# A Proposal of a Troposphere Model in a GNSS Simulator for VANET Applications
## 6 Performance Evaluation
### Experimental Results  
The results of the conducted experiments are shown now in order to discuss the goodness of the proposal. The line called \"real\" path, colored in red, is related to the real coordinates given in input to the simulator. In Figure 7a it is possible to observe a comparison between the \"real\" path and the two simulated ones calculated on the GPS receiver (the smartphone in the vehicle in our case): coordinates given in input to the simulator are depicted in red. This red line represents the reference for the other two lines representing the coordinates (in decimal degree (dd)) calculated by GPS receiver: the blue line (with the marker \"*\") indicates the use of simulator with correction algorithm disabled, and the black one (with the marker \"+\") indicates the use of the correction algorithm activated. GPS receiver should not deviate too much from points of red line in order to guarantee a correct GPS operation and, then a correct position. The figure shows that, in this case, the difference between curves representing the calculated path with and without troposphere correction is very small and not appreciable in this  
Figure 5: KML example file loaded with SatGen software. Figure 6: Command used to transfer the binary file to the HackRF One card. graphic, but the details about real error in meters is appreciable in the Figure 6(b). Moreover, in order to show better the results and differences between the considered approach, we have increased path points extending the considered path in the three scenarios. The graphic in Figure 6(b) shows the positioning error of the two simulated paths in meters in respect to the real considered path. We precise that the positioning error represents the error committed by the calculated path with and without troposphere correction module considering the distance in meters between the coordinates of calculated path in respect to the real path. These two graphics show the results obtained starting from a path located at a middle latitude and an altitude of about 200 m above sea level. The graphic in Figure 6(c) shows the error committed in calculating the altitude above the sea level by the receiver. As it is possible to observe in this figure, the error on latitude and longitude is on average lower in the case in which the tropospheric algorithm is activated, for each point of the considered path. The goodness of the proposal has been assessed also for different latitudes: an equatorial latitude by a route in Brazil and an extreme latitude with a route in Norway have been considered and extrapolated by Google Earth Pro software. Figure 7: Experimental results for Middle Latitude (route in Italy). Figure 8a-c show the same output parameters illustrated above (in the case of middle latitudes) considering the extreme latitude coordinates. The same consideration, made for the previous case, is possible to do also for this new simulative campaign. It is possible to observe a better behavior of the system when the proposed module is activated in respect to the one with troposphere module disabled. The third campaign is related to experiments considering equatorial latitudes. As it is possible to observe in Figure 9a-c, the results show how the obtained curves have the same trend of the previous cases. Comparing the graphics of the different campaigns, it is possible to observe a better behavior of the system at equatorial latitudes in respect to extreme ones. The graphics show an error lower in the equatorial case. Instead, taking into account extreme latitudes, an higher difference between the \"real path\" curve in respect to the simulated one (using the troposphere model) is possible to observe. Figure 8: Experimental results for Extreme Latitude (route in Norway). Finally, in Figure 10 we present the estimated probability density functions, the histograms for a considered Middle Latitude experiments on a path of 1.8 km and taking into account 1500 path points.