# Fast 50 Hz Updated Static Infrared Positioning System Based on Triangulation Method
## 3 Results  
This section describes and discusses the results of the experimental studies. The measured data for measurements at tripod positions 1 to 11 (see Figure 10) were statistically processed and then presented in Table 1. Figure 11 shows an example of the experimental results: the determined positions and receiver orientations for the tripod in position 3.  
Based on the experimental data shown in Table 1, the accuracy of measurement of the angle \(\varphi\) was 0.51\({}^{\circ}\). This is comparable to the other triangulation systems presented in the papers ([PERSON] et al., 2016) (\(\Delta\varphi\) = 0.6\({}^{\circ}\), \(f_{update}\) = 10 Hz), ([PERSON] et al., 2016) (\(\Delta\varphi\) = 2.0\({}^{\circ}\), \(f_{update}\) = 10 Hz), ([PERSON] et al., 2016) (\(\Delta\varphi\) = 1.5\({}^{\circ}\), \(f_{update}\) = 1 Hz) and ([PERSON] et al., 2016) (\(\Delta\varphi\) = 0.24\({}^{\circ}\), \(f_{update}\) = 10 Hz). However, the update frequency in our STS triangulation system, which is \(f_{update}\) = 50 Hz, is several times higher than in the above-mentioned systems. In addition, our STS system contains no moving  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Tripod** & \(x_{real}\) & \(y_{real}\) & \(\bar{x}\) & \(\bar{y}\) & \(\sigma_{x}\) & \(\sigma_{y}\) & \(\sigma_{R}\) & \(rmse_{R}\) & \(\sigma_{\gamma}\) & \(rmse_{\varphi}\) \\
**Position** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[cm]** & **[\({}^{\circ}\)]** & **[\({}^{\circ}\)]** \\ \hline
1 & 301.6 & 60.32 & 303.53 & 61.59 & 4.62 & 2.35 & 4.47 & 5.67 & 0.36 & 0.48 \\
2 & 301.6 & 120.64 & 302.75 & 122.91 & 3.36 & 2.35 & 2.99 & 4.83 & 0.4 & 0.49 \\
3 & 301.6 & 180.96 & 302.26 & 184.03 & 2.39 & 2.63 & 2.31 & 4.74 & 0.43 & 0.48 \\
4 & 361.92 & 60.32 & 361.91 & 62.32 & 4.24 & 2.13 & 3.99 & 5.14 & 0.46 & 0.46 \\
5 & 361.92 & 120.64 & 361.62 & 122.83 & 4.09 & 3.13 & 3.32 & 5.61 & 0.37 & 0.53 \\
6 & 361.92 & 180.96 & 364.01 & 184.64 & 3.06 & 2.46 & 2.13 & 5.77 & 0.35 & 0.61 \\
7 & 422.24 & 60.32 & 421.93 & 60.84 & 5.72 & 3.02 & 5.32 & 6.49 & 0.45 & 0.46 \\
8 & 422.24 & 120.64 & 421.94 & 122.67 & 5.16 & 3.74 & 4.21 & 6.69 & 0.5 & 0.55 \\
9 & 422.24 & 180.96 & 422.2 & 182.99 & 4.06 & 4.85 & 2.45 & 6.64 & 0.47 & 0.51 \\
10 & 482.56 & 120.64 & 480.69 & 122.96 & 5.24 & 4.9 & 4.01 & 7.76 & 0.42 & 0.47 \\
11 & 482.56 & 241.28 & 479.56 & 247.7 & 4.62 & 6.36 & 2.34 & 10.57 & 0.44 & 0.51 \\ \hline
**Pooled:** & & & & & **4.34** & **3.68** & **3.56** & **6.55** & **0.42** & **0.51** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experiment results.  
Figure 11: Experimental results for the tripod in position 3.  
parts, and is therefore simpler to build and more resistant to disturbances. The most important indicator of the triangulation system accuracy is the precision of angle determination. This accuracy translates directly into positioning accuracy, which averaged \(\Delta R=6.55\) cm in our experiment. Position accuracy decreases with distance from the centre of the triangle, as can be seen in the \(r\text{\emph{r}mse}_{R}\) column in Table 1. It should be emphasized that the data in Table 1 come from an experiment where there were no obstacles in the close vicinity of the system, so reflections of the IR signals were minimized. In such measurement systems, signal reflections from objects (e.g., walls) interfere with the measurement spectrum and affect positioning accuracy.