining high accuracy within 5 cm, even in the event of a GNSS failure for 700 s.  
To determine the geometric parameters of the track, a mobile measurement platform with two GNSS receivers was used to determine the basic vector, and this measurement system was supplemented with an inertial measurement unit (IMU) [6]. The measurement platform enables determining the direction of the track and the longitudinal and transversal inclination angles. This makes it possible to verify the track geometry in the horizontal plane, i.e., to locate straight sections, transition curves and constant-radius curves. The measurement results were shown to be repeatable despite the dynamic interaction between the track and the measurement platform. The results confirmed the usefulness of the applied GNSS and IMU signal processing method for monitoring the geometrical parameters of the railway line under operational conditions. The RTKRCV method and the RTKLIB computational library for ROS [7] have been developed for the application of the RTK method using multiple GNSS receivers.