#### Abstract

The range measurement is the premise for location, and the precise range measurement is the assurance of accurate location. Hence, it is essential to know the accurate internode distance. It is noted that the path loss model plays an important role in improving the quality and reliability of ranging accuracy. Therefore, it is necessary to investigate the path loss model in actual propagation environment. Through the analysis of experiments performed at the wheat field, we find that the best fitted parametric exponential decay model (OFPEDM) can achieve a higher distance estimation accuracy and adaptability to environment variations in comparison to the traditional path loss models. Based on the proposed OFPEDM, we perform the RSSI-based location experiments in wheat field. Through simulating the location characteristics in MATLAB, we find that for all the unknown nodes, the location errors range from 0.0004 m to 5.1739 m. The location error in this RSSI-based location algorithm is acceptable in the wide areas such as wheat field. The findings in this research may provide reference for location estimation in large-scale farmland.

#### 1. Introduction

In recent years, wireless sensor network (WSN) has become a hot research topic. The WSN has application potentials in a variety of fields, such as habitat monitoring, environment monitoring, and target tracking [1]. It is known that the location information of sensor node is a premise for perceiving and collecting data. Hence, location technique plays a crucial role in WSN applications [2]. Due to the constraints of hardware cost and energy consumption, only a few sensor nodes, that is, anchor nodes are configured with location information. Other sensor nodes locate themselves by the internode distance measurements [3–5].

Generally, the WSN location techniques can be classified into two categories, that is, range-free and range-based localization. Concretely speaking, range-free localization can estimate the relative distance by considering the internode connectivity and the network topology relationship. Compared with range-free localization, the range-based localization owns higher accuracy. There are some common range-based approaches, such as time of arrival (TOA) [6, 7], time difference of arrival (TDOA) [8], angle of arrival (AOA) [9, 10], and received signal strength indication (RSSI) [11, 12]. Among them, TOA, TDOA, and AOA methods have high accuracy, but they require complex hardware and additional energy consumption [13]. The RSSI-based method utilizes the information provided by radio frequency (RF) apparatus, and does not need additional cost [14]. Hence, WSN systems are apt to adopt the RSSI-based methods to estimate the location of sensor nodes.

Obviously, range measurement is the premise for location, and the precise range measurement is the assurance of accurate location. Hence, it is essential to know the accurate internode distance. The RSSI-based ranging methods can be conveniently implemented since most RF IC chips of WSN nodes can directly provide the information of RSSI [15]. The essence of the RSSI-based ranging is that the average power of radio signal decays with the distance between transmitter and receiver according to some deterministic law, which can be referred to as path loss model [16]. It is noted that the path loss model plays an important role in improving the quality and reliability of ranging accuracy [17]. Hence, it is needed to search an accurate path loss model to describe the relationship between RSSI and distance. In present, the traditional path loss models have been adopted to estimate the transmitter-receiver (T-R) distance [18, 19]. Due to the impact of reflection, diffraction, and scattering, the values of received signal are affected by multipath interference [19]. The multipath interference can cause signal fluctuations with respect to the free space propagation model. Therefore, it is necessary to investigate the path loss model in actual propagation environment.

With the increasing of population, the demand for food is growing. The emergence of precision agriculture (PA) makes it possible to improve the yield and quality of crop. The data acquisition is the bottleneck problem in PA application, and WSN is identified as one of the best solution for data acquisition. For the research of farmland monitoring based on WSN, a particular focus has been put on wheat field since wheat is one of the major crops in the world. To better describe the monitored information from wheat field, it is necessary to know the precise geographical location of sensor nodes. In view of the characteristics of RSSI-based range measurements and particular situation of large-scale farmland, to improve the accuracy of location estimation, some RSSI-based experiments are conducted. In this study, we investigate the impact of signal propagation model on location estimation. First, we propose a new path loss model on the basis of the influence of multipath interference on signal propagation characteristics. Then, we study the accuracy and adaptability of the proposed path loss model in terms of distance estimation. Finally, we focus on the location estimation based on the proposed path loss model. To the author’s knowledge, this is the first study of RSSI-based location estimation in wheat field. The findings in this report will have great significance in improving the location accuracy in large-scale farmland.

The rest of the paper can be organized as follows: Section 2 gives a basic overview of RSSI-based localization. Section 3 introduces the ranging methods and the theoretical models of RF signal propagation. The corresponding ranging experiments and location result analysis are described in Section 4. Finally, the conclusions are summarized in Section 5.

#### 2. Related Work

There are some works focused on studying the RSSI-based location issues from different perspectives. For example, Kumar et al. adopted RSSI-based location technique to estimate the internode distances which further used for estimating the nodes’ location [20]. They concluded that the distance-estimated error for RSSI-based location scheme in WSN is roughly identical under ideal deployment conditions. Awad et al. proposed a distance-based location technique in WSN based on RSSI measurements [21] and found that the main effect on the distance measurements is the power transmission. Alippi and Vanini proposed an RSSI-based centralized location technique for outdoor environments and found that this approach is the easiest implemented way in RSSI-based multihop location systems [22]. Subaashini et al. studied the relationship between ZigBee sensor node’s RSSI values and the surrounding environment specifications for variant types of obstacles placed between transmitter and receiver [23]. They found that some RSSI value in online phase has not been fingerprinted in the training phase, and hence, the location cannot be determined. Adewumi et al. computed the internode distance of a WSN relying on RSSI-based model and discovered that the distance-estimated error in indoor environment is greater than that in outdoor environment [24]. Palazon et al. utilized an RSSI-based location scheme to study the location accuracy and how it can be affected when deploying different number of anchor nodes [25]. It is found that the location accuracy can be improved as the density of anchor nodes increases. Rasool et al. examined the performance of RSSI-based location using linear least squares algorithm [26] and found that the path loss exponent and the location coordinates performs considerably better in terms of root mean square error. Whitehouse et al. performed an experimental study of the RSSI measurements and the RSSI-based ranging in outdoor scenarios [27]. They concluded that the RSSI-based ranging can provide reasonable location performance in outdoor environments but sensitive to the environmental conditions and the experimental setup. Xu et al. [28] proposed an RSSI-based distance measurement model using log-normal shadowing model with dynamic variance propagation model and found that the proposed propagation model owns strong self-adaptability to various environments. Livinsa and Jayashri [29] proposed an RSSI-based location algorithm for distance estimation and location estimation under outdoor environment and indoor environment. They discovered that the performance of distance estimation in outdoor environment is better than that in indoor environment. Hamdoun et al. [30] proposed the RSSI-based location algorithm by using multiple antennas at the transmitter side, the receiver side or at the both sides to calculate the location error in indoor environment. They found that the location performance for multiple antennas at the both sides is better than that for antennas at either the transmitter or the receiver side. Chuku et al. [31] proposed an RSSI-based location scheme to mitigate the effects of shadowing caused by obstacles that are scattered in the field of operation. They found that the proposed scheme can effectively eliminate the RSSI signals that are affected by obstructions. Xu et al. [32] proposed an RSSI-based differential correlation algorithm to correct the distance measurement results and found that the proposed algorithm can improve the absolute accuracy as well as the relative accuracy of the location. Daiya et al. [33] performed the RSSI measurements between two sensor nodes at a varying distance for indoor and outdoor environment. They found that the estimation errors for approximate location of the sensor node are 5–10%.

#### 3. RSSI-Based Location Method

##### 3.1. The Traditional RSSI-Based Ranging Model

As is known, the estimation of internode distance is the premise for node location. Herein, the accuracy of distance estimation depends heavily on the accuracy of the signal propagation model. The traditional signal propagation models include free space model (FSM), two-ray ground model, and log-normal shadowing model (LNSM). Specifically, FSM is an ideal model, and the received power decays as a function of transmitter-receiver (T-R) distance. The FSM can be expressed as follows [34]:
where PL, *d*, and *f* are the path loss of signal energy, the signal transmission distance, and the wireless signal frequency, respectively. The two-ray ground model can be represented as follows [35]:
where *h*_{t} and *h*_{r} are the antenna heights of transmitter and receiver, respectively. The LNSM can be represented as follows [36]:
where *d*_{0} is the near-earth reference distance which depended on the experimental value, *n* is the path loss index in a specific environment, and *X _{σ}* is a zero-mean Gaussian random variable.

The mature wheat plant grows more lush and flouring, and the plant height can reach to a height of 1.2 m. In this circumstance, the wireless signal is affected by the scattering, refection, and diffraction, which can cause multipath propagation. Due to the wheat plant usually block the path between the transmitter and receiver, the radio propagation environment in wheat field is complex. As shown in Figure 1, the radio waves arrive at the receiver from different directions, and there are slightly difference in propagation delays. It can be seen that the multipath occurs due to the reflection from ground along with reflection, scattering, and diffraction from wheat plant. The received signal at any point in space may consist of a number of waves owning randomly distributed amplitudes, phases, and angles of arrival. These multipath components are combined vectorially at the receiver, thus resulting in the distortion or fading of the received signal strength, i.e., multipath fading. That is, the multipath fading can result in the distortion of RSSI measurements, further reduce the accuracy of distance estimation. The existing empirical vegetation models include Weissberger model, ITU-R model, and COST-235 model. Concretely speaking, the Weissberger model can be represented as follows [37]:
where *f* and *d* are the frequency in GHz and the depth of the foliage in meter, respectively. The Weissberger model is applicable for the frequency ranging from 230 MHz to 35 GHz. The ITU-R model can be defined as follows [38]:
where *f* and *d* are the frequency in MHz and the depth of the foliage in meter, respectively. The ITU-R model is applicable in the situation when the frequency is ranging from 0.2 GHz to 95 GHz. Moreover, the COST-235 model can be expressed as follows [39]:
where *f* denotes the frequency in MHz, and *d* represents the depth of foliage in meter.

##### 3.2. The Proposed Ranging Model

Based on our previous study in [40], we select the optimal fitting parametric exponential decay model (OFPEDM) as the signal propagation model in wheat field. The general form of OFPEDM can be represented as follows:
where *f* is the frequency of RF signal, and *d* is the T-R distance. It is worth mentioning that *X*, *Y*, and *Z* are parameters which can be determined by the actual propagation environment. Further, the estimated distance can be represented as follows:
where RSSI* _{i}* represents single measurement value.

##### 3.3. Node Location Method

To estimate the location of targeted node, this targeted node must be capable to detect at least three anchor nodes’ location information. Each anchor node owns the ability to store position coordinates itself and the RSSI value receiving from the targeted node. The estimated distance between the targeted node and anchor node can be calculated by the proposed OFPEDM. Based on the estimated distance, we further adopt trilateration technique to estimate the position of targeted node. As presented in Figure 2, the coordinates of three anchor nodes are labeled as (*x*_{1}, *y*_{1}), (*x*_{2}, *y*_{2}), and (*x*_{3}, *y*_{3}), respectively. The actual distance between targeted node and three anchor nodes is denoted as *d*_{1}, *d*_{2}, and *d*_{3}, respectively. The circle can be given by:
where *x _{i}* and

*y*denote the coordinates of anchor nodes.

_{i}*x*and

*y*are the coordinates of targeted nodes. Moreover,

*d*is the actual distance between targeted node and anchor node

_{i}*i*. Further, the intersection of three circles can be calculated as follows:

Equation (10) can be changed into the linear expression as follows: where

Further, the least squares solution can be expressed as follows:

The ranging error can be defined as the difference between the estimated distance and the actual distance, which can be represented as follows:
where *r _{i}* is the estimated distance between targeted node and anchor node

*i*.

The location error of targeted node can be defined as follows:
where *x* and *y* denote the actual coordinates of the targeted node. Moreover, *x _{e}* and

*y*represent the estimated coordinates of the targeted node.

_{e}#### 4. Ranging Experiments and Location Analysis

##### 4.1. Ranging Experiments

###### 4.1.1. Experimental Setup

The ranging experiment is conducted in the wheat field in Xiaotangshan National Precision Agriculture Research Demonstration Base. The measurements adopt CC2530 wireless sensor node in Webee Company to support the ZigBee protocol at frequency of 2.4 GHz. The measurement apparatus in the experiments includes the transmitter and receiver part. During the process of measurement, the transmitter configuration is arranged in a fixed location. The measurements are taken every 2 m for T-R distance ranging from 1 m to 100 m. Moreover, the antenna heights of transmitter and receiver are fixed at 1 m. The receiver supports a maximum bitrate of 250 kbit/s, with −110 dBm of sensitivity. The RSSI measurement process is as follows: the transmitter sends a packet to the receiver and the receiver incorporates the RSSI of the received packet. Then, the receiver can forward the RSSI value to the base station which is connected with the laptop through USB cable. It is worth mentioning that the RSSI in every measuring point is recorded 100 times.

###### 4.1.2. Distance Estimation Results Analysis

In order to gain insight into the performance of the proposed OFPEDM, we investigate the accuracy of distance estimation and adaptability to environment variations. The ranging measurement in a wheat field is depicted in Figure 3. In this circumstance, the base station is located at the edge of the field. The transmitter is placed at the source spots and moved forward in steps of 2 m. After sampling process, the corresponding T-R distance is calculated by FSM, LNSM, and the proposed OFPEDM. Herein, *X*, *Y*, and *Z* in the proposed OFPEDM are 0.051, 0.832, and 0.253, respectively [40]. The distance estimation results by three path loss models are illustrated in Figure 4. It can be seen that the proposed OFPEDM performs better than the FSM in terms of distance estimation accuracy for T-R distance larger than 5 m. For FSM, as T-R distance increases, the accuracy of distance estimation fluctuates obviously and gradually gets worse since multipath fading. Compared with FSM, the proposed OFPEDM can significantly mitigate the multipath fading effect and reduce the negative effect on the accuracy of distance estimation. Moreover, the proposed OFPEDM performs better than LNSM in terms of distance estimation, which can be attributed to the fact that the proposed OFPEDM can better describe the signal propagation in wheat field.

To further evaluate the performance of three path loss models, we calculate the distance estimation errors of FSM, LNSM, and the proposed OFPEDM, as presented in Figure 5. It can be seen that the distance estimation error of FSM is always the largest, which is consistent with the distance estimation accuracy. While the distance estimation errors of LNSM and the proposed OFPEDM are relatively small. To make the distance estimation error for three path loss models more clear, we perform the statistical analysis, and the results are illustrated in Figure 6. For FSM, LNSM, and the proposed OFPEDM, the distance estimation errors smaller than 1 m account for 1.96%, 15.68%, and 17.64%, respectively. The distance estimation errors in the range of 0–2 m for FSM, LNSM, and the proposed OFPEDM are 3.92%, 27.44%, and 31.37%, respectively. The distance estimation errors smaller than 5 m for FSM, LNSM, and the proposed OFPEDM are 11.76%, 62.73%, and 68.62%, respectively. Moreover, the distance estimation errors smaller than 10 m for FSM, LNSM, and the proposed OFPEDM are 17.64%, 92%, and 98%, respectively. In brief, the distance estimation error of the proposed OFPEDM is the smallest during the ranging measurement.

**(a)**

**(b)**

**(c)**

To evaluate the adaptability of three path loss models to environment variations, we calculate cumulative distribution function (CDF) of ranging errors, as presented in Figure 7. For FSM and LNSM, the probability of ranging errors smaller than 10 m is 0.18 and 0.92, respectively. While for the proposed OFPEDM, the probability of ranging errors smaller than 10 m has been up to 0.98. That is, the proposed OFPEDM performs better than FSM and LNSM in terms of adaptability to environment variations.

##### 4.2. Location Estimation Results Analysis

To evaluate the performance of the RSSI-based location algorithm, the simulation experiments are achieved by MATLAB. The location experiments are conducted at 100 m × 100 m region area. The schematic of node deployment is presented in Figure 8. The number of anchor nodes is 20, and the number of targeted nodes is 80. The actual coordinates of anchor nodes are (0.933, 91.50), (17.92, 96.89), (32.68, 88.03), (40.75, 84.45), (46.50, 81.40), (87.72, 78.49), (37.75, 73.50), (90.20, 70.21), (33.43, 59.66), (95.41, 54.28), (9.299, 46.35), (89.84, 42.92), (47.11, 40.4), (61.53, 37.66), (54.01, 31.11), (3.039, 20.85), (19.82, 19.51), (7.123, 18.2), (45.50, 12.73), and (64.27, 0.142), respectively. Moreover, the communication radius for each node is set to 30 m.

The flow chart of RSSI-based location algorithm is presented in Figure 9. Through simulating in MATLAB, the location results of unknown nodes are presented in Figure 10. As listed in Table 1, the location estimation errors for all the unknown nodes range from 0.0004 m to 5.1739 m. Moreover, the location estimation error decreases as the targeted node moving towards the center of the field, which can be attributed to the fact that the density of anchor nodes in the center of the field is larger than that in the edge of the field.

#### 5. Conclusions

Through the analysis of ranging experiments performed at the wheat field, we find that the proposed OFPEDM can achieve a higher estimation accuracy and adaptability to environment variations in comparison to the FSM and LNSM. Hence, we adopt OFPEDM to describe the relationship between RSSI value and the internode distance. To evaluate the performance of the RSSI-based location algorithm, the simulation experiments are achieved by MATLAB. For all the unknown nodes, the location errors range from 0.0004 m to 5.1739 m. The location error of RSSI-based method is influenced not only by the location algorithm, but also by the ranging accuracy. The location error in this RSSI-based location algorithm is acceptable in the wide areas such as wheat field. The findings in this research may provide reference for location estimation in large-scale farmland.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This work is supported by the Beijing Natural Science Foundation (4172024) and Natural Science Foundation of China (61571051).