# Target Localization via Integrated and Segregated Ranging Based on RSS and TOA Measurements
## 5 Simulation Results  
In this section, a set of simulation results are presented with the objective to analyze the performance of the considered algorithms and compare them with the performance of their counterparts that make use of RSS-only and TOA-only observations. Note that HWLS in [18], NR in [23] and JAH [20] were all implemented here with perfect knowledge of noise powers and perfect knowledge of \(b_{i}\) and \(\beta_{i}\), which does not hold in practice. Hence, the results presented herein can be seen as lower bounds for these estimators, rather than their true achievable performance. All presented results were acquired by using MATLAB. Two main scenarios are considered: (1) random deployment of all sensors inside a quadratic region of length \(B\) in each Monte Carlo, \(M_{c}\), run, and (2) fixed placement of anchors according to Table 2 and random deployment of the target within a quadratic region of length \(B_{t}\). The second scenario is adopted here with the purpose of guaranteeing a steady distance between the target and anchors. Note that the first \(N\) anchors were always employed for this scenario, in concordance with Table 2. RSS and TOA measurements were generated according to (1a) and (1b). Unless stated otherwise, fixed simulation parameters are summarized in Table 3. For the ease of expression, \(\sigma_{i}\) (dB, m) and bias\({}_{i}\) (dB, m) are used to denote the noise powers and the NLOS biases of both the RSS and TOA measurements, respectively. Moreover, the NLOS biases were drawn randomly from an exponential distribution whose rate parameter is drawn from a uniform distribution on the interval \([0,\text{bias}_{\text{max}}]\) (dB, m), i.e., \(\text{bias}_{i}\sim\text{Exp}(\mathcal{U}[0,\text{bias}_{\text{max}}])\), \(i=1,...,N\), in each \(M_{c}\) run. The main performance metric is the root mean squared error (RMSE), \(\text{RMSE}=\sqrt{\sum_{i=1}^{M_{c}}\frac{\|\mathbf{x}_{i}-\widehat{\mathbf{x}}_{i}\|} {M_{c}}}\), where \(\widehat{\mathbf{x}}_{i}\) denotes the estimate of the true target location, \(\mathbf{x}_{i}\), in the \(i\)-th \(M_{c}\) run. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(i\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(\mathbf{a}_{i}\) & \(\begin{bmatrix}0\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ B\end{bmatrix}\) & \(\begin{bmatrix}0\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B\end{bmatrix}\) & \(\begin{bmatrix}0\\ B/2\end{bmatrix}\) & \\ \hline \(\mathbf{a}_{i}\) & \(\begin{bmatrix}0\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/3\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B/2\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B/2\end{bmatrix}\) & \(\begin{bmatrix}0\\ B/2\end{bmatrix}\) & \(\begin{bmatrix}2B/3\\ 0\end{bmatrix}\) \\ \hline \(\mathbf{a}_{i}\) & \(\begin{bmatrix}0\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ B\end{bmatrix}\) & \(\begin{bmatrix}0\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/3\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B/3\end{bmatrix}\) & \(\begin{bmatrix}0\\ B/2\end{bmatrix}\) & \(\begin{bmatrix}2B/3\\ 0\end{bmatrix}\) \\ \hline \(\mathbf{a}_{i}\) & \(\begin{bmatrix}0\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ B\end{bmatrix}\) & \(\begin{bmatrix}0\\ B\end{bmatrix}\) & \(\begin{bmatrix}B/3\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B/2\\ B/3\end{bmatrix}\) & \(\begin{bmatrix}0\\ B/2\end{bmatrix}\) & \(\begin{bmatrix}2B/3\\ 0\end{bmatrix}\) & \(\begin{bmatrix}B\\ 2B/3\end{bmatrix}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fixed anchors locations (m) in the second considered scenario.