## 1 Introduction  
The geometric layout of a railway track axis plays a crucial role in enabling higher permissible speeds for rail vehicles. To ensure safety and performance, the designed alignment must be precisely staked out in the field, with actual parameters closely matching the design specifications. An additional challenge arises when the track axis must be identified based on an existing railway line, particularly during modernization projects where the new alignment is derived from evaluating the current condition of the track. This situation is common when upgrading existing lines to improve operational parameters. Often, modernized tracks lack an accurate digital model of their geometry, necessitating the inventory of horizontal and vertical coordinates of the track. For this data to support reliable identification of geometric parameters, it must be obtained through precise, accurate, and quasi-continuous measurements. Traditionally, this is accomplished using geodetic methods based on high-precision takeometry, where surveying instruments refer to a stable geodetic control network established along the railway line. However, such measurements are both time-consuming and costly, especially when applied across extensive railway corridors [1; 2; 3; 4]. Tacheometric measurement methods have a long-standing tradition and, despite ongoing innovations, remain labor-intensive and require the involvement of multiple personnel. Nonetheless, they provide measurements characterized by low uncertainty and high precision. A second category of techniques for determining the position and geometry of the track axis consists of mobile measurement methods, primarily based on Global Navigation Satellite System (GNSS) technologies combined with inertial measurement units (IMUs) [5; 6; 7; 8; 9]. These methods offer significantly greater efficiency due to the higher speeds that can be achieved by measurement platforms. However, the uncertainty of the resulting track axis coordinates depends on numerous factors, including the current satellite constellation configuration--an inherently variable parameter--and local terrain conditions such as vegetation, buildings, and other obstructions, which are relatively fixed. Additionally, these measurements require a methodology that accounts for the spatial offset between the GNSS antennas or IMU sensors and the actual track axis, as direct placement of sensors on the track axis is typically infeasible [10]. Currently, the uncertainty of GNSS-based measurements is typically evaluated using quality coefficients: CQ2D for horizontal positioning and CQ3D for three-dimensional positioning, each assigned to individual measurements [11]. This approach is particularly appropriate in the context of static measurements, where long time series consisting of tens of thousands of individual position recordings are collected. Through statistical analysis of such datasets, measurements with CQ values exceeding predefined thresholds can be identified and excluded [12]. Provided that the proportion of these outliers within the dataset is small, their impact on the overall measurement result remains negligible. In the case of mobile measurements, however, each recorded position must be treated as a single, non-repetitive observation. Consequently, assessing uncertainty solely based on CQ quality indicators is insufficient. These coefficients represent the standard deviation, indicating the probability that the true measurement value (i.e., the coordinates) lies within the spatial region defined by the CQ value [12]. Therefore, it is possible that the true value deviates only slightly from the indicated measurement, even when the CQ coefficient suggests high uncertainty. According to traditional GNSS positioning analysis methods, such samples would be discarded for failing to meet accuracy requirements, despite potentially being usable in practice [13].