## 3 Results
### Frame Geometrical Analysis  
The principal assumption of the research project was the constant configuration of six GNSS receivers. The frame consisted of fixed distances and right angles between the receivers' positions. In this subsection, the distances and angles calculated from averaged initial and LS-adjusted coordinates are compared with theoretical values from the frame. Table 3 presents the distance analysis, and Table 4 presents the angle analysis. The theoretical assumptions of the receiver positioning during the stationary survey corresponded to the target configuration used during mobile survey campaigns conducted on railway routes. The reference distances between six receivers (D \({}_{\text{ref}}\)) correspond to Figure 1, presenting a typical sensor configuration on the mobile railway platform. Reference distances represent the main along-and cross-track directions and two platform frame \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Angle (L-C-R)** & \(\boldsymbol{\alpha_{\text{ref}}}\) [\({}^{\circ}\)] & \(\boldsymbol{\mathrm{d}\alpha_{\text{init}}}\) [\({}^{\prime\prime}\)] & \(\boldsymbol{\mathrm{d}\alpha_{\text{OLS}}}\) [\({}^{\prime\prime}\)] & \(\boldsymbol{\mathrm{d}\alpha_{\text{RIS}}}\) [\({}^{\prime\prime}\)] & \(\boldsymbol{\mathrm{d}\alpha_{\text{CLS}}}\) [\({}^{\prime\prime}\)] \\ \hline CF-LF-LB & 90 & 633.6 & \(-13.9\) & \(-574.1\) & \(-0.9\) \\ LF-LB-CB & 90 & \(-701.8\) & \(-734.9\) & \(\boldsymbol{-1.1}\) & \(0.9\) \\ RB-RF-CF & 90 & \(-190.0\) & \(-207.9\) & \(-944.5\) & \(-5.7\) \\ CB-RB-RF & 90 & \(-514.8\) & \(-112.8\) & \(-35.1\) & \(5.7\) \\ RF-CF-LF & 180 & \(-854.2\) & \(-209.0\) & \(1320.4\) & \(6.6\) \\ RB-CB-LB & 180 & \(\boldsymbol{-1627.3}\) & \(-1278.5\) & \(-234.4\) & \(6.6\) \\  & **mean**\(\,\mathrm{l}\,\boldsymbol{\mathrm{d}\alpha}\,\mathrm{l}\) & **753.6** & **426.2** & **518.3** & **4.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The differences in angles in relation to the theoretical frame fixed values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Distance** & \(\boldsymbol{\mathrm{D}_{\text{ref}}}\) [m] & \(\boldsymbol{\mathrm{d}D_{\text{init}}}\) [mm] & \(\boldsymbol{\mathrm{D}_{\text{OLS}}}\) [mm] & \(\boldsymbol{\mathrm{d}D_{\text{RLS}}}\) [mm] & \(\boldsymbol{\mathrm{d}D_{\text{CLS}}}\) [mm] \\ \hline LF-LB & 7.000 & 2.1 & 4.0 & 1.3 & \(-0.1\) \\ CF-CB & 7.000 & 1.9 & 1.3 & \(-0.8\) & \(-0.1\) \\ RF-RB & 7.000 & 4.4 & 2.5 & 2.8 & \(-0.1\) \\ LF-CF & 0.750 & \(-7.7\) & \(-8.8\) & \(-1.8\) & \(0.0\) \\ CF-RF & 0.750 & \(\boldsymbol{10.3}\) & \(\boldsymbol{11.9}\) & \(\boldsymbol{3.5}\) & \(0.0\) \\ LB-CB & 0.750 & \(-9.3\) & \(-9.4\) & \(\boldsymbol{-3.3}\) & \(0.0\) \\ CB-RB & 0.750 & \(-2.1\) & \(-2.1\) & \(-1.8\) & \(0.0\) \\ LF-RF & 1.500 & 2.5 & 3.1 & 1.7 & \(0.0\) \\ LB-RB & 1.500 & \(\boldsymbol{-11.4}\) & \(\boldsymbol{-11.6}\) & \(\boldsymbol{-5.1}\) & \(0.0\) \\ LF-RB & 7.159 & 0.5 & 0.9 & 1.0 & \(-0.1\) \\ LB-RF & 7.159 & 4.0 & 3.7 & 2.2 & \(0.0\) \\  & **mean**\(\,\mathrm{l}\,\boldsymbol{\mathrm{d}D}\,\mathrm{l}\) & **5.1** & **5.4** & **2.3** & **0.0** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The differences in distances in relation to the theoretical frame fixed values. diagonals. The third column (D \({}_{\text{init}}\)) contains the differences values with respect to the reference distances. The remaining three columns present the differences obtained from the coordinates of three compared LS adjustment methods. The distances calculated from the initial coordinates from post-processing in two cases exceeded the 1 cm threshold value. The mean average distance difference equaled 5.1 mm and 5.4 mm in initial and OLS datasets, respectively, which showed that the application of standard LS adjustment did not improve the compliance of the estimates with theoretical platform frame configuration. The mean value was reduced twice to 2.3 mm in robust RLS adjustment, however, in three cases the differences exceeding 3 mm were noted.