# Designation of the Quality of EGNOS+SDCM Satellite Positioning in the Approach to Landing Procedure
## 4 Results
### Validity of the Applied Research Method
If we use the arithmetic mean model for the Multi-SBAS solution and mathematical Equations (7) and (8), then the resultant availability and continuity will be underestimated by 50% in reference to the nominal results. Moreover, the resultant availability and continuity will be inadequate compared to the weighted mean model. Taking an objective approach to Equations (10) and (11), one may notice the importance of the weighted mean model for the strategy of calculating the resultant values of availability and continuity. The last stage of analysis in the first part of the discussion concerns the evaluation of the results of the determination of the integrity parameter of SBAS positioning. Figures 17 and 18 show the results of integrity parameters (HPL, VPL) from the weighted mean model and the arithmetic mean model. The values from the weighted mean model were interpreted and presented in Figure 9. However, it is worth explaining why the weighted mean model is better than the arithmetic mean model for the integrity parameter. Namely, the maximum integrity values for the arithmetic mean model were, respectively: 5.30 m for the HPL parameter, and 9.01 m for the VPL parameter. As a result, comparative analysis reveals an improvement in the integrity results  
In the case of determining the integrity of SBAS positioning in air navigation, it is crucial from the point of view of flight safety to determine the risk indexes in the form of the Integrity Risk (_IR_) parameter [78]. In the case of the weighted average model, it can be written that the _IR_ parameter can be determined as follows:  
\[IR_{m}=\frac{IR_{EGNOS}\cdot\alpha_{E}\ +\ IR_{SDCM}\cdot\alpha_{S}}{\alpha_{E}\ +\ \alpha_{S}} \tag{12}\]  
where:  
\(IR_{EGNOS}=\frac{const\cdot t_{period}}{t_{approach}}=\frac{10^{-5}\cdot 150\ s}{10 49\ s}=1.429933\cdot 10^{-6}=IR_{SDCM}\),  
\(IR_{EGNOS}\)-_IR_ value from EGNOS solution,  
\(IR_{SDCM}\)-_IR_ value from SDCM solution,  
\(const=10^{-5}\)[78],  
\(t_{period}=150\ s\), primary test time for the _IR_ parameter [78],  
\(t_{approach}\)-duration of approach and landing operations [78]. In the analysed case, the value of the resultant \(IR_{m}\) parameter will be equal to the _IR_ parameters from the single solution of EGNOS (\(IR_{EGNOS}\)) and SDCM (\(IR_{SDCM}\)). However, this is the case where we have continuity of EGNOS and SDCM solution for the same instant of time. Moreover, the parameter \(t_{approach}\) in the EGNOS and SDCM solution takes the same time interval. The proposed Equation (12) is universal, because in case of loss of solution from a single SBAS (EGNOS or SDCM), the value of \(IR_{m}\) parameter will still be constant and equal to the value obtained from the weighted average model, i.e., \(1.429933\cdot 10^{-6}\). Of course, the calculated value of \(1.429933\cdot 10^{-6}\) is only constant for the analysed case of the aircraft approach and landing. In another aviation experiment it will take a different value adequate to the duration of the approach and landing. If, in turn, we used the arithmetic mean model then Equation (12) will take the form:  
\[IR_{m}=\frac{IR_{EGNOS}\ +\ IR_{SDCM}}{2} \tag{13}\]  
Figure 18: The comparison of results of parameter VPL based on weighted mean model and arithmetic mean model. This, consequently, will make the \(IR_{m}\) parameter for the arithmetic mean model in the analysed case equal to 0.714966\(\cdot 10^{-6}\). So, it can be said that there is an underestimation of \(IR_{m}\) parameter at the level of 50%. The value of \(IR_{m}\) parameter will be underestimated by 50% in case of arithmetic mean model.