# Designation of the Quality of EGNOS+SDCM Satellite Positioning in the Approach to Landing Procedure
## 4 Results
### Validity of the Applied Research Method
Continuing the analysis of positioning accuracy, it should also be explained why the Multi-SBAS solution is far more effective than a single SBAS solution from the EGNOS supporting system. To do so, a comparison of the results for parameters (\(dr\), \(dh\)) was conducted between the proposed weighted mean model and the single SBAS/EGNOS solution. Figure 15 shows the results of comparison of the \(dr\) parameter between the weighted mean model and a single SBAS/EGNOS solution. It is worth noting that the Multi-SBAS solution improves the value of the \(dr\) parameter by 1% to 37% in comparison to a single SBAS/EGNOS solution. The obtained improvements expressed in per cent are rather significant. Moreover, Figure 16 shows the results of comparison of the \(dh\) parameter between the weighted mean model and a single SBAS/EGNOS solution. As far as the positioning of the vertical component is concerned, the results obtained from the weighted mean model were significantly better than those from the single SBAS/EGNOS solution. The accuracy of the vertical component calculated with use of the weighted mean model improved by 1% to 73%. Based on these results, one may claim that the application of the Multi-SBAS positioning method in the accuracy analysis is justified. This solution is significantly more effective, especially as the results apply to aviation applications. Figure 13: The comparison of results of parameter \(dr\) based on weighted mean model and arithmetic mean model. Figure 14: The comparison of position errors of parameter \(dh\) based on weighted mean model and arithmetic mean model. Figure 15: The comparison of results of parameter \(dr\) based on weighted mean model and EGNOS solution. Further comparative analyses refer to two quality parameters of SBAS satellite positioning, in this context, respectively, to availability and continuity. The comparative analysis should be based on Formulas (7) and (8) from Section 2. Namely, it is necessary to demonstrate the reasonability of implementation of the Formulas (7) and (8) in the Multi-SBAS solution. Let us analyse a case where one of the single SBAS solutions loses its availability and continuity. In this case, it was assumed that no solution from the SDCM system was available for the given measurement epoch. Then, Equations (7) and (8) in the Multi-SBAS model will take the following form:  
\[\left\{ \begin{array}{l}A_{m}=\frac{A_{ECNOS+x}}{a_{E}}=A_{EGNOS}\\ C_{m}=\frac{C_{ECNOS+x}}{a_{E}}=C_{EGNOS}\end{array} \right. \tag{10}\]  
What does the above Equation (10) actually mean in mathematical terms? If one single SBAS solution is lost (the SDCM solution, in this case), it will still be possible to determine the resultant values of availability and continuity, which will be determined from the EGNOS solution. It can be noted that the availability will still equal 100%, and the continuity will range from 0.0000699 to 0.0005595, according to Table 3. The weighted mean model is characterised by the fact that, if one of the parameters involved in the model is absent for the given epoch, then a resultant solution based on the results for the second parameter still exists. In aviation, this information is very important, as the determinability of the user's position every measurement epoch, e.g., at 1 s intervals, will be maintained. It is also worth analysing the case where the Multi-SBAS solution is considered for the arithmetic mean model. Then, Equations (7) and (8) will take the following form:  
\[\left\{ \begin{array}{l}A_{m}=\frac{A_{ECNOS}+A_{SDCM}}{2}\\ C_{m}=\frac{C_{EGNOS}+C_{SDCM}}{2}\end{array} \right. \tag{11}\]  
Figure 16: The comparison of results of parameter \(dh\) based on weighted mean model and EGNOS solution. Based on Equation (11) one may draw the conclusion that the resultant availability \(A_{m}\) will equal 50%, and, respectively, the resultant continuity \(C_{m}\) will range from 0.000035 to 0.0002798, i.e., it will be lower by half. What does this mean in practice for the proposed Equations (7) and (8)?