## 1 Introduction
This conservative approach may result in overly strict evaluation criteria, rendering measurements in challenging environments--such as areas with significant terrain obstructions--difficult or nearly impossible to conduct. Moreover, practical experience demonstrates the opposite scenario: a measurement with a relatively low CQ value may exhibit a significant deviation from the receiver's true position. In such instances, an erroneous estimation of the track axis position could be mistakenly accepted as valid. This article presents an innovative method for evaluating recorded railway track axis positions obtained from a mobile rail-based measurement platform [13; 14; 15]. The proposed approach relies on continuous monitoring of the geometric configuration of a multi-receiver GNSS measurement system, enabling a reduction in measurement uncertainty and enhancing the reliability of GNSS-based railway track axis positioning. By applying this approach, an acceptable level of measurement precision can be achieved even in challenging terrain conditions that limit satellite signal availability. Theoretical considerations and the developed method were tested on measurement data collected during field experiments on operational railway lines. The resulting uncertainties of the measured track axis positions were then compared with conventional CQ quality indicators. In the field of inventory and maintenance measurements using GNSSs, a significant problem is the conditions (especially terrain conditions generating apertures on the satellite-receiver path), which affect the quality of position determination. The process of identifying the defined receivers' geometric frame on railway lines is particularly affected by this problem due to the fact that it runs through a terrain that is diversified in terms of the immediate surroundings and due to the need to achieve high positioning accuracy. In order to ensure the required quality of measurement signals, a number of methods have been developed in which techniques such as RAIM (Receiver Autonomous Integrity Monitoring), ML (machine learning) or DF (Data Fusion) are implemented [16, 17, 18]. This paper presents a certain narrow approach using analytical processing of data from a multi-antenna measurement system, which uses geometrical relations of the GNSS receiver antenna system. The computational algorithm uses criteria and conditions related to the assessment of the uncertainty of individual positions. The advantage of this approach is that it includes a clearly defined set of equations in an analytical form--the solutions are exact and reliably guarantee the speed of calculations on arbitrarily large datasets and a relatively simple implementation--which makes this approach practical. The effectiveness of the method was presented on the CQ2D indicator, which is commonly used in RTK measurements and in the analysis of the reliability of GNSS measurements. It should be emphasized, however, that referring to other uncertainty measures (e.g., RMSH and RMSV) does not affect the structure of the computational algorithm, but may change the percentage of line sections in which the aforementioned position uncertainty is effectively reduced. Therefore, the presented algorithm is not particularly related to any uncertainty measure used in the RTK technique. As part of future research, the authors intend to assess the reduction in uncertainty using other measures provided by RTK/RTN services. The research presented in this article was conducted within the framework of the InnoSatTrack research project, which aimed to develop a set of methods for efficient, relatively fast, and sufficiently accurate mapping of the railway track axis into a geometric layout. The software system developed as part of the project supports this functionality; however, precise identification of geometric parameters--expressed in the form of a curvature diagram--requires a relatively dense distribution of track axis positions, preferably with minimal data gaps.