## 4 Result and Discussion
### Effect of Coupled Similar Sensors
Analysis of Figure 11e shows that the effect of sensor combination is not as evident for HC-SR04 sensors when compared to ToF sensors. However, carefully studying the performance of HC-SR04 sensors shows their improving accuracy with distance increment. The most significant impact of the sensor combination is observed in the experiment when the target object is at a distance of 29 cm. In that experiment, the error of a single sensor in the worst-case scenario improves from 6.7% to 5.9%, with eight ultrasonic sensors fused in selecting the worst-case combination. Further analysis of Figure 11 shows that the sensor combination improves the estimation accuracy of VL53L0X and VL53L1X sensors more than that of the HC-SR04. ToF sensors (such as VL53L0X and VL53L1X) are known to experience more noises than ultrasonic (such as HC-SR04) sensors. Consequently, the data acquisition of ToF sensors is usually postprocessed for noise reduction and signal improvement [58]. Averaging the results of a number of similar sensors helps to reduce individual noises or imperfections of the used sensors. Since ToF sensors are influenced by more environmental parameters (color, material, distance, and lighting), their combination shows a more significant accuracy improvement than ultrasonic sensors that are only affected by fewer environmental parameters (such as temperature). Most improvement occurs when at least two sensors are combined. In such cases, the overall error for the worst-case scenario is 6.33%. Even though the error from combining eight VL53L1X for all experiments in the absence of ambient light was between 3% and 12%, a single HC-SR04 reports errors between 1% and 7%, which is very low. Here, the precision of a single ultrasonic sensor for the distance measurement of semi-controlled laboratory experiments is higher than eight fused VL53L1X sensors. The price of a single VL53L1X is about five times more than that of a single HC-SR04. As a result, the low cost of HC-SR04 makes it the best candidate for sensor combination applications. This work presents a way of improving the accuracy of low-cost sensors without postprocessing or manipulating the outputs. In the current form, a device made from only ultrasonic sensor combinations can be used in different locations of a dam to measure the approximate water level. The device is not currently tailored to be used in the industry. This device contains 75 sensors (analog and digital) with a radius of 250 mm, which is used to research and analyze the impact of combining similar sensors. The results of this paper can be used further in making tailored devices with an acceptable range of accuracy for a known ambient situation. For example, in a dark place with a measuring range of 540 mm, two combined VL53l1x have up to 3.7% error. The size of a device made from these two sensors would be 26 \(\times\) 8 \(\times\) 2 mm. The price and size of any sensor combination can be calculated from the data available in Table 1.  
It is essential to mention that combining commercial circuits will oversize the final product. To reduce this enlargement, the Printed Circuit Board (PCB) of the sensor can be redesigned for specific measuring purposes. Therefore, the proposed device of this paper with the current resolution is suitable for remote liquid level detection where the size of the object under study (water level) is large enough for the oversized device made from sensor combination. In civil engineering, this level detection is commonly used for imposed load calculation of dams [59] and safety and water level of open and closed canals [60] and bridges [61].