# Spoofing Detection Using GNSS/INS/Odometer Coupling for Vehicular Navigation
## 5 Spoofing Detection Performance
### Results of Data Set 2 (Dense Urban Environment)  
Figure 10 shows the trajectory analysed in downtown Calgary, which is surrounded by buildings of up to 80 stories in height. The green and red plots show the correct reference and GPS-based trajectories. The reference trajectory was provided by the NovAtel SPAN system described earlier with accuracy of 1 to 2 m. The GPS trajectory was obtained with a u-blox receiver. In this dense area, the GPS trajectory deviates from the reference one by up to 50 m horizontally due to GPS multipath, high measurement noise and poor geometry. The data set includes repeated runs of the above trajectory. The authentic scenario refers to the case when the GPS and RIO trajectories are synchronized both in time and location. The spoofing case refers to the scenario where the GPS and RIO trajectories do not match either in time and/or in location; this is done by deliberately introducing a time lag between the GPS and RIO trajectory data. Different time lags (50 s to 200 s in 10 s intervals) were utilized to generate detection statistics. Figure 11 shows the RIO errors for MEMS IMU and different update intervals (\(t_{u}\)) for the correct reference (green) and GPS-based (red) trajectories. The errors significantly increase in the GPS-based case due to multipath, measurement noise and geometry, which will increase spoofing detection false alarm probability. The error values of the true-reference trajectory shown in Figure 11 are similar to those of the GPS-based trajectory in open sky condition shown in Figure 7. To reduce a false alarm probability of the spoofing detection metric, one can increase the threshold but at the cost of reducing detection probability. As expected, increasing the update interval increases the error values. For \(t_{u}\) = 20 s, the errors exceed 10 m after a few epochs in the case of the true trajectory. However, threshold crossing happens in all \(t_{u}\) cases in the GPS-based trajectory case. Poor GPS performance in dense urban environments affects the performance of the proposed spoofing detection metric in the null-hypothesis. Figure 12 shows the histogram of the detection metric using true and GPS-based trajectories. This information will be used to determine the performance of the proposed method in terms of the receiver operation characteristics (ROC) plots. Figure 13 shows the mean RIO errors for various combinations of GPS and IMU sensors in the authentic case. The Ref-Tactical case shown in Figure 13 refers to the true-reference trajectory and tactical IMU. This case has the lowest errors compared to other cases and causes the lowest probability of false detection. The worst performing scenario belongs to the GPS-MEMS case. In all the cases increasing the update interval (\(t_{u}\)) increases the error values. Figure 9: RIO horizontal errors for various update intervals (\(t_{u}\)) in the spoofing case using the cellphone MEMS IMU. Figure 14: Horizontal trajectory for spoofed GPS, GPS/RIO, RIO with 20 s correction updates for MEMS IMU. Figure 12: Histogram of the detection metric values for reference and GPS trajectories for different update intervals. Figure 13: Mean trajectory errors for various combinations of GPS and IMU sensors for different update intervals. Receiver operation characteristics (ROC) which shows the performance of a detector was evaluated under different scenarios. Figure 16a shows ROC curves for the proposed detection metric for various update intervals using the u-blox GPS trajectory. Increasing \(t_{u}\) enhances both probability of false alarm and detection. However, as shown, for a given false alarm probability, increasing \(t_{u}\) enhances the detection performance. Figure 16b shows ROC plots for \(t_{u}\) = 10 s for true-reference and GPS trajectories, demonstrating that spoofing detection performance is degraded in dense urban environments due to satellite geometry, high noise and multipath as mentioned earlier.