## 4 Evaluation
### Effect of Malicious Attacks on Positioning Accuracy
#### 4.2.1 Timestamp Data Tampering  
Initially, we tampered with the reception timestamp, which is recorded on the device when an anchor node receives a UWB message. As mentioned in Section 3.2.1, the implemented module records the timestamp data that the DW1000 chipset generates and records internally. Therefore, the minimum interval of recordable timestamps was 15.65 ps, and we refer to this value as a time slot. We generated tampered timestamp data by adding Gaussian noise of various scales to one anchor node. We conducted experiments for a total of eight cases, including the steady state, and collected data for three minutes for each case. Table 3 and Figure 5 present the experimental results.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Node** & **Tag 1** & **Tag 2** & **Tag 3** \\ \hline Average Positioning Error (cm) & 10.50 & 10.82 & 13.10 \\ Standard Deviation (cm) & 5.10 & 4.41 & 6.07 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Positioning performance of the proposed localization system.  
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**State** & **Steady** & **500** & **1000** & **2000** & **5000** & **10,000** & **50,000** & **100,000** \\  & & **Time Slots** & **Time Slots** & **Time Slots** & **Time Slots** & **Time Slots** & **Time Slots** \\ \hline Average & \multirow{2}{*}{0.115} & \multirow{2}{*}{5.839} & \multirow{2}{*}{17.925} & \multirow{2}{*}{42.895} & \multirow{2}{*}{170.638} & \multirow{2}{*}{552.038} & \multirow{2}{*}{1.287 \(\times\) 10\({}^{4}\)} & \multirow{2}{*}{4.345 \(\times\) 10\({}^{4}\)} \\ Error (m) & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Positioning performance under normal and timestamp data tampering conditions.  
Table 3 first shows the average error, representing the mean error of the localization data collected from the three tag nodes. The steady state case performed normal localization without data tampering. The seven noise-generating cases added Gaussian noise with the respective mean and 10% of the numerical standard deviation to each of the message reception timestamp data. The experimental results showed that even a slight time data manipulation of an average of 500 time slots can increase the error to nearly 6 m, an unacceptable error range for most tasks requiring precise localization. Additionally, as a result of performing timestamp modulation over 1000 time slots, it can be seen that the position estimation error was too large to say that positioning was being performed.  
To the average error values shown in Table 3, we graphed the cumulative distribution function for the positioning error data collected from a total of eight cases, including the steady state. Figure 5 shows the CDF of the positioning error data for each case from the same experiment, with the x-axis representing the positioning error in a log scale. As seen in the table and figure, when a time data attack occurred, the positioning performance deteriorated severely, not only in cases of significant numerical manipulation, but also in cases of minor alterations. As can be seen in the graph, the steady state showed stable results with very low positioning errors for most data. For the remaining seven cases that included noise, most of the data collected over 3 min showed highly large positioning errors at a similar level.