# UWB Positioning Algorithm Based on Fuzzy Inference and Adaptive Anti-NLOS Kalman Filtering
## 5 Experimental Results and Analyses
### Static Positioning Experiment  
The static positioning experiment was performed in a rectangular region with a length of 200 cm and a width of 300 cm in the laboratory (Figure 6). The three base station nodes, numbered A\({}_{1}\), A\({}_{2}\) and A\({}_{3}\) in a sequence, were placed at three corners of the rectangular region, corresponding to the coordinates (0, 0), (200, 0) and (0, 300), respectively. The iron plate obstacle was placed at (0, 68) and the wooden board obstacle at (0, 270). Finally, the tag nodes were placed sequentially at (50, 150), (50, 175), (50, 200), (75, 200) and (100, 200) for positioning testing.  
Figure 6: Environment of the static positioning experiment.  
The settings of parameters of the positioning algorithm based on fuzzy inference and adaptive anti-NLOS KF and the adaptive anti-NLOS KF positioning algorithm are shown below [28]:  
\[Q=\begin{bmatrix}4&0\\ 0&0.4\end{bmatrix},R=10,T=0.5,b=0.25\]  
\(Q\) is the process noise matrix, \(R\) is the observation noise matrix, \(T\) is the sampling time, \(b\) is the maximum reduction in the correction factor.  
The positioning experiment system performed positioning every 0.5 s and closed the serial port whenever over 600 pieces of positioning data were collected. Then, the position of the tag nodes was adjusted for the positioning experiment at the next position until tests at all positioning points were completed. The static positioning data at the five testing points were analyzed to obtain the corresponding RMS errors (RMSEs) of the three algorithms (Table 2).  
As shown in Table 1, in the five positioning tests, the positioning algorithm combining fuzzy inference with adaptive anti-NLOS KF had the smallest RMSE; the fuzzy inference algorithm had four RMSEs less than 20 cm; and the adaptive anti-NLOS KF positioning algorithm had four RMSEs larger than 20 cm.  
In order to more intuitively compare the performance of the three algorithms, the scatter diagram and cumulative distribution function (CDF) diagram were drawn to analyze the experimental data of the tag node at (50,150) (Figures 7 and 8, respectively).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Positioning Algorithm** & **(50, 150)** & **(50, 175)** & **(50, 200)** & **(75, 200)** & **(100, 200)** \\ \hline Adaptive Anti-NLOS KF & 21.5767 & 29.6724 & 28.3351 & 12.8494 & 29.5745 \\ Positioning Algorithm & 15.5637 & 19.4664 & 28.5161 & 14.5265 & 16.7417 \\ \hline Positioning Algorithm & & & & & \\ Combining Fuzzy Inference with Adaptive & 14.8205 & 19.1152 & 25.2317 & 12.8007 & 15.1546 \\ Anti-NLOS KF & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: RMSEs of static positioning under NLOS conditions.  
Figure 7: Scatter diagram of static positioning by three positioning algorithms.  
According to Figure 7, compared with those of the positioning algorithm based on fuzzy inference, the center of the scatter diagram of the positioning algorithm combining fuzzy inference with adaptive anti-NLOS KF was closer to the actual coordinate, and the scatter diagram was more concentrated. Therefore, before the integration of the positioning algorithm based on fuzzy inference with the adaptive anti-NLOS KF positioning algorithm, there might be a large deviation between the estimated NLOS error and the actual NLOS error in some cases, which was significantly improved after the integration. In Figure 8, the probability of producing an error range of less than 19.1 cm by the positioning algorithm combining fuzzy inference with adaptive anti-NLOS KF was 0.93; that of the positioning algorithm based on fuzzy inference was 0.83; and that of the adaptive anti-NLOS KF positioning algorithm was only 0.06.