Sensors in Precision Agriculture for the Monitoring of Plant Development and Improvement of Food Production
View this Special IssueResearch Article  Open Access
A Preliminary Study of Seeding Absence Detection Method for Drills on the Soil Surface of Cropland Based on Ultrasonic Wave without Soil Disturbance
Abstract
Seeding absence detection is essential during seeding operation, since it affects the subsequent crop performance. Existing methods cannot detect the seeding absence position immediately after planting without soil disturbance. In this paper, a nondestructive detection method for finding out the seeding absence position of drills is put forward. It focuses on the echo energy reflected by the circle energy inside the tilled cropland soil, to which the sensor is attached directly on the soil surface, not on ultrasonic waves that penetrate the soilseed medium below tilled soil. Firstly, the energy circle is used to analyze the sound field distribution characteristics of the sensor in cropland soil. According to the size difference of the seeding absence length value and energy circle diameter, the total energy for three different cases with eight steps for each case is discussed in detail, and in order to find the left and right boundary lines and the length value of seeding absence, a program is designed to help with calculating four base positions automatically. At last, the nondestructive detection method is evaluated by the experiments, and the results demonstrate that the proposed method is accurate, efficient, and convenient in finding the seeding absence position of drilling seeds on the soil surface without soil disturbance.
1. Introduction
During seed drilling, such as wheat seeding, the soil is tilled and moves to both sides by openers, and seeds fall into the soil, forming a seed layer, and are covered by returning the tilled soil. Hence, the soil is divided into two parts by a seed layer: tilled soil above the seeds and untilled soil below the seed layer. Tilled soil, formed by openers, is softer than untilled soil (Figure 1).
Seed position or seed distribution in the soil is an essential performance indicator of seed drills, since seed absence affects the subsequent crop performance. It can be characterized in , , and dimensions with coordinates [1, 2], as shown in Figure 2. The crop row, shown as in Figure 2, is easy to be obtained by a dip stick, as there are some traces on the soil surface. However, the seed distribution or seeding absence position in and are difficult to measure without soil disturbance. At present, there are mainly the following commonly used measurement methods, including seed metering measurement, seed tube measurement, and manual measurement after sowing or emergence.
The seed metering measurement methods are based on sensors, which monitor seed flow in seed metering in real time. The uniformity of seed flow is detected to predict the seed uniformity after falling into the soil [3]. The seed flow goes through the seed tube and opener and falls into the soil after seed metering. So, seed uniformity is also affected by the seed tube, openers, and even the soil touched by the seed. Hence, some researchers monitor seed flow in the seed tube to get more accurate results of seed uniformity [4]. The trace of seeds’ bounce after falling into the soil is affected by soil types and components of seed drill [5, 6]. Then, differences occur on the final position of seeds between real and predicted, which affects the accuracy of seed uniformity measurement.
The third type of method is manual measurement after sowing. The soil is removed and the seeds are found, and thus the seed distribution is obtained [7]. However, the soil structure covered on the seeds is destroyed, and only several random sites could be measured.
The fourth type of method, which is also a common method for seed detection, is manual measurement after emergence. When seedlings come out of the ground, about 715 days after sowing, the distance between adjacent seedlings is measured and compared with plant spacing [8]. Meanwhile, measured seedlings are pulled out from the soil, and the distance of seedlings under the soil is measured as the sowing depth [9]. There are two problems: first is poor time effectiveness. Seed distribution information is obtained about 715 days after sowing, and reseeding will lead to uneven growth. Second is huge destructiveness. Measured seedlings, which are pulled out of soil, cannot continue to grow, and the surrounding soil environment is destroyed. This will give a negative effect on the growth for adjacent seedlings.
Given the analysis of the strengths and weaknesses of the above methods (37), this paper tries to present a noninvasive method based on ultrasonic waves, of which the research focuses on the preliminary estimation of the feasibility of this method.
In recent years, the application of the ultrasonic detection method in agriculture is more and more extensive. The ultrasonic detection method, as an ultrasonic pulse wave transceiver, was devised and tested in corn, soybean, rice, and sorghum fields for sensitivity to canopy structural differences by measuring the echo above the canopy surface of 3050 cm in [10]. Also, a 3D reconstruction and volume measurement of fruit tree canopy based on an ultrasonic sensor was developed in [11]. And the ultrasonic method was used to probe root locations without removing sediments from the surface, measure their length, and estimate rootsoil plate dimensions in [12]. Furthermore, an ultrasonic soil water content detector was developed in [13], which can detect the ultrasonic information of soil with 10 cm depth. All these references show that it may be a feasible method for seeding absence detection by ultrasonic waves when seed drilling.
In this study, tilled soil and untilled soil are divided into two parts by a seed layer, above and below seed layers, respectively, during normal seeding. However, when seeding absence occurs, the tilled soil directly covers the untilled soil. Since untilled soil is less soft than tilled soil, the properties of tilled soil, untilled soil, and seeds are different. Ultrasonic waves will reflect back at both the tilled soilseed interface (normal seeding) and the tilled soiluntilled soil interface (seeding absence). For the difference of the ultrasonic reflection coefficient of seeds and untilled soil, the different echo energy obtained from different interfaces can be used to judge if seeding absence occurs and to obtain the position of seeding absence.
2. Theory and Methods
The proposed method uses one transmitting transducer and one receiving sensor to achieve an accurate seeding absence measurement on the soil surface. The seeding absence states or seed distribution is determined by echo energy inside the tilled soil above the seed layer or untilled soil layer, to which the sensor is directly attached on the soil surface. In this study, the concept of energy circle [14] is used based on which the model of seeding absence measurement is established, and an algorithm is designed for calculating the position and length value of seeding absence dynamically to improve the detection accuracy.
2.1. The Energy Circle Used in the Seeding Absence Measurement
The concept of energy circle in the seeding absence measurement is shown in Figure 3. The sound field of the axial response for a sensor in a solid medium consists of two parts: the nearfield region known as the Fresnel zone and the farfield region, on the basis of the Schmerr model [15, 16], and the sound field analysis by RoaPrada et al. [17, 18]. In the near field, the amplitude of sound pressure has many maxima and minima, and they will reduce as the distance increases in the far field. The acoustic beam propagates in a circle with the radius of and diffuses with an angle . According to the basic theory of ultrasonic, and the length value of nearfield and the diameter of an energy circle are calculated by the following equations [14]: where is the ultrasonic wave wavelength, and other symbols are shown in Figure 3.
According to [14], the echo energy received by the sensor was different with different medium. In this study, the medium during normal seeding (seeds) is different with that during seeding absence (untilled soil). With this mechanism, we can obtain the position of seeding absence.
2.2. Seeding Absence Analysis of Drills Based on the Energy Circle
2.2.1. Seed Detection Case Analysis
In the actual seed detection process, we adapt a pair of sensors with the function of transmitting and receiving ultrasonic waves. One sensor is excited by a momentary pulse as the transmitting sensor, and another one is used for receiving. When the detection sensor moves along the seed zone on the soil surface, the energy circle evolves in different states, respectively. According to the size relationship of energy circle diameter and absence length , there are three cases, shown in Figure 4. The detailed analysis for each case will be given in the following text.
(a)
(b)
(c)
2.2.2. Variation Process Analysis of Energy Circle for Each Case
For the sake of analysis, we assume that the variation state for each case is normal seeding—seeding absence—normal seeding.
Case one: . In this case, there are 8 steps during the detection process, as shown in Figure 5: the energy circle starts from the location full of seeds (Figure 5(a)), until its rightmost peak (A) moves to the left boundary line of seeding absence (Figure 5(b)); as it goes on, the seeding absence zone continues to increase (Figure 5(c)) until the rightmost peak reaches the right boundary line of seeding absence (Figure 5(d)) and keeps moving in the zone of seeding absence for a while (Figure 5(e)) until the leftmost peak (B) moves to the left boundary line of seeding absence (Figure 5(f)). The area of seeding absence in the energy circle starts to decrease (Figure 5(g)) until the leftmost peak (B) moves to the right boundary line of seeding absence (Figure 5(h)), and the energy circle gets into the next location full of seeds immediately. In this process, (the length of seeding absence in the energy circle) increases from 0 to a certain value until the energy circle reaches the right boundary line of seeding absence (Figures 5(a)–5(d)) and then keeps constant for a while (Figure 5(e)) until the energy circle reaches the left boundary line of seeding absence (Figure 5(f)), and decreases to 0, and then keeps constant (Figures 5(g) and 5(h)).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
In the same way, for case two: . There are also 8 steps during the detection process, as shown in Figure 6: the energy circle starts from the location full of seeds, then moves to the position of seeding absence for a while, and then passes the seeding absence position, and gets the next location full of seeds. There are three different steps in this case with case one: steps d, e, and f. Since , the whole circle energy in the position without seeds between tilled and untilled soil. Thus, during this period. Therefore, increases from 0 to (replaced in case one) until the energy circle reaches the left boundary line of seeding absence (Figures 6(a)–6(d)) and then keeps constant for a while (Figure 6(e)) until the energy circle reaches the right boundary line of seeding absence (Figure 6(f)), and decreases to 0, and then keeps constant (Figure 6(g) and 6(h)).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
In the same way, for case three: . increases from 0 to , and immediately decreases from to 0 without staying at , and then keeps constant. Since at the point of , both the left and right boundaries of the energy circle contact the seedsoil interface (Figure 4(b)) and will come into the seed medium immediately, so combining steps d, e, and f in Figure 6 with those of Figure 4(b), there are 6 steps in this case.
2.3. The Total Energy Analysis for All Steps with Each Case
It can be seen from the above analysis that all steps can be divided into three states in any case: (1) the energy circle full of seeds (Figures 5(a), 5(b), and 5(h), 6(a), 6(b), and 6(h)), (2) the energy circle without any seeds (Figures 6(d)–6(f)), and (3) the total energy circle divided by seeds and untilled soil (other subfigures in Figures 5 and 6). And state (3) is a regular combination of state (1) and state (2). Therefore, the total energy of states (1) and (2) is analyzed first, and that of state (3) is analyzed.
2.3.1. The Total Energy Received by the Sensor in the Energy Circle Full of or without Seeds
According to the propagation and attenuation characteristics of ultrasonic, the following equations can be used to calculate the total echo energy for different states.
In the energy circle full of seed state (state (1)), the total energy received by the receiving sensor is obtained by Equation (2): where refers to acoustic intensity and and refers to the reflection coefficient of seed and tilled soil, respectively.
The reflection coefficient (, , and ) is determined by [14, 19] where is the density of the tested medium, is the sound speed in the tested medium, is the incidence angle, and is the transmission angle.
In the same way, when the energy circle is without any seeds (state (2)), the ultrasonic waves are reflected by the untilled soil below the tilled soil, and the total energy is calculated by where refers to the reflection coefficient of untilled soil.
When the soil and seeds are fixed in a given testing environment, the incident frequency can be considered as a constant value, then the sound pressure is constant, and the values of and received by the sensor will also be constant.
2.3.2. The Total Energy Received by the Sensor in the Whole Energy Circle Divided by Seeds and Untilled Soil State
In state (3), the energy circle is divided into at least two parts by the seeds and untilled soil (Figures 5 and 6), even three parts as shown in Figure 5(e), including one part of untilled soil and two parts of seed. The total area of energy circle is denoted by . When there is absence of some seeds on the seed zone, the length of seeding absence in the energy circle is , where and ; the area of energy circle in the seeding absence zone is denoted by . Considering the whole energy circle divided into two states, the total energy should be the combination of the seeds and untilled soil parts of the energy circle and it can be determined by
If is viewed as a value of 0 or 1, Equation (5) will become Equation (2) or Equation (4), respectively.
Through the above analysis, when the sensor moves gradually along the soil surface from normal seeding—seeding absence—normal seeding, the total energy received by the receiving sensor in different states is determined by Equations (2), (4), and (5), respectively.
2.3.3. Calibration of Seeding Absence Position
The value of seeding absence length is denoted by from Figure 3 to Figure 6. To determine the precise position, the left and right boundary lines and the length of should be obtained.
For step e in case one (Figure 5(e)), and can be obtained by using Equations (6) and (7), respectively, where and .
For steps c, d, f, and g in case one (Figures 5(c), 5(d), 5(f), and 5(g)) and c and g (Figure 6(c) and 6(g)) in case two, the length value of seeding absence in the energy circle and the ratio can be obtained by using Equations (8) and (9), respectively, where . Its meaning is shown in Figures 5 and 6:
When the tilled soil, untilled soil, and seed medium and other initial conditions are fixed, Equation (5) can be rewritten as Equation (10):
Since , , there is the following relationship between and : where and are constant values for a given detection environment and condition. Based on Equations (11), (12), (13), and (14), and . Therefore, with the drilling operation, if there is seeding absence existing, during the detection process, the relationship between the total energy received and the ratio is negatively linear. According to Equations (8), (9), and (10), the diagram of the relationship between and can be determined. Figure 7 demonstrates this relationship with , , , and .
If , we can find four critical lengths , , , and which correspond to the two base states described in Section 2.3.1; the left and right boundary lines and the length value of will be determined by Equations (15), (16), and (17), respectively. And the geometric description is shown in Figure 8:
In the same way, if , the left and right boundary lines of will be determined by Equations (18) and (19), respectively. And the geometric description is shown in Figure 9:
Then, the length value of will be determined by Equation (20), and the geometric description is shown in Figure 9:
If , then ; thus, the equations of the left and right boundary lines and the length value of under the conditions of and are both suitable for .
In the actual process, when the four base positions are found, the values of , , , and are obtained via the use of distance measuring instruments.
After the above analysis, this method was used for detecting drilling seeds, which was distributed as seed flow, such as wheat seeds, as shown Figure 10. And it could not detect precision planted crops, such as maize seeds, shown in Figure 11. For this measure method, the sensitivity is different when the parameters are different, such as seed type, soil depth, and ultrasonic signal. In the following section, wheat seeds as an example were tested to verify the feasibility of this method.
3. Experiment Results
3.1. Material and Methods
A series of cropland soil with different thickness and seed media, which contain tilled soil, untilled soil, and wheat seeds, are used to assess the proposed method.
In order to obtain the actual seed flow state in the soil as close as possible, the seeding rate was designed as 375 kg/ha and the row space as 20 cm. According to calculation, the center distance between adjacent seeds was about 5 mm. The mean length of 100 measured wheat seeds was 6.8 mm (Table 1). Therefore, according to the movement rule, in the ideal state, the seed flow was distributed without gap between seeds (Figure 10).

Soil was obtained from a test field in the ZhuoZhou Experimental Station. The soil properties are shown in Table 2. Soil was crushed and sieved with particles less than 2 mm, which is used as tilled soil. And the soil after being sieved is compacted as untilled soil.

 
The average values of measured information for three times are presented in Table 3. and represents the actual left and right boundary lines of seeding absence, respectively. and are the average measured results of the proposed method, and and are the average errors. The results show that, in the measured environment and condition, the errors and are less 5 mm, in line with the accuracy range of ±5 mm. 
The temperature of the tested environment is about 10–40°C. According to the detection environment, there are , . Considering the propagation characteristics of ultrasonic in soil, a Zhibolian 5200 ultrasonic detection instrument is used to obtain ultrasonic information. The instrument includes a pair of sensors for transmitting and receiving, respectively, with center frequency of 46 kHz and diameter of 35 mm. Excitation voltage used in the experiment is 500 V. The repetition frequency of excitation pulse is 2.5 MHz, with a repetition period of 0.4 μs. The parameters it measures include sound speed (), time (), and amplitude ().
Then, the total energy received by the receiving sensor is calculated by where is the density of the medium and is the center frequency.
To avoid the mutual effect of two sensors for transmitting and receiving, the detection length . and are selected to discuss the main detection process. In the experiments, the measurement process can be divided into the following seven steps. The diagram of operation is shown in Figure 12.
The first step is to detect ultrasonic parameters in the two base states: energy circle full of or without seed states, and calculate the total energy and , respectively.
The second step is to find the first base position and calculate the total energy . The sensor is moved from the reference position to the right slowly above the surface of the tilled soil to keep a good coupling. The value of echo energy does not change until the sensor is moved to the first base position on the left boundary line of seeding absence. At that time, the scale value of was read, and total energy was calculated.
The third step is to find the second base position . Continue to move the sensor from position to the right until the echo energy value does not change, which means that the sensor reaches the second base position , and the scale value of and total energy can be obtained.
The fourth step is to determine the size difference between and . Compare the size of and : if , then , or else .
The fifth step is to find the third base position . Continue to move the sensor from position to the right; the value of echo energy does not change until the sensor is moved to the third base position . At that time, the scale value of was read.
The sixth step is to find the fourth base position . Continue to move the sensor from position to the right until the echo energy value does not change, which means that the sensor reaches the last base position , and the scale value of can be obtained.
The seventh step is to determine the left and right boundary lines and and the length value of . According to result of the fourth step, if , the values of , , and are obtained by substituting , , , and into Equations (15), (16), and (17); else, if , they are obtained by Equations (18), (19), and (20).
3.2. Results Analysis
Figure 13 demonstrates the actual measurement results with and . Compared with Figure 7, the results demonstrate that the variation of total energy received by the receiving sensor is consistent with the variation regulation of the curve for theoretical values.
(a)
(b)
4. Discussion
Compared with other methods mentioned in the Introduction, the proposed ultrasonic method for seeding absence detection meets the requirement of nondestructive measurement with the latest position of seeds as other methods cannot reach. The proposed method does not need to remove the soil covered on seeds and does not damage the seedlings. It can also detect the final position of seeds in soil immediately after seeding. Therefore, the proposed method is more accurate than the seed metering or seed tube measurement methods, more efficient, convenient, and conducive to crop growth than manual measurement is after sowing or emergence.
However, the proposed method also has three uncertain factors influencing the detection result. First, incident ultrasonic waves are easily influenced by the coupling layer. Energy circle theory used in this study is based on the variation of echo energy in tilled soil, so the key premise is to keep the energy of incident ultrasonic waves constant during sensors moving to different positions. Nevertheless, due to the difference roughness of the soil surface, incident ultrasonic waves are difficult to control in the detection process. Thus, a couplant is needed in some conditions to obtain satisfactory results. Second, the discrepancy size of the reflection coefficient between untilled soil and seeds will affect the detection result. If the discrepancy is so small that the echo energy in the position of seeds and untilled soil is similar to each other received by the sensor, then it is impossible to detect. Third, the number of sensors may also influence the detection result. In this study, a transmitting sensor and a receiving sensor are used, respectively. Thus, the premise is receiving the sensor surrounded inside the energy circle, so that the echo energy could be detected by the receiving sensor. If the diameter of the energy circle is equal to the diameter of the transmitting sensor, then it is impossible to detect. Thus, one sensor with the function of both transmitting and receiving is needed in some detection conditions.
In this paper, the theory of nondestructive seeding absence detection for drill seeders on the soil surface of cropland based on ultrasonic wave was highlighted and analyzed. Due to the time limit, the results are preliminary. More work, such as small stone and insects’ effects, should be done to verify the effectiveness and feasibility of the method proposed in the future.
5. Conclusions
The theoretical and experimental results show that the proposed method is effective and accurate for seeding absence detection above the soil surface. This method has the advantages of nondestructive measurement with the latest position of seeds immediately after seeding. The selection of the center frequency and diameter of the sensors is crucial in this approach, which affects the magnitude and scope of echo energy in the tilled soil, which covers the seeds. In actual measurement operation, a selection program needs to be designed to obtain suitable center frequency and diameter. Furthermore, one sensor with the function of both transmitting and receiving can be chosen to satisfy the condition that the diameter of the energy circle is equal to the diameter of the transmitting sensor. As the aim is only a basic attempt to find out the feasibility of this method, the instrument used in this test is a mature product, produced by Beijing Zhibolian Science and Technology Co. Ltd, whose diameter and frequency are specific (, ). Due to the limit of the diameter and frequency of the detector, only two states of seed depth (25 mm and 30 mm) were tested. In actual detection, different crops, soil types, and depths require different ultrasonic frequencies, which will be studied in the future. Meanwhile, some works talk about the damage caused by using ultrasound in plant sensing and applications; it will be also part of the contents of future study.
Data Availability
The datasets used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare no conflict of interest.
Acknowledgments
This research was funded by the Program for Innovative Research Team in Ministry of Education of China grant number IRT13039 and Fundamental Research Funds for the Central Universities grant number 2018QC153. Thanks are due to the technical staff and students in Conservation Tillage Research Center of China Agricultural University for their valuable suggestions.
References
 S. Zhao and Y. Chen, “Seed distribution in soil and its effects on early plant growth,” Applied Engineering in Agriculture, vol. 31, no. 3, pp. 415–423, 2015. View at: Publisher Site  Google Scholar
 D. Karayel and A. Ozmerzi, “Comparison of vertical and lateral seed distribution of furrow openers using a new criterion,” Soil and Tillage Research, vol. 95, no. 12, pp. 69–75, 2007. View at: Publisher Site  Google Scholar
 D. Y. Huang, L. T. Zhu, H. L. Jia, T. T. Yu, and J. Yan, “Remote monitoring system for corn seeding quality based on GPS and GPRS,” Transactions of the Chinese Society of Agricultural Engineering, vol. 32, no. 6, pp. 162–168, 2016. View at: Publisher Site  Google Scholar
 C. Y. Lu, W. Q. Fu, C. J. Zhao et al., “Design and experiment on realtime monitoring system of wheat seeding,” Transactions of the Chinese Society of Agricultural Engineering, vol. 33, no. 2, pp. 32–40, 2017. View at: Publisher Site  Google Scholar
 R. Yuan, Research of Its Displacement after Seeds Touching Soil Controlled by the Furrow Opener of Precision Planter and Its Parts, [Ph. D. Thesis], Jilin University, Jilin, 2006.
 J. L. Wang, The Research of Position Control after Seed Contacting Soil in the Process of Soil Covering and Rolling with Precision Seeder, [Ph. D. Thesis], Jilin University, Jilin, 2012.
 C. Y. Lu, H. W. Li, J. He, H. B. Zhu, and D. J. Xu, “Floated support antiblocking device of wheat notill seeder,” Transactions of the Chinese Society for Agricultural Machinery, vol. 44, no. 12, pp. 52–55, 2014. View at: Publisher Site  Google Scholar
 R. Zhang, Study on DepthControl Mechanism of Corn NoTill Planting with Wheat Stubble in DoubleCropping Area, [Ph. D. Thesis], China Agricultural University, Beijing, 2016.
 P. Suomi and T. Oksanen, “Automatic working depth control for seed drill using ISO 11783 remote control messages,” Computers and Electronics in Agriculture, vol. 116, pp. 30–35, 2015. View at: Publisher Site  Google Scholar
 S. Michio and A. Tsuyoshi, “A portable field ultrasonic sensor for crop canopy characterization,” Remote Sensing of Environment, vol. 18, no. 3, pp. 269–279, 1985. View at: Publisher Site  Google Scholar
 L. Yu, T. S. Hong, Z. X. Zhao, J. Huang, and L. Zhang, “3Dreconstruction and volume measurement of fruit tree canopy based on ultrasonic sensors,” Transactions of the Chinese Society of Agricultural Engineering, vol. 26, no. 11, pp. 204–208, 2010. View at: Google Scholar
 G. V. Alejandra, M. C. Beatriz, B. Guadalupe, B. Uta, and L. P. Jorge, “A simple and costeffective method for cable root detection and extension measurement in estuary wetland forests,” Estuarine, Coastal and Shelf Science, vol. 183, pp. 117–122, 2016. View at: Publisher Site  Google Scholar
 J. Li, Y. Xu, R. Jiang, Z. Yang, and H. Z. Lu, “Establishment and verification of model for ultrasonic soil water content detector,” Transactions of the Chinese Society of Agricultural Engineering, vol. 33, no. 13, pp. 127–133, 2017. View at: Publisher Site  Google Scholar
 B. Zhang, Y. J. Wei, W. Y. Liu et al., “A liquid level measurement technique outside a sealed metal container based on ultrasonic impedance and echo energy,” Sensors, vol. 17, no. 12, p. 185, 2017. View at: Publisher Site  Google Scholar
 L. W. Schmerr, Fundamentals of Ultrasonic Nondestructive Evaluation: a Modeling Approach, Plenum press, USA, 1998.
 L. W. Schmerr Jr. and A. Sedov, “An elastodynamic model for compressional and shear wave transducers,” The Journal of the Acoustical Society of America, vol. 86, no. 5, pp. 1988–1999, 1989. View at: Publisher Site  Google Scholar
 D. J. Vezzeti, “Propagation of bounded ultrasonic beams in anisotropic media,” The Journal of the Acoustical Society of America, vol. 78, no. 3, pp. 1103–1108, 1985. View at: Publisher Site  Google Scholar
 S. RoaPrada, H. A. Scarton, G. J. Saulnier et al., “An ultrasonic throughwall communication (UTWC) system model,” Journal of Vibration and Acoustics, vol. 135, no. 1, article 011004, 2013. View at: Publisher Site  Google Scholar
 R. Bass, “Diffractions effects in the ultrasonic field of a piston source,” The Journal of the Acoustical Society of America, vol. 30, no. 7, pp. 602–605, 1958. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2019 Caiyun Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.