## 3 Testing and Results
### Test-1: Hovering by a Tunnel Entrance  
Test-1 was performed by running the cart carrying the navigation system back and forth from a position where the sky visibility was good enough to fix the phase ambiguities to a tunnel denying the satellite signals (blue dots in Figure 2) simulating the inspection of the bridge piles, which are otherwise hard to access without using a drone. The test began with the rover solutions in a fixed condition in a location where the sky visibility was good enough to see satellites in all directions, at least those with an elevation above 20 degrees. This starting position was close to a metal covered bike shelter that could  
Figure 2: The ITC building tests site. The picture shows the tracks used for test-1, test-2, and test-3 in blue, orange, and red, respectively. have induced some multipath effect. Then, the cart was moved toward the building facade, which is about 7 m high in that position, and under the tunnel passing through it. Therefore, both a partial obstacle (the facade) and a total obstacle (the tunnel) to sky visibility occurred. After a time span ranging from 5 to 20 s under the tunnel, the cart was moved back to the initial position. This was repeated 24 times, always starting only once the receiver had re-gained the fixed condition. The cart was moved at a speed of about 1 m/sec. Figure 3 shows the time series of the elevation (up coordinates) recorded during the whole test, together with their estimated precision (bottom graph) in terms of RMS (1\(\sigma\) confidence level). Note that the estimated precision of the GNSS position provided by the QGround Control is split into the vertical and the horizontal directions, providing the VRMS and the HRMS, respectively. These precision estimates are also available in real time to the pilot and could in principle be used to decide how much trust to give to the positioning system. The red break lines represent the starting time of the cart from the initial position, whereas the blue ones indicate when the cart moved back from under the tunnel. The black dots represent the solutions obtained in fixed conditions, while blue dots refer to floating solutions and red ones indicate single solutions. The choice to show the vertical component in the time series is because this direction is the only one well constrained by the ground floor along the cart path, thus avoiding further variability of the coordinates other than coming from GNSS positioning errors. Figure 3: Time series related to test-1. The (**central**) chart shows the elevation (up direction). The black, blue, and red dots are used to represent fixed, floating, and single solutions, respectively. The  
red and blue lines represent the epochs when the cart started from the initial position and moved back from the tunnel, respectively. The two (**upper**) plots highlight typical cases from the time series. In particular, the left one shows the solution's behavior under regular working conditions, whereas the left plot evidences a case of failure in the ambiguity fixing. The (**bottom**) chart shows the estimated vertical precision parameters related to the fix solutions only, while for float and single solutions, it goes by far out of scale. Figure 4 shows the horizontal trajectories of the rover, where the dots' colors have the same meanings as in Figure 3. The top left plot represents the runs from the initial position to the tunnel, showing the overall good quality of the coordinates during the approach of the cart to the obstacle, even when the solutions are marked as floating (red dots). In contrast, in the top right chart, the runs back from the tunnel to the initial position are reported. In these cases, the significant difference between the trajectories for the floating solutions (blue dots) is evident. The full precision is resumed as soon as the fixing conditions are re-gained. This sometimes happens only after the return of the cart to the initial position.