# Utilizing Ensemble Learning to Improve the Distance Information for UWB Positioning
## 4 Experimental Results
We applied the \(k\)-means prefilters to improve the performance, which can be observed via the differences among the same refinement algorithm with various prefilters. Second, it is obvious that the refinement of the UWB positioning topic is not a linear or simple polynomial issue due to the effects of signal attenuation and multipath propagation. Since MLP can be applied to complex nonlinear problems, the introduction of ANN helps us improve the performance further for the viewpoints of accuracy (error) and stability (standard deviation), which can be observed via the differences among the distinct refinement algorithms. This conforms with the characteristics of ANN as well. For the last declaration in the beginning of this paper: the authors in [5] utilized the positioning error to conduct their evaluation. However, the positioning information and error was calculated by a trilateration, which may implicitly include some error-tolerant or optimization design. Here, some results about the distance and positioning error are provided in Table 3 to address this viewpoint, where the trilateration algorithm was realized via invoking the \(solve\) function provided by SymPy [21; 22]. Figure 7: The ANN architecture for the refinement in the experiments. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Scene** & \multicolumn{4}{c}{**Classroom**} & \multicolumn{4}{c}{**Parking Grange**} & \multicolumn{4}{c}{**Parking Lot**} \\ \hline Filtering algorithm & Max/Ave & MaxCen & Cen/Ave & Cen/Ave & Cen/Ave & 10\% & Max/Ave & MaxCen & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & 10\% \\ \hline Average error (cm) & & & & & & & & & & & & & & \\ for LW refinement & 13.4840 & 13.5016 & 12.9833 & 12.9509 & 13.1802 & 13.1247 & 13.1195 & 13.2806 & 13.3082 & 13.2374 & 5.5774 & 5.5771 & 5.2287 & 5.2522 & 5.2791 \\ \hline Average error (cm) & & & & & & & & & & & & \\ for 3d order PR refinement & 14.7483 & 14.6830 & 14.1591 & 14.1242 & 14.4526 & 13.7075 & 13.7217 & 14.3688 & 14.3690 & 14.3312 & 7.0026 & 6.9436 & 6.7687 & 6.7979 & 6.8600 \\ \hline Average error (cm) & & & & & & & & & & & & & \\ for ANN refinement & 16.2367 & 16.2464 & 16.0984 & 16.0911 & 16.1965 & 14.1433 & 14.0594 & 14.1278 & 14.1456 & 14.1336 & 7.7564 & 7.7698 & 7.6098 & 7.6510 & 7.7056 \\ \hline Average error (cm) & & & & & & & & & & & & & \\ for ANN refinement & 13.9084 & 12.7475 & 14.0147 & 13.3212 & 14.1257 & 12.7099 & 12.5266 & 12.8038 & 11.9679 & 12.6255 & 6.2953 & 6.2102 & 5.3152 & 4.9925 & 6.0157 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experimental results about accuracy. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Scene** & \multicolumn{4}{c}{**Classroom**} & \multicolumn{4}{c}{**Parking Grange**} & \multicolumn{4}{c}{**Parking Lot**} \\ \hline Filtering algorithm & Max/Ave & MaxCen & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & Cen/Ave & 10\% \\ \hline Standard deviation (cm) & & & & & & & & & & & & & & \\ for LR refinement & 4.9911 & 5.0357 & 4.4573 & 4.4348 & 4.4121 & 11.2675 & 11.3058 & 11.1558 & 11.1844 & 11.2332 & 1.7559 & 1.7165 & 1.6711 & 1.8744 & 1.6475 \\ \hline Standard deviation (cm) & & & & & & & & & & & & & & \\ for 3d order PR refinement & 7.4616 & 7.3711 & 6.5284 & 6.5000 & 6.6460 & 10.4364 & 10.4098 & 11.8883 & 11.8629 & 11.7947 & 1.4641 & 1.4836 & 1.7100 & 1.7309 & 1.6900 \\ \hline Standard deviation (cm) & & & & & & & & & & & & & & \\ for 5 th order PR refinement & 6.4702 & 6.4784 & 6.1868 & 6.2237 & 6.3537 & 11.4880 & 11.4833 & 11.8216 & 11.7886 & 11.6871 & 1.4185 & 1.5199 & 1.6037 & 1.6316 & 1.5720 \\ \hline Standard deviation (cm) & & & & & & & & & & & & & & \\ for ANN refinement & 4.2665 & 4.4225 & 3.1471 & 3.2531 & 3.6112 & 9.8709 & 10.0507 & 9.3053 & 9.7154 & 9.2710 & 1.4387 & 0.6929 & 1.4117 & 1.5468 & 1.1412 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimental results about stability.