# Integrity Analysis for GPS-Based Navigation of UAVs in Urban Environment
## 4 Discussion  
According to the above results, one can see that the number of visible satellites along with the cut-off elevations can be used to characterize integrity based on observed DOP values. In order to derive limiting cut-off elevations based on the acceptable integrity risks, we first explore the relationship between satellite visibility and DOP. For this purpose, 99.99998 th percentiles of HDOP and VDOP are  
Figure 9: Number of visible satellites based on cut-off elevations. calculated from the results of the second simulation for each number of visible satellites, as shown in Figure 10. In this figure the relationship between DOP and satellite visibility can be analyzed independently from the cut-off elevations. It shows the necessary number of visible satellites that provides the required, for a given integrity, the upper boundary of DOP, which is especially important at high blockage conditions. For horizontal positioning integrity, at least five visible satellites are required to ensure HDOP < 5.581, seven visible satellites are required to ensure HDOP < 2.291 and eight visible satellites are required to ensure HDOP < 1.534. HDOP below 1.123 can be achieved if at least ten satellites are visible. For vertical positioning integrity, at least seven visible satellites are required to ensure VDOP < 7.45, eight visible satellites are required to ensure VDOP < 3.575, eleven visible satellites are required to ensure VDOP < 2.165 and twelve visible satellites are required to ensure VDOP < 2.083. According to these results, DOP-based indirect protection levels can be specified using cut-off elevation and satellite visibility to describe GPS-based positioning integrity in terms of protection level zones. To explain how this can be achieved, let us consider an example of the protection level zone in Figure 11 expressed in the form of HDOP < 1.3373, which corresponds to Figure 12. HPL = 7.7973 m and 5\({}^{\circ}\) cut-off elevation with regards to Table 7. The smallest number of visible satellites observed during the simulation corresponding to 5\({}^{\circ}\) cut-off elevation is 8, following results shown in Figure 9. These two parameters define the primary boundaries of the protection level (integrity) zone. Inside each zone, it can be considered that integrity requirements can be guaranteed for specified protection levels. To define secondary boundaries, the minimum number of visible satellites to guarantee HDOP < 1.3373 is taken from Figure 10 as 10. According to Figures 9 and 10 visible satellites can be observed only up to 15\({}^{\circ}\) cut off elevation. Hence, 10 visible satellites and 15\({}^{\circ}\) cut-off elevation forms secondary boundaries of the protection level zone. These secondary boundaries are required to cover the cases where cut-off elevation is exceeded, but there are still enough satellites to satisfy integrity requirements. Finally, the union of these two zones defines the integrity zone based on indirect protection levels considering both cut-off elevation and satellite visibility. Following this idea, we have compiled results of the second simulation in Figure 12, which visualizes indirect protection levels (in the form of the limiting DOP values) with respect to cut-off elevations and number of visible satellites. Figure 10: Relationship between number of visible satellites and DOP. Considering that the integrity failure condition when HPL > HAL, we specify integrity zones based on HPL = HAL and VPL = VAL. To maintain the required integrity level UAV should stay within these zones during the flight. Assumed in Section 2 HAL and VAL for the scenario of UAV flight in urban environment (10 and 25 m, respectively) transform into limits of HDOP < 1.87 and VDOP < 3.68 according to our simulation results. From Figure 12, it follows that UAV should be within green, yellow or orange zones in order to satisfy these requirements. The conditions can be checked using observables obtained from the receiver position solution and environmental parameters.