# Designation of the Quality of EGNOS+SDCM Satellite Positioning in the Approach to Landing Procedure
## 4 Results
### Validity of the Applied Research Method  
From the point of view of the applied research method, the first part of the discussion is the most important. In fact, demonstrating the validity of the presented research method requires conducting numerous additional comparative analyses for the parameters obtained from the mathematical Equations (1)-(9). Firstly, the obtained standard deviation results were evaluated and analysed. Figures 10-12 show a comparison of the standard deviations obtained from the weighted mean model (see Equations (1)-(3)) and the arithmetic mean model (62). The values from the weighted mean model were interpreted and presented in Figure 6. However, it is worth explaining why the weighted mean model is better than the arithmetic mean model for the standard deviation parameters. Namely, for the arithmetic mean model, the maximum standard deviation results are, respectively: 0.65 m for the \(\delta B\) parameter, 0.63 m for the \(\delta L\) parameter, and 1.69 m for the \(\delta h\) parameter. As a result, comparative analysis reveals an improvement in the standard deviation results for the weighted mean model (Equations (1)-(3)). The results were improved by 61-65% for the horizontal components, and by 63% for the vertical component. This also demonstrates the validity of the adopted calculation strategy for the weighted mean model for the Multi-SBAS solution. The further part of the discussion focuses on the comparative analysis of the accuracy parameter. Such comparative analysis was conducted of the accuracy from the weighted mean and the arithmetic mean models. Then, it was demonstrated how the weighted mean model improves the positioning accuracy for a single SBAS solution from the EGNOS supporting system. Figure 13 presents the comparison of the results of positioning accuracy in the 3D space, i.e., in fact of the \(dr\) parameter. The comparison was based on the results of the \(dr\) parameter from the weighted mean model and the arithmetic mean model. The values of the \(dr\) parameter from the weighted mean model were interpreted and presented in Figure 8. On the other hand, in Figure 13 the results of the \(dr\) parameter from the arithmetic mean model were added. The results of the comparative analysis of the \(dr\)  
Figure 10: The comparison of results of standard deviations along B axis. parameter revealed that the weighted mean solution proposed by the authors improved the results of the \(dr\) parameter by 1% to 7% in comparison to the arithmetic mean model. It should be noted that this applies to accuracy in the 3D space, which is influenced to the greatest extent by errors in the position of \((dB,\ dL,\ dh)\), as shown in Equations (4) and (6). Figure 11: The comparison of results of standard deviations along L axis. Figure 12: The comparison of results of standard deviations along h axis. As far as the comparative analysis of the accuracy between the weighted mean and arithmetic mean models is concerned, it is worth mentioning the position errors determined for the vertical component. Figure 14 presents the results of the comparison of the position errors for ellipsoidal height that were calculated with use of the weighted mean and arithmetic mean models. The values of the \(dh\) parameter from the weighted mean model were interpreted and presented in Figure 7. The results of the comparative analysis of the \(dh\) parameter revealed that the weighted mean solution proposed by the authors improved the results of the \(dh\) parameter by 1% to 14% in comparison to the arithmetic mean model. The effectiveness of the proposed solution for the weighted mean model and the vertical component is quite important for the phase of approach to landing and the landing itself. The results presented in Figure 14 demonstrate that the practical application of the weighted mean model yields better results than that of the arithmetic mean model. Improved vertical positioning accuracy is also crucial for the safety of flight.