## 3 Results  
### Results of Measurements--Evaluation of Algorithm Effectiveness  
To validate the theoretical framework, the described algorithm was implemented to evaluate the track axis computed from mobile GNSS measurements on an operational railway line. The measurement platform carried six geodetic GNSS receivers arranged as shown in Figure 3b. During data acquisition, real-time RTK (Real-Time Kinematic) corrections were applied, and IMU measurements recorded platform tilt angles. Figure 5a illustrates the measured railway route in red, while Figure 5b depicts the computed track axis for the Osowa-Gdynia segment. Blue points denote high-quality positions--where the fixed-base deviation was under 1 cm--and red points denote low-quality positions, with deviations up to 20 cm. The fixed-base length for each epoch was computed according to Equation (42).  
\[L_{\text{FB}}=\sqrt{\left(X_{\text{AC}}-X_{\text{BC}}\right)^{2}+\left(Y_{\text {AC}}-Y_{\text{BC}}\right)^{2}} \tag{42}\]  
The selected route features complex geometry in both plan and longitudinal profiles, with numerous terrain obstructions that impede satellite signal reception. The urban segment from Gdansk Glowny to Gdansk Wrzeszcz traverses a densely built environment, punctuated by viaducts and other infrastructural barriers. In contrast, the stretch from Gdansk Wrzeszcz through Gdansk Osowa to Gdynia Glowna resembles a mountainous line, with tight curves and steep longitudinal gradients. Much of this section runs through forested areas and deep cuttings, and is intersected by footbridges, bridges, and similar obstacles. These conditions reduce satellite visibility and challenge GNSS-based measurements, making the route an ideal testbed for validating the proposed method's robustness.  
Figure 6 presents the measurement results in the form of coordinate points of the track axis overlaid on an orthophotomap. The points are divided on a similar basis: blue points represent high quality (\(\Delta L_{\text{FB}}<1\) cm), while red points indicate low-accuracy measurements (\(\Delta L_{\text{FB}}>20\) cm). Figure 6a shows the measurement of the entire section from Osowa to Gdynia. Figure 6b illustrates the route in an open area, where the quality is only reduced at one location due to a viaduct acting as an infrastructural obstruction. Figure 6c,d present sections of the line located in open terrain without point obstructions.  
Figure 5: Measurement wagon route: (**a**) entire route marked on the map, (**b**) track axis in the geodetic national coordinate system PL-2000. Blue segments—high measurement quality; red segments—unacceptable measurement quality.  
Figure 6e demonstrates the impact of high-rise buildings characteristic of urbanized areas, whereas Figure 6f,g indicate the influence of obstructions in the form of trees located close to the track.  
From an uncertainty-analysis standpoint, it is notable that both high- and low-quality measurements tend to cluster into relatively long route segments, with only isolated obstructions (e.g., viaducts, tall buildings) breaking these clusters. This creates an undesirable outcome for track inventory: entire horizontal curves--or even sequences of curves--may be excluded due to prolonged sections of insufficient accuracy. Such extended low-quality segments also hinder precise reconstruction of the track's horizontal geometric layout.