# GNSS Spoofing Identification and Smoothing Localization Method for GNSS/Visual SLAM System
## 4 Simulation results  
### Experimental Conditions and Data Set  
In order to analyze the proposed GNSS spoofing identification and smoothing localization method based on GNSS/Visual SLAM system (referred to as PTC-SLM), this paper selects the commonly used autonomous driving data set KITTI [24,25] for simulation verification and performance evaluation. The rural and urban scenes in the KITTI datasets are used, and the ground-truth of the two scenes are shown in Figure 5. The sensors we use  
Figure 4: Flow-chart.  
are a GNSS navigation system and a binocular vision system composed of two identical gray-scale cameras. The parameters of sensors are shown in Table 1.  
In order to verify the proposed PTC-SLM method, we performed a spoofing simulation on the GNSS data in the two KITTI datasets. From the analysis in Section 3.3, it can be seen that the performance of GNSS spoofing in the mobile terminal is the deviation of the localization domain. In the spoofing process, since the spoofing terminal does not know the destination of the terminal, in order to deceive the terminal to the target point, it is necessary to adjust the magnitude of the spoofing distance when each spoofing signal is sent. Therefore, the GNSS spoofing attack shown in Equation (34) is injected into the GNSS measurement data in the KITTI dataset.  
\[\hat{l}_{i}=l_{i}-\Delta l_{i}\,\ \hat{b}_{i}=b_{i}-\Delta b_{i} \tag{34}\]  
where \(l_{i}\) and \(b_{i}\) are the actual measurement longitude and latitude of the terminal at time \(i\), \(\Delta l_{i}\) is the longitude error at time \(i\) and \(\Delta b_{i}\) is the latitude error at time \(i\). In our forwarding spoofing simulation, we pull the terminal to a place parallel to the actual direction of travel, then the spoofing distance becomes a fixed value (\(\Delta l_{i}=\Delta b_{i}=\delta_{\rm s}\)). In our inducing spoofing simulation, we gradually induce the terminal, so that every moment the spoofing terminal will increase the spoofing distance by a small displacement. Assume that the spoofing superimposed by the spoofing terminal is linearly increasing and assume the spoofing starts at time \(i+1\), then the cumulative drift of inducing spoofing at time \(j\) (\(j>i\)) is  
\[\Delta l_{j}=\sum_{t=i}^{j}\Delta l_{t}=\frac{j(j+1)}{2}\Delta l_{s}\,\ \Delta b_{j}=\sum_{t=i}^{j}\Delta b_{t}=\frac{j(j+1)}{2}\Delta b_{s} \tag{35}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor** & **Model** & **Sensor Error** & **Number** \\ \hline GNSS & OXTS RT 3003 & \multicolumn{2}{c}{open sky localization errors \(<5\) cm} & 1 \\ Camera & FL2-14S3M-C & \(1392\times 512\) pixels, \(1/2^{\rm w}\) Sony ICX267 CCD & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of sensor simulation parameters.  
Figure 5: Trajectories of ground-truth in (**a**) rural and (**b**) urban scenes.  
where \(\Delta l_{s}\) and \(\Delta b_{s}\) are the distance of spoofing superimposed in the longitude and latitude directions. After the spoofing attack is injected, the localizations of the mobile terminal are gradually deviated from the correct track. If the GNSS spoofing is not detected in time, the mobile terminal is likely to be kidnapped on other paths or directly damaged by a collision accident. Next, we analyze the parameters of the PTC-SLM method to confirm that the time and localization verification parameters are reasonable.