# Optimization of Protection Level of GBAS with Gaussian Mixture Model
## 5 Testing and Simulation
### Global GBAS Service Performance Simulation Verification
Considering the computational capability on the airborne side, the performance of the global protection level improvement was simulated for the traversal depth being 0 to 6, including a maximum set of \(2^{6}=64\) solution sets. The statistical analysis of the vertical protection level component's reduction of global CAT-II/IIIa and CAT-I ground ranging errors is shown in Figures 5 and 6. It can be seen that when the number of solution sets was increased, that is, with the increase in traversal depth, the vertical protection level component of the GBAS ground ranging error decreased effectively. Under the same traversal depth, the protection level of the GBAS ground ranging error CAT-I vertical protection component was significantly lower than for the CAT-II/IIIa vertical protection component. When the traversal depth was 2, the change in the degree of vertical protection was the largest. When the traversal depth was greater than 2, the change in the degree of vertical protection gradually became  
Figure 5: Comparison chart of GBAS vertical protection level reduction with different traversal depths. Figure 6: Comparison chart of the variation in GBAS vertical protection level reduction with different traversal depths. smaller. When the travel depth was 4, the CAT-II/IIIa ground ranging error protection level component was reduced by 10.0% and the CAT-I ground ranging error protection level component was reduced by 14.5%. When the traversal depth was 6, the CAT-II/IIIa ground ranging error protection level component was reduced by 13.9%, and the CAT-I ground ranging error protection level component was reduced by 18.6%. A \(5^{\circ}\times 5^{\circ}\) grid was used to compare the global CAT-I and CAT-II/IIIa vertical protection level simulations based on the single constellation GBAS of BeiDou-3. With a traversal depth of 4, the CAT-II/IIIa vertical protection level was reduced by 7.7% and the CAT-I protection level component was reduced by 10.3%. With a traversal depth of 6, the CAT-II/IIIa vertical protection level was reduced by 10.3% and the CAT-I protection level component was reduced by 13.1%. It can be seen that the required solution set traversal depth was 4 for CAT-I demand and 6 for CAT-II/IIIa demand with the goal of reducing 10% of the vertical protection level of the GBAS of BeiDou-3. Taking the CAT-II/IIIa traversal depth of 6 as an example, the global \(5^{\circ}\times  
As shown in Figures 7-9, the global vertical protection level of the different methods was highly correlated with latitude, and generally showed that the protection level decreased as the latitude changed from southern to northern latitudes, and the lowest protection level was found between 40 and 70 degrees north latitude, and the average values of the protection level of 99% availability for this method and Gaussian over-bounding method with the traversal depth of 6 were lower than 2.25 m and 2.5 m, respectively. The details are shown in Figure 10. Meanwhile, since China and neighboring regions can receive 3 IGSO more than other regions, the protection level in China and its surrounding areas is much lower than that in other areas at the same latitude, and is comparable to the protection level from 40 degrees to 70 degrees north latitude. Further analysis of the correlation between the performance of the proposed method and latitude showed that the proposed method had a higher level of performance im  
Figure 10: Latitude correlation diagram of global CAT II/IIIa GBAS vertical protection level under 99% availability of this method with traverse depth of 6 and Gaussian over-bounding method.