## 5 Simulation Results
It shows that the localization RMSE of the proposed solution matches the CRLB very well and is about an order of magnitude lower than that of [PERSON]'s method and [PERSON]'s method at a low-to-moderate BR measurement noise level. Although it deviates from the CRLB when the BR measurement noise level is large, it is still much smaller than that of other two methods. The deviation from the CRLB, known as the thresholding phenomenon, is due to the ignored second order error terms in the design of the solution, which is invalid for large error levels. Owing to considering the statistical distributions of the transmitter/receiver position error, the RMSEs produced by [PERSON]'s method is generally lower than that by [PERSON]'s method. But compared with the use of the calibration targets in the proposed solution, the localization accuracy improvement brought by the consideration of transmitter/receiver position error in [PERSON]'s method is not so significant. Figure 5b gives the RMSE curves of the methods versus the transmitter/receiver position error level. It can be seen that, the superiority of the proposed solution in localization accuracy is mainly reflected at moderate to high transmitter/receiver position error level. When the transmitter/receiver position error is small, the localization accuracy of the proposed solution and the other two methods is comparable. This again agrees very well with the theoretical performance in Section 3. Figure 5c compares the RMSEs from the methods with respect to different calibration target position error levels. As is illustrated in Figure 5c, the proposed solution always offers a remarkable advantage over the other two methods at different calibration target position error level, even when the calibration target position error is extremely large. This is in agreement with the previous simulation results for the CRLB in Section 3. Next, the same set of simulations was repeated for a near-field target, whose position is set to be \(\mathbf{u}^{\mathrm{o}}=[12000,1200,1200]^{\mathrm{T}}\mathbf{m}\). The results are provided in Figure 6, from which we observe that the proposed solution still performs much better than the other methods. However, comparing with the corresponding results in Figure 5, we find the localization accuracy for near-field target is generally better than a far-field target, given the same noise and error levels. One reason may be that, when the target is close to the MPR system, the transmitters/receivers are far apart relative to the distance between the target and the MPR system. Thus, the localization geometry would become more regular and the corresponding geometric dilution of precision (GDOP) value would be smaller compared to the far-field case. However, on the other hand, comparing the thresholding values in Figures 5 and 6 indicates that the RMSE curves for the near-field target deviate from the CRLB at smaller values than those for the far-field target. This phenomenon is consistent with the analysis under (83) that the equivalency between the estimate variance and the CRLB is more affected by the BR measurement noises when the target is close to the MPR system. At an intuitive level, the more calibration targets are used, the better the localization accuracy is. In what follows, we will quantitatively analyze the effect of number of calibration targets on the localization accuracy by varying the number of calibration targets from 1 to 10. The positions of the transmitters and receivers remain the same as before. The positions of calibration targets and unknown target are chosen randomly from the 50 km \(\times\) 40 km \(\times\) 5 km volume as presented in Figure 2. The simulation results are depicted in Figure 7.  
Figure 7 shows the RMSE, as well as the CRLB, versus the number of calibration targets. As expected, when the number of calibration targets is small, the localization accuracy improves significantly as the number of calibration targets increases.