## 1 Theoretical Background  
The demand for efficient and low-cost monitoring continues to increase. This matter can be the first step toward reducing the uncertainty of building monitoring by increasing the density of measurement points. Bilro et al. reviewed the potential application of optical sensors based on plastic fibers used for low-cost structural response monitoring [1]. Barrias et al. presented the theoretical background of distributed optical fiber sensors and their multiple applications in building monitoring [2]. Mobaraki et al. provided a systematic literature review of low-cost sensor applications for building monitoring [3]. Rodrigues and Li reviewed the recent achievements in low-cost Doppler radar systems for displacement measurement and Time-Doppler analysis for structural monitoring [4]. Kohler et al. installed cheap seismometers in a building in Los Angeles to assess the shaking intensity caused by earthquakes [5]. The primary objectives of the developed protocol were to compute the modal characteristics of the structure, such as mode shape and frequencies. Due to the high level of earthquake activity in New Zealand, Simkin et al. installed low-cost accelerometers in a couple of houses in Wellington to monitor the dynamic behavior of the buildings during earthquake excitations [6]. Application of low-cost accelerometers for monitoring dynamic behavior of scale structures in laboratory were carried out in [7; 8]. Researchers have proposed various methods for the low-cost monitoring of structural deformation and strain measurements at multiple parts of buildings [9; 10; 11]. Caponero et al. presented a demonstrative monitoring system based on fiber optic sensors installed on early emergency reinforcements of a church in Italy [12]. Figure 1 illustrates the growing significance of low-cost sensors in the civil engineering sector based on information extracted from the SCOPUS database between 2011 and 2021. Figure 1 shows that, from 2011 to 2017, the quantity of the publications associated with the use of low-cost sensors for structural monitoring is negligible (18.2%) and more than 81% of the found articles have been published in the last 4 years (from 2018 to 2021). To further develop structural system identification methods, standard deviation and distribution functions for measurement devices are required in modeling theoretically physical models. However, these values are usually estimated since researchers who are experts in the analytical analysis may not have access to experimental databases [13; 14; 15]. This paper studies various distance sensors. Then, through laboratory experiments, this study provides standard deviation and distribution functions for different range distance estimations in various ambient scenarios for several distance sensors. Distance sensors are typically categorized based on their measuring method. The most widely recognized types include:  
1. Ultrasonic sensors: These sensors, also known as sonar sensors, are among the most common distance measuring tools. They detect their distance from the target by emitting high-frequency ultrasonic waves. Then, the wave hits any object within the ultrasonic sensor range, bounces off it, and reflects the signal toward the sensor. The sensor calculates the distance by using the time of wave travel and the speed of the signal [16]. Figure 2 shows the performance of an ultrasonic sensor. Ultrasonic measuring tools are not affected by the color or transparency of the object. Furthermore, these sensors are not affected by the brightness of their ambient environment. However, they cannot measure the distance of objects with a complex surface (such as  
Figure 1: The growth of low-cost sensors in civil engineering sector. Figure 2: The principle behind distance measurement with sonar sensors. a sponge). Additionally, since the speed of sound is sensitive to humidity and temperature, this sensor is usually coupled with humidity and thermometer sensors to make ultrasonic sensors more accurate [17]. 2.