## 5 Experiments
### Properties of VL53L1X Proximity Sensor
The distances measured with VL53L1X and estimated ranging bias values are shown in Figure 7. Ranging standard deviation is presented in Figure 8.  
During the tests, the maximum range, for which it was possible to properly measure distance from a person was about 3.5 m. At close ranges, up to 2 m, the measures are very accurate and the bias does not exceed 0.1 m. For larger distances, it rises and for 3.5 m is higher than 0.3 m. The measures show no clear dependence on the reflective surface (clothing color) or lightning conditions. Therefore,  
Figure 7: Ranging accuracy test results. (**a**) Distance measured from a person clad in different clothes. The grey dashed line is the actual distance drawn for reference. (**b**) Ranging bias. The coefficients of the fitted model are stored in Table 2.  
it makes sense to model the bias and introduce the correction in the localization algorithm. Ranging bias was modeled with a third degree polynomial and the resulting curve was plotted in Figure 7b. The polynomial coefficients are stored in Table 2.  
Ranging standard deviation also depends on the measured distance. For ranging from close objects, it is relatively small (lower than 5 cm for distances up to 2.5 m). At the edge of the sensor range, measurement noise is significantly higher--for 3.5 m, in case of the black clad man in a bright room, standard deviation approaches 0.2 m. Based on the measurement results, standard deviation was modeled as a third degree polynomial. The coefficients are stored in Table 2. Large ranging errors caused by high measurement noise can be clearly seen on a ranging results boxplot presented in Figure 9. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & \(\mathbf{a_{0}}\) & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) \\ \hline bias & \(-0.0303\) & \(0.0385\) & \(-0.0293\) & \(0.0151\) \\ standard deviation & \(0.0151\) & \(-0.0229\) & \(0.0068\) & \(0.0031\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The bias and standard deviation models coefficients. Figure 8: Ranging standard deviation for reflections from a person clad in different clothes. The coefficients of the fitted model are stored in Table 2.  
Figure 9: Boxplot of ranging results for the person dressed in a black shirt and located at larger distances. Large standard deviations at long distances might pose a problem in terms of accurate localization. As it can be seen, for distances over 2.5 m, ranging errors sometimes have few dozen centimeter magnitudes. Such high errors can easily lead to very inaccurate localization. Therefore, the proposed localization algorithms (proximity sensors based localization and hybrid algorithms) will utilize both the above fitted models to mitigate ranging bias and lower the impact of low accuracy measurements on the final localization result. The second phase of the VL53L1X properties testing was measurement of the sensor's FoV. The experiment was conducted in a bright, large (6\(\times\)8 m) laboratory room. The test consisted of placing an A3 paper sheet attached to the utility cart in front of the sensor and moving it sideways till the sensor lost visibility of the object. The border positions at both sides were noted and the sensor's actual FoV was evaluated. For the conditions in the laboratory room and the tested object, the measured FoV was smaller than claimed in the application note. For distances up to 50 cm, they were very similar, whereas at 3 m, the difference in the width of the covered area was almost 80 cm. Based on the measurement results, a model of FoV was created. Sensor FoV was modeled as the conical beam of 20.3\({}^{\circ}\) width. The measured and modeled FoV is shown in Figure 10.  
The above results show that the VL53L1X meets the requirements to be used in the proposed hybrid localization scheme. The ranging results are accurate for close objects, and since the bias for large distances does not depend on lightning conditions and reflecting surface, it is easy to correct.