# Target Localization via Integrated and Segregated Ranging Based on RSS and TOA Measurements
## 5 Simulation Results
It also illustrates a comparison of cumulative distribution function (CDF) versus localization error (LE), defined as \(\|\widehat{\mathbf{x}}_{i}-\mathbf{x}_{i}\|\) (m) in the same scenario. The figure presents the results of the estimator when it uses the proposed heuristic approach, denoted as \"Selection\", as well as the results of the estimator utilizing double RSS-only and double TOA-only measurements. Although the comparison in terms of quantity of the acquired information is fair, it is important to note that, in order to acquire the double measurements, SR-WLSRSS and SR-WLSTOA require two signal transmissions. This might affect the sensors' battery lives in the long term, as well as the utilization efficiency of the radio spectrum (doubling the measurement time and increasing the risk of message collisions). On the other hand, the hybrid algorithms require a single transmission to acquire two measurements (RSS and TOA), at a cost of a somewhat increased complexity of the sensors in terms of hardware. Nevertheless, recent advances in micro electro-mechanical systems allow practically all modern devices to measure these two quantities [1; 10]. Figure 4: RMSE versus \(N\) comparison for HWLS. From Figure 6 one can see that our procedure for choosing _the best_ alternative for each link works well, since such estimator matches or even betters the performance of the previously best option in all considered scenarios. This estimator consistently shows the best performance, while a tendency of the estimators using RSS-only and TOA-only observations to worsen and improve as \(B\) increases is noticed, respectively. Please note that in this work, NLOS environments were considered, whereas the authors in [20] considered that all links were LOS. Although our general findings are in line with the ones presented there, the difference in the considered scenarios might explain why they do not have a perfect alignment in the case where \(B\) is large. In order to check the robustness of the proposed heuristic approach to different values of \(\epsilon_{\min}\) and \(\epsilon_{\max}\), the RMSE versus \(N\) for the heuristic approach applied to SR-WLS algorithm in the first considered scenario for different set of values of these parameters is presented in Figure 7. Note that all three sets of values chosen as the limits for \(\epsilon\) are reasonable in the sense that they capture what is considered to be short/long inter-sensor distance. It can be seen from Figure 7 that there is only marginal difference in the performance for different settings of the parameters of interest, indicating that the proposed heuristic approach is robust to them. Figure 5: RMSE versus \(N\) comparison for NR and JAH. Figure 6: Simulation results for SR-WLS, when \(\text{bias}_{\text{max}}=6\) (dB, m), \(\text{bias}_{i}\sim\mathcal{U}[0,\text{bias}_{\text{max}}]\) (dB, m). Figure 7: _Cont._  
In practice, it is likely to have a mixture of LOS/NLOS links; hence, it is of interest to study the performance of an algorithm against different values of \(|\mathcal{L}_{n}|\). To do so, the RMSE versus \(|\mathcal{L}_{n}|\) performance comparison of the proposed heuristic approach applied to SR-WLS in the first considered scenario when \(N=10\) is presented in Figure 8. Moreover, to account for realistic measurement model mismatch and the robustness of the proposed heuristic approach to imperfect knowledge of the PLE, in Figure 8 the PLE is chosen randomly for each link, i.e., it is chosen from a uniform distribution from the interval \([2.7,3.3]\), \(\gamma_{i}\sim\mathcal{U}\{2.7,3.3\}\). Figure 8 shows that the proposed heuristic approach is robust to the number of LOS/NLOS links in general. However, in the case where \(B=50\) m, one can notice a clear tendency of its performance to degrade as the number of NLOS links is increased. This result is interesting and not foreseen. Although there is no evidence, it is most likely caused by the poor quality of long inter-sensor RSS measurements, which in NLOS environments suffer additional deterioration.