# An Efficient Single-Anchor Localization Method Using Ultra-Wide Bandwidth Systems
## 5 Experiment and Analysis
### Performance Evaluation
#### 5.2.1 Static test point  
We first evaluate the performance of the proposed SAL method under static scenarios in E1. Figure 5a also shows the results of the localization of the agents at different positions. We randomly select \(N_{t}=20\) test points and performed \(N_{m}=1000\) measurements at each test point. We compare our proposed method with the normal SAL method (SAL-Normal) without any filtering algorithm [43],  
Figure 5: Localization results in E1 and the cumulative distribution function (CDF) comparison. (**a**) The mean localization results (blue plus sign) and the root mean squared error (RMSE) (black circles for SAL-Normal, and magenta circles for the proposed SAL method) on each selected test point (black cross). (**b**) The CDF comparison of the two localization methods in E1. Figure 6: Localization results in E2 and the CDF comparison. (**a**) The mean localization results (blue plus sign) and the RMSE (black circles for SAL-Normal, and magenta circles for the proposed SAL method) on each selected test point (black cross). (**b**) The CDF comparison of the two localization methods in E2. where the anchor locates each agent in order, and compare the performance under different number of agents. We first let \(N_{\rm a}=1\) and place one agent on all test points in turn to collect the localization results. Then, for \(N_{\rm a}=2\), we randomly select 10 pairs of test points from all test points, and place two agents at each pair of test points at the same time for testing. For \(N_{\rm a}=3\), we randomly select 3 test points from all test points to place agents every time. For simplicity, we analyze the results of \(N_{\rm a}=3\) and present other results in the final table (Tables 1 and 2). In practice, due to the electromagnetic coupling between the antenna elements, there is a different bias for different angles of arrival. Thus, we use polynomial regression method [48] to reduce the fixed bias, and then the array will have a near-unbiased AOA estimation. Similarly, we also calibrate the ranging results, so that the ranging error is less than 10 cm. An illustration of the received CIR is shown in Figure 7. We randomly put three agents in the E1 environment (named Agent 1, Agent 2, and Agent 3, respectively), and set \(\delta_{1}=0\) ns, \(\delta_{2}=150\) ns, and \(\delta_{3}=300\) ns, which means that Agent 2 will wait for an additional 150 ns before responding, and Agent 3 will wait for an additional 300 ns before responding. Note that the response of Agent 3 appears at the front of the CIR. This is because the CIR is the accumulation of the correlation results, and the part that exceeds the current window will be moved to the front [46]. As shown in Figure 5a, The black cross indicates the true position of the test points, the blue plus sign indicates the mean of the actual localization results, the black circle represents the RMSE when the anchor locates three agents using the SAL-Normal, and the magenta circle represents the RMSE when the anchor locates three agents using the proposed SAL method. As expected, the estimated position of the agents is close to the ground truth, and the Euclidean distance between the mean of the localization result and the ground truth is less than 10 cm. Moreover, the localization RMSE when the anchor locates three agents using the proposed SAL method is greater than the localization RMSE when using SAL-Normal. The reason is that when using the proposed SAL method, the anchor can obtain delay and phase observation of multiple agents in a single CIR estimation. The phase of arrival of the first path estimated by the UWB chip is more accurate than other phase of arrival estimations. It can be expected that as the number of agents increases, the localization accuracy will decrease more and more slowly. The reason is that only the first responding agent has high-precision phase observation.