## 4 Result and Discussion
### Effect of Coupled Similar Sensors  
This subsection investigates the beneficial impacts of adding an increasing number of fused sensors in detail. Error measurements were calculated by a steel measurement pattern to compare all sensors (see Table 3). A combinatory program written in MATLAB found the least effective sensor combination for each experiment. This code first opens all the documents related to filtered outputs of similar sensors for all the experiments. Second, the code generates various sensor combination probabilities for the 25 sensors. Since the server computer used for this experiment could not calculate more than eight fused sensor combinations, this study's most effective fused sensor combination is eight. Even though 25 similar sensors were mounted on the distance sensing device in this work, only up to eight sensors were used for the combinatory analysis. Experimental tests show no significant improvement as of eight combined sensors. Figure 11 shows the maximum possible error for every sensor combination for different experiments with different distances. Analyses of Figure 9(a),b reveal the limited distance range of VL53L0X for experiments with and without ambient light. Despite the high errors associated with this type of sensor when used alone, the error decreases with and without ambient light when multiple sensors are fused together. Even though the results of a single sensor in the worst-case scenario  
Figure 10: Combined outputs of similar sensors. are 19% in the absence of ambient light, the exact measurement with eight fused sensors shows only 13% error, which confirms the benefit of combining sensors. This sensor is more accurate for intermediate ranges but does not work very well for very close or very far distances. Its lowest error appears when measuring a distance of 54 cm regardless of the number of fused sensors or the ambient light situation. The most significant effect of the sensor combination is seen with three VL53L0X sensors coupled together. Figure 9c,d detail the outputs of VL53L1X for experiments with and without ambient light. This sensor offers a broader range and more minor errors than VL53L0X. Like VL53L0X, this sensor works better for intermediate distances. These figures show how combining sensors reduces the overall estimation errors for both experiments with and without the ambient light. Figure 11d shows that the worst-case estimation error scenario for a single sensor is 9%. In contrast, the worst-case combination of eight fused sensors has an estimation error of 4% in the same experiment. This sensor, like the VL53L0X, estimates distance in an intermediate range. However, the medium range of VL53L1X is more significant and is between 34 cm and 64 cm. Figure 11: _Cont._  
Figure 11: Comparing the worst-case sensor combination with different distance measurement technologies: (**a**) VL53L0X distance estimations affected by an excessive light source, (**b**) VL53L0X distance estimations in darkness, (**c**) VL53L1X distance estimations affected by an excessive light source, (**d**) VL53L1X distance estimations in darkness, and (**e**) HC-SR04 distance measurements. The combinatory analysis of Figure 11c shows that, while the error of a single VL53L1X in the worst-case scenario is between 5% and 22%, when coupling eight sensors, the error range in the worst-case combination of the chosen sensors is between 4% and 15% when the projector is on. The highest and lowest error for a single sensor in the absence of high ambient light is between 4% and 18%, and by combining eight sensors, that range becomes 3% to 12%. The error continues to lower more with a higher number of combined sensors. The most significant effect of sensor coupling for VL53L1X is observed with at least four averaged sensors. Figure 11e shows the high accuracy and low data fluctuation of the HC-SR04 sensor, although combining sensors increases the accuracy and describes the estimation error.