## 5 Simulation and Analysis
### Performance Analysis of Identification Algorithm  
First, we discuss how to choose the proper identification threshold in the first step of the one-bounce scattering signal identification algorithm. Assuming scatterers are generated by the ROS model, the scattering radius is 50 m and the error of TOA satisfies \(N\big{(}0,1^{2}\big{)}\) and the error of AOA satisfies \(N\big{(}0,0.5^{2}\big{)}\). For the first step of the proposed algorithm, false alarm probability and alarm dismissal probability versus identification threshold are shown in Figure 4. With the increasing threshold value, false alarm probability increases but alarm dismissal probability decreases, and when the threshold value is 35 m, the sum of false alarm probability and alarm dismissal probability attains a minimum value of 27.51%, therefore, we adopt 35 m as the threshold value in the following simulations. Figure 3: Localization of geometry. The \(P_{IE}\) versus scattering radius comparison is presented in Figure 5. The scattering radius is 10 m, 20 m, 30 m, 40 m, 50 m, 60 m and 70 m, respectively. The scatterers are generated following the ROS model or DOS model. The error of TOA satisfies \(N\big{(}0,1^{2}\big{)}\), and that of AOA satisfies \(N\big{(}0,0.5^{2}\big{)}\). It can be observed that with the increasing scattering radius from 10 m to 70 m identification algorithm's performance is improved, and \(P_{IE}\) of the two-step algorithm, up to 95%, the probability of scattering signal misidentification of a scatterer is just 5%, which is small enough. The two-step algorithm outperforms the one-step algorithm indicating that the second step is necessary. As Figure 5 shows, for the same scattering radius, the \(P_{IE}\) under the condition of ROS mode is superior to that of the DOS model, this is because the distance between two scatterers under the condition of the ROS model is larger than that of the DOS model for the same scattering radius, which is in favor of distinguishing scattering signals. We vary the standard deviations of TOA error to evaluate the algorithm's performance. The scatterers are generated following the ROS model or DOS model, respectively, scattering radius is 50 m. The error of TOA satisfies \(N\big{(}0,\,\delta_{r}^{2}\big{)}\), \(\delta_{T}\) is 1 m, 2 m, 3 m, 4 m and 5 m, respectively, and the error of AOA satisfies \(N\big{(}0,\,0.5^{2}\big{)}\). As depicted in Figure 6, the growth  
Figure 4: Effect of identification threshold on false alarm probability and alarm dismissal probability. Figure 5: \(P_{IE}\) versus scattering radius. of the standard deviation of the TOA error has little effect on the one-step algorithm, whereas, with the growth of the standard deviation of the TOA error, the performance of the two-step algorithm deteriorates. This is because, in the identification procedure, the second step of the two-step algorithm adopts the measurements of TOA to estimate the coordinates of the scatterer first, and then on this basis, adopts the scattering signals combination that minimizes the sum of absolute values of the difference between the estimates and measurements of AOA, this procedure is sensitive to the variation of scatterer coordinate, thus, with the increasing standard deviation of the TOA, the \(P_{IE}\) performance of the two-step algorithm deteriorates. Similar to Figure 5, the \(P_{IE}\) performance of the two-step is superior to that of the one-step algorithm, and the \(P_{IE}\) performance under the condition of the ROS model is better than that of the DOS model. The \(P_{IE}\) versus AOA error comparison is presented in Figure 7. The scatterers are generated following the ROS model or DOS model, respectively, scattering radius is 50 m. The error of AOA satisfies \(N(0,\delta_{A}^{2})\), \(\delta_{A}\) is 0.2\({}^{0}\), 0.4\({}^{0}\), 0.6\({}^{0}\), 0.8\({}^{0}\), and 1\({}^{0}\), respectively, and the error of TOA satisfies \(N(0,1^{2})\).