# A Novel UWB Positioning Method Based on a Maximum-Correntropy Unscented Kalman Filter
## 4 Results and Analysis
### Test Verification  
To verify the MCUKF method, a UWB positioning system based on the base station and the label was designed. The system included four base stations, one label, a computer and a trolley; the specific block diagram is shown in Figure 5. The computer was responsible for recording information about the distance from the label to the four base stations, as well as the positioning results. The test system was built as shown in Figure 6, according to the framework above. The test area was an underground garage. One of the base stations was taken as the coordinate origin, and the four UWB base stations were each placed in a different corner. The label was placed on the trolley, and the trolley ran according to the specified route. The UWB update frequency was 2 Hz. The whole test was divided into two parts: a static test and a dynamic test. It mainly verified the performance of the MCUKF algorithm under external interference. Figure 7 shows the distribution of the positioning results of the three methods when the label was stationary. The figure shows that due to the influence of external interference, the positioning results of the least squares method and the UKF method fluctuated. The MCUKF method reduced the external interference and had high positioning accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **X-Direction Error (m)** & **Y-Direction Error (m)** & **Horizontal Position Error (m)** \\ \hline LSM & 0.1655 & 0.1190 & 0.2038 \\ UKF & 0.1059 & 0.0828 & 0.1372 \\ MCUKF & 0.0753 & 0.0565 & 0.0942 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation of RMS of UWB positioning errors. Figure 4: Horizontal position-error simulation curve based on MCUKF method. To facilitate analysis of the above results, the distribution curve of the standard deviation of the positioning results was drawn, as shown in Figure 8. The standard-deviation curves of the positioning results in the X and Y directions in the figure show that the standard deviation of the positioning results in the lowest multiplication method was the largest. The MCUKF method presented in this paper had the minimum standard deviation distribution. Figure 5: Block diagram of UWB positioning system. Figure 6: Field-test diagram of UWB positioning system. Figure 7: Comparison of positioning results of different methods under static conditions. Statistical analysis of the results in Figure 8 obtained the average-standard-deviation statistical results shown in Table 2. The average standard deviations of the MCUKF method proposed in this paper, in the X direction and the Y direction, were 1.6075 m and 0.7472 m, respectively. As seen in this table, the MCUKF method had the smallest mean standard deviation compared with the LSM and the UKF method. This table also shows that the proposed UWB localization method based on the MCUKF method is robust. In order to illustrate the universal applicability of this method, the static-positioning test was redesigned. Figure 9 shows the UWB positioning results under the condition of double interference. The figure shows that when there was external interference, the positioning results of the least squares method and the UKF method both had outlier fluctuations. The MCUKF method proposed in this paper still maintained high robustness and positioning accuracy. Figure 10 is the standard-deviation distribution curve under the condition of interference drawn on the basis of Figure 9. This figure shows that the standard-deviation curve also fluctuated greatly due to the influence of large outliers. The standard-deviation curve of the MCUKF method proposed in this paper remained stable under the influence of large outliers. Similarly, the average standard-deviation statistical results of the different methods shown in Table 3 are listed according to the results in the figure above. The average standard deviations of the MCUKF method were 1.661 m in the X direction and 0.752 m in the Y direction, respectively.