# Risk-Aware Wireless Positioning in
## 5 Numerical Results  
In this section, we evaluate our proposed wireless positioning scheme. We first explain the RSS map and the risk map modeling, by which our proposed localization scheme is evaluated and then compare our proposed scheme with the conventional one. Note that Figure 5 is based on the actual measurement and Figure 6 is based on our modeling for performance evaluation. Also, Figures 7-10 are from the simulation.  
Figure 5: The Received Signal Strength (RSS) map (dBm).  
Because our proposed localization scheme is based on the fingerprinting scheme, we first model the RSS map. We consider two BSs of the IEEE802.11g (i.e., WiFi) standard, of which the positions are (\(-20\), \(0\)) and (\(20\), \(0\)), respectively, in meters. Then, we obtain the received signal strength (RSS) map by measurement. Figure 5 shows the geometry we considered with the measured RSSs at each cell. As can be seen in Figure 5, we consider a total of 28 cells (i.e., \(N=28\)), where each cell is a square with sides 20 m in length and the measured RSS values from \(BS_{1}\) and \(BS_{2}\) are marked from the center of each cell.  
Because we are considering maritime safety, we need to define the risk with respect to the user's position. To model the risk at each cell (i.e., \(R_{i}(f_{i})\) given in (6)), we consider the parameter \(\alpha=1\), which means that the risk linearly decreases with respect to the positioning signal frequency. Then, to model the risk from depth, we consider the geometry given in Figure 6 with the parameter \(\beta=2\), which means that the risk increases with respect to the square of the depth. For other risk factors, we simply consider \(k_{1}=\ldots=k_{28}=1\). As a result, the risk is modeled as in Figure 7.  
Figure 6: The water depth modeling for the performance evaluation.  
Figure 7: The risk map that represents \(R_{i}(f_{i})\) given in (6).  
For other parameters, we assume that the power consumption for a single time positioning signal transmission is \(1\) watt (i.e., \(W=1\) W). In Figure 8, we plot the achievable average risk of a user with respect to the user's battery power budget (i.e., \(E\)), when the user device lifetime is two hours (i.e., \(L=7200\) s). As can be observed in Figure 8, the user's average risk decreases as the user's battery budget increases both in our proposed scheme and in the conventional scheme. This is because with greater battery power budget, the user can more frequently transmit the positioning signal during the device lifetime. However, with the same power budget, we observed that our proposed scheme decreases average risk by adaptively transmitting the positioning signal according to the position.  
Figure 8: The average risk with respect to the power budget of the user.  
Figure 9: The average risk with respect to the sensitivity of the risk to the position accuracy (i.e., \(\alpha\)).  
Figure 9 shows the average risk with respect to the different sensitivities of the risk to the accuracy (i.e., \(\alpha\)), where \(E=10\) Wh, \(\beta=2\) and all other parameters are same. In Figure 9, we can observe that our proposed scheme outperforms to the conventional scheme for any value of \(\alpha\). Also, in Figure 10, we show the average risk per different sensitivities of the risk to the water depth (i.e., \(\beta\)), where \(E=10\) Wh, \(\alpha=1\) and all other parameters are same. As we can see in Figure 10, our proposed scheme outperforms to the conventional scheme for any value of \(\beta\).