# An Anchor Node Selection Scheme for Improving RSS-Based Localization in Wireless Sensor Network

Authors: Jing Cheng; Ya Li; Qingyuan Xu
Journal: Mobile Information Systems
 (2022)

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## Abstract

Accurate location information is essential for various emerging applications in wireless sensor network (WSN). In order to improve localization accuracy, it is of paramount importance to reduce the effects of noisy distance measurements. This paper proposes an anchor node selection scheme for Received Signal Strength- (RSS-) based localization in WSN. In the proposed approach, the nodes are sorted firstly to select anchor nodes reasonably, and to further reduce the influence of range error, the weight is assigned to each selected anchor node. Finally, an effective modified cuckoo search algorithm is used to compute the coordinates of unknown nodes. Extensive experiments are conducted to study the effects of anchor node ratio, ranging error factor and node density on the localization accuracy performance of the proposed method. The experimental results demonstrate that the proposed method performs better in improving localization accuracy compared with the localization technique without special anchor selection scheme which selects all anchors’ information received and the localization technique selecting nearest anchors.


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## Body

## 1. Introduction

Wireless sensor network (WSN) is a network composed of tiny, battery-powered sensor nodes that communicate with each other through a wireless communication link [1, 2]. In recent years, localization is a fundamental requirement in a variety of WSN application domains [3], such as environmental monitoring [4], healthcare monitoring [5], traffic monitoring [6], fire detection [7], and precision agriculture [8]. Once location information of the node is obtained, people can estimate the origins of the sensed events and then make timely and effective measures for those events. In addition, the location information of sensor nodes can also provide important basis for WSN key technologies such as topology control [9], routing design [10, 11], and energy management [12]. Therefore, it is highly important to obtain accurate location information of sensor nodes in WSN.Dedicated localization systems (global positioning system (GPS) and BeiDou Navigation Satellite System (BDS)) can be used to localize sensor nodes highly accurately. However, due to various constraints, such as cost and energy consumption, it is impractical to locate all the nodes using these special systems. In addition, GPS/BDS requires line-of-sight between the sensor node and the satellites which is impossible in indoor environments [13]. These constraints motivate the rise and development of localization techniques, such as range-free and range-based localization algorithms [14]. These techniques are employed to derive the location of sensor nodes whose coordinates are unknown based on a few of anchor nodes. The anchor nodes are some sensor nodes equipped with special GPS/BDS module. The range-free localization methods exploit the connectivity or hop-count information between the unknown node and its neighbors, such as DV-HOP algorithm, centroid localization, and approximate point-in-triangulation test (APIT) [15]. The range-based localization assumes that the node can obtain the range or angle measurements from anchor nodes within its communication range [16]. Compared with range-free localization, the range-based localization can provide higher localization accuracy. The typical methods to measure range are Received Signal Strength (RSS), Time of Arrival (TOA), and Time Difference of Arrival (TDOA) [17]. Since RSS can be easily measured without additional hardware support under actual deployment scenario, it is always used for node localization in WSN. However, radio signal is easily affected by multipath and obstacles blocking which can result in ranging error and thus deteriorating localization accuracy [18]. Therefore, effective localization strategies need to be designed to solve the problems.Motivated by the above observations, this paper proposes a new anchor node selection scheme for RSS-based localization which is aimed at reducing the effect of ranging error on localization accuracy in WSN. The main work of this paper is that the approach first utilizes the difference of the maximum and minimum RSS from anchors to identify whether an unknown node is a boundary node. For each boundary node, the approach selects a fraction of anchor nodes with higher RSS that can reduce the influence of ranging error on localization accuracy. Conversely, it selects all the anchors within its communication range. In addition, to further enhance the contribution of the distance measurements which are expected to be accurate, each selected anchor node is assigned to different weight which is determined by the size of distance measurements between the unknown node and anchors belonging to the selected anchor node set. Considering the modified CS (cuckoo search, CS) algorithm in our previous research [19] can not only increase convergence rate but also reduce average localization error compared with standard CS algorithm and PSO (Particle Swarm Optimization, PSO) algorithm. In this paper, the modified cuckoo search algorithm is used to compute the coordinates of unknown nodes. Extensive simulation experiments are studied on the effects of anchor node ratio, ranging error factor and node density with respect to the average localization error. The experimental results demonstrate that the proposed method can perform better in improving localization accuracy compared with other localization techniques.The rest of this paper is organized as follows: Section2 presents the related works. Section 3 describes the RSS-based localization problem. The proposed anchor node selection scheme based localization algorithm is introduced in Section 4. Simulation experiments and results are discussed in Section 5. Section 6 gives the conclusion.


## 2. Related Works

A detailed survey of the research on anchor selection is available in the literature [20, 21]. Chuang and Wu [20] proposed a new scheme employing PSO algorithm to increase localization accuracy, by using the location data of remote anchors (provided by the closest neighbor nodes of an unknown node). Artemenko et al. [21] analyzed several most promising optimum anchor selection algorithms that can contribute to improve localization precision. Cheng et al. [22] confirmed that anchor node selection is a significant factor to determine the localization accuracy and first demonstrated that using all anchor nodes to locate unknown nodes does not give the most precise position. Then, this paper developed an improved APS algorithm which chooses the nearest 3 anchors with respect to each individual sensor node. This approach reduces the maximum average estimate error to almost half of that attained by the original APS method. Note that the proposal mainly is aimed at the anisotropic sensor networks and may not always give the best position estimate for each individual sensor node. In addition, Woo et al. [23] advocated a reliable anchor node selection strategy in which each unknown node selects three anchor nodes with triangular rule to enhance localization accuracy, and the selected anchor nodes must be located within 4-hop. The proposed scheme can enhance localization accuracy compared with DV-Hop in anisotropic WSN. Based on [23], El Assaf et al. [24] proposed a new reliable anchor selection strategy that ensures an accurate distance estimation. The proposed scheme makes their localization algorithm more precise even with the presence of nonuniform node distribution or radiation irregularities. Moreover, Yao and Niang [25] devised a distributed weighted search-based localization algorithm (WSLA) and its refinement algorithm (WSRA). WSLA employs weighted two-dimensional logarithmic search- (TDLS-) search algorithm to estimate the position of nodes, and WSRA employs distance-hop contradiction to improve localization accuracy. The proposed algorithms work better than Maximum Likelihood Estimation (MLE), Robust Second-order Cone Programming+nonconvex sequential greedy (RSOCP+NCSG), and Particle Swarm Optimization (PSO) and have lower time complexity than RSOCP+NCSG and PSO. On the other hand, Bouchoucha and Ding [26] proposed a general formulation to the anchor node selection problem and then relaxed the optimization problem by deriving an upper-bound of the objective function. Finally, the anchor node is selected based on the connectivity information. The experiments indicated that the proposed method is robust to improve network topology inference and routing performance. The above strategies of anchor node selection are based on the use of network connectivity whereas they ignore the use of range measurement techniques. The range-based RSS localization can achieve high localization accuracy; however, it is very susceptible to noise and obstacles, particularly for indoor environment. To overcome the problem, several algorithms exist in the following literatures which depend on optimizing anchor selection. Fang et al. [27] firstly sorted the anchor nodes according to the RSSI value received from the node; the Gaussian elimination method is used to select four anchor nodes with higher RSSI values. This paper demonstrated the localization accuracy is improved by the proposed method. Amin et al. [28] developed an anchor selection algorithm which depends on the energy harvesting-aware weighted average function. The proposed scheme can enhance network lifetime compared with the traditional lifetime maximization algorithms in Cheng et al. [29] designed a reliable selection strategy of anchor nodes, and these factors are considered to conduct the fitness function, such as the localization accuracy, communication overhead, and energy consumption, and then, the particle swarm algorithm is used to iterate to get the optimal anchor combination. The results show that the proposed strategy brings small calculation, fast convergence and positioning accuracy. Elgamel and Dandoush [30] proposed a novel optimized Trigonometric Ad-hoc Localization System (OTALS) based on the modified Manhattan distance norm and the selection of base anchor. The proposed method presents superior performance compared to other localization techniques. Zhu et al. [31] designed a node selection algorithm based on the software-defined and the CRLB. This approach makes use of the global network knowledge provided by the SDN controller to formulate the localization node selection into a 0-1 programming problem on the premise of energy satisfaction. The simulation results present a significant improvement in localization performance. More recently, Ahmadi et al. [32] introduced an improved anchor selection strategy that selects the three anchors nearest to the target for the generation of the training test and during the testing phase. The method is evaluated using real measurements acquired in office rooms, and the results show that the proposed method provides an increased accuracy compared to the localization algorithm using standard regression tree. To the best of our knowledge, challenges still exist in the research for RSS-based localization. In this paper, we mainly analyze the problems of RSS-based localization and propose a novel anchor selection scheme.


## 3. Problem Statement

Considering a WSN is composed ofN anchor nodes xi,yi, 1≤i≤N, whose coordinates are known and M unknown sensor nodes located at some unknown location x,y. We assume that each sensor node is randomly deployed in a two-dimensional mission field. When the number of anchor nodes within communication range is more than or equal to 3, unknown nodes can locate themselves through the anchor coordinates within communication range and the distance measurements. Localization can be carried out by using some algorithms which compute positions for unknown nodes by solving a set of equations or by minimizing the objective function using an optimization algorithm. This paper belongs to the latter, that is, we aim to estimate the positions of unknown nodes as accurately as possible by minimizing the objective function defined as Equation (1):
(1)fxi,yi=1n∑j=1ndij−dij′2.The above functionfxi,yi represents the mean of square of ranging error between the unknown node xi,yi and anchor nodes within communication range, where n denotes the number of anchors within communication range, n≥3. When the objective function is minimized, the corresponding coordinate xi,yi is the location of ith unknown node. Here, dij represents the actual distance between the unknown node xi,yi and the anchor node xj,yj, and it can be expressed using the Equation (2):
(2)dij=xi−xj2+yi−yj2.The measured distancedij′ between unknown node xi,yi and the anchor node xj,yj can be modeled using the Equation (3):
(3)dij′=dij+Nij,whereNij is the ranging error between unknown node xi,yi and anchor node xj,yj.From Equation (1), we can see that this kind of localization algorithm requires distance measurements. As referred in Section 1, measuring the distance-based RSS is one of the simplest and efficient methods. In free space, the RSS decays proportional to the distance between the transmitter and receiver [33, 34], as shown in the Equation (4):
(4)RSSd=PTGTGrλ4πd2,wherePT is the transmitting power at the anchor node, GT is the gain at the anchor node, Gr is the gain at the unknown node, λ is the wavelength, and d is the distance between anchor node and the unknown node. However, in real scenarios, RSS measurements are often affected by multipath signals and shadowing; in this paper, we assume that the RSS follows the log normal channel model which is given as Equation (5):
(5)RSSd=PT−PLd0−10αlog10dd0+Xσ,wherePLd0 is the signal power loss in dB unit at 1 m distance, α is the path loss exponent which typically ranges between 2 and 4 depending the environment, d is the distance between the transmitter and receiver, d0 is the reference distance, and Xσ represents the noise in RSS, which is a zero-mean Gaussian random variable with standard deviation σ, that is, Xσ~0,σ2. Under the influence of log normal model, the standard deviation σ is proportional to the actual distance dij between ith unknown node and the jth anchor node, as shown in the Equation (6):
(6)σ2=γ2∗dij2,whereγ denotes the ranging error factor. According to the experimental study [21], in practical WSN environment, the farther distances between sensor nodes will produce larger the ranging error and localization error and vice versa.


## 4. Proposed Anchor Node Selection Scheme Based Localization Algorithm

In order to reduce the influence of the ranging error and improve localization accuracy, in this section, we propose an anchor node selection strategy for RSS-based localization in WSN. The flow chart of the proposed localization algorithm is shown in Figure1.Figure 1
Flow chart of the proposed localization algorithm.It is assumed thatN anchor nodes and M unknown nodes are deployed in a two-dimensional WSN field. From Figure 1, the proposed localization algorithm mainly consists of the following several phases. First, the proposed approach utilizes the difference of the maximum and minimum RSS from anchors to identify whether an unknown node is a boundary node. Second, the anchor nodes are selected according to different types of each unknown node. Third, to further enhance the contribution of the distance measurements which are expected to be accurate, each selected anchor node is assigned to a different weight which is determined by the size of distance measurements between the unknown node and anchors belonging to the selected anchor node set. Then, a modified cuckoo search algorithm is adopted to yield more desirable localization accuracy and convergence rate in WSN. The following subsections introduce the proposed algorithm in detail.


### 4.1. Identifying and Classifying Unknown Sensor Nodes

In the first step, the proposed method identifies and classifies the unknown sensor nodes. Each unknown node can measure a set of RSS values from anchor nodes within its communication range according to Equation (5) in Section 3, for example, RSS1,RSS2,⋯,RSSNr,0≤Nr≤N. Considering that the farther the distances between the unknown node and anchor nodes are, the smaller the RSS will be likely. In addition, no matter anchor nodes are deployed on the perimeter of sensor area or deployed randomly in the sensor area, the difference between measured RSS values will be larger when the unknown node is deployed around the edge of the sensor area. On the contrary, if the unknown node is located near the inner part of sensor area, the difference between measured RSS values will be relatively smaller. Based on the above idea, we propose the Equation (7) to identify and classify unknown sensor nodes.
(7)i∈boundarysensornodeDIFi≥Td,non‐boundarysensornodeotherwise,whereDIFi=RSSmaxi−RSSmini, which represents the difference between measured RSS values for ith unknown node; RSSmaxi and RSSmini, respectively, represent the maximum and minimum RSS from anchors. In addition, Td is the threshold to identify whether the unknown node is a boundary node; in this paper, it is defined as Equation (8).
(8)Td=l∗RSSmaxi.The scale factorl in Equation (8) is set to be 0.25 in this paper. From Equation (7), it can be seen that if the difference between measured RSS values is greater than the threshold Td, the ith unknown node is identified to be a boundary node, and conversely, it is a nonboundary node.


### 4.2. Anchor Node Selection

Research has proved that it is usually not the best choice to calculate the locations of unknown nodes using all the anchor nodes within communication range [22]. Therefore, in the second step, a new anchor selection strategy is proposed. The main goal of the anchor selection strategy is to reduce the noise level of the selected anchor nodes, which is more favorable to improve localization accuracy, given that the measured RSS from different anchor nodes is different due to the different noise level caused by the temporal and spatial changes of the environmental conditions affecting the transmission of radio signal. The measured RSS at an unknown node is a function of its distance to the anchor node and the farther anchor node makes the RSS measurements affected more serious. According to the above analysis, the main idea of anchor selection strategy is that if the unknown sensor node is a boundary node, the proposed method will sort the received RSS values and select a fraction of anchor nodes with higher RSS. Conversely, if it is a nonboundary node, the proposed method will select all the anchors within its communication range. The proportional value for the boundary node is set to 0.75 through extensive experiments and the comprehensive consideration of localization accuracy and computational consumption. The advantage for such an anchor node selection is that it can reduce the influence of ranging error caused by farther distance measurements on location accuracy.


### 4.3. Enhancing Localization Accuracy

The real distance between sensor nodes is seriously influenced by RSS ranging error and the estimated location often deviates from the actual location. In addition, the larger the distance measurement is, the more serious the RSS ranging error is and finally the worse the location result is. Therefore, if the number of the selected anchors is greater than or equal to three, in order to enhance the contribution of those anchors from the distance measurements which are likely accurate, in this step, we assign a different weight to each selected anchor node, and the normalized weight can be modeled using Equation (9):
(9)wj=1/dij′k∑j=1Ns1/dij′kj=1,2,3,⋯,Ns,wherewj denotes the weight factor for the jth selected anchor node and is derived from the distance measurements between ith unknown node and selected anchor nodes, where Ns denotes the number of the selected anchor nodes and dij′ represents the measured distance between the ith unknown node and jth anchor node. Extensive experiments are conducted to derive the reasonable k value in Equation (9). In our experiments k is set to be 1. As shown in Equation (9), the weight wj is determined by the size of distance measurements between unknown node i and the anchor nodes belonging to the selected anchor node set. We can see that the farther the distances between the unknown node and anchor nodes are, the smaller the contribution of the anchor nodes in localization process will be.


### 4.4. Location Estimation

Location estimation in WSN is always treated as multidimensional optimization problem and can be solved through metaheuristic algorithms [35, 36]. Once the anchors are selected according to the proposed strategy described in the above subsections, each localizable unknown node locates itself through running the modified cuckoo search algorithm [19].This algorithm estimates the coordinates by minimizing the objective function which represents the mean of square of ranging error defined in Equation (10):
(10)fxi,yi=1Ns∑j=1Nswj∗dij−dij′2,whereNs denotes the number of selected anchor nodes and wj is the weight of the selected anchor node j, which is defined in Equation (10). As it can be noticed, the above Equation (10) is very similar to Equation (1) which is introduced in Section 3, apart from the weighting factor that mainly enhances the contribution of those selected anchor nodes from which the measured RSS value is higher. When the objective function is minimized, the corresponding xi,yi will be the coordinate of the ith unknown node.In the modified cuckoo search algorithm, the initial values for all the nests (solutions) are generated randomly and each solution is evaluated by calculating the objective function in Equation (10) to find the corresponding fitness of the solution. The fitness depends on the quality of the solution. The smaller the value of objective function is, the higher the quality of the solution is, and consequently, the closer the solution is to the real location of the unknown node. If the fitness of the current solution is better than that in previous generation, the previous solution will be updated by the current solution with better fitness. To find the global optimal location for each localizable unknown node as efficiently as possible, the modified cuckoo search algorithm adopts three schemes to control the generation of the new random solutions.First, the modified cuckoo search algorithm computes the step sizeα for Lévy flight using the Equation (11):
(11)α=αmax−N_iterN_itertotal∗αmax−αmin,whereamax and amin denote the maximum and minimum of step size, respectively; N_iter and N_itertotal denote the current iteration number and total number of iterations, respectively. Once we get the step size α, for a cuckoo (solution) i, the new solution xit+1 is generated by Lévy flight using the following Equation (12):
(12)xit+1=xit+α⊕Le′vyλ,where⊕ represents entry-wise multiplications, and the Lévy flight is a random walk that is characterized by a series of instantaneous jumps chosen from a probability density function which has a power law tail. And the step length of random walk formed by Lévy flight can be calculated by using Equation (13):
(13)Le′vyλ=uv1/λ,whereλ is a constant, 1<λ≤3, and u and v are drawn from normal distributions as Equation (14):
(14)u~N0,σu2,v~N0,σv2,where(15)σu=Γ1+λsinπλ/2Γ1+λ/2λ2λ−1/21/λ,σv=1.Briefly speaking, the step sizeα decreases as the increasing of the iteration numbers. The modification of the step size can make the population promote the global search ability at the beginning of iterations and enhance the local search by decreasing the step size. Based on the modification of the step size, some new solutions generated by Lévy flight will tend to the global optimum solution gradually as the iterations proceed.Second, the modified cuckoo search algorithm employs the fitness of the solution to build the mutation probabilityPa (a fraction Pa of n solutions replaced by new random solutions) using Equation (16):
(16)Paj=Pamin+Pamax−Pamin∗K,K<1PamaxN_iter,otherwisej=1,2,3,⋯,n,whereK=fitnessj−fmin, which depends on the quality of the jth solution. fitnessj and fmin denote the current fitness of the jth solution and current global best fitness of the population, respectively; Pamax and Pamin represent the maximum and minimum of the mutation probability Pa, respectively. In brief, when the quality of current jth solution is close to the current global optimum solution, the higher the quality of the solution is, the smaller the mutation probability Pa is. In contrast, the mutation probability Pa will decrease with the increasing of iterations. Based on the modification about Pa, the modified cuckoo search algorithm enhances the population diversity and thus can avoid the local convergence.Finally, each solution generated is restricted in the certain range so that the modified cuckoo search algorithm can reduce energy computation caused by meaningless search. What is more, the global optimum solution can be found at a faster rate.Based on the above three aspects, new solutions are generated and evaluated depending on Equation (10). Global optimum solution is updated as the iterations proceed. Once the global optimum solution stops updating or the termination conditions are reached, the current solution is the best location of the unknown node xi,yi. Otherwise, the modified cuckoo search algorithm continues to the next generation. For each unknown node, step 4.1~step 4.4 are conducted repeatedly unless no unknown nodes can be localized or the termination conditions are reached.The detailed experimental process of the proposed localization algorithm is described in Algorithm1.Algorithm 1: The proposed localization algorithm based on anchor node selection scheme.
1.Begin2.For each unknown node do3.Indentifying the unknown node and performing anchor selection according to the different types of the unknown node4.Calculating the weight for each selected anchor node5.Building the objective function using the Equation (10)6.Generate initial population of n nests(solutions)xixi,i=1,2…n7.Set the range ofα and Pa: amin, amax, Pamin, Pamax8.Set the range of the nest(solution):Xmin, Xmax9.Set the maximum number of iterations:N_itertotal10.Calling Algorithm211.EndAlgorithm 2: The modified cuckoo search algorithm.
1.For allxi do2.Calculate the fitnessFi using the Equation (10)3.End For4.N_iter=15.While (N_iter<N_itertotal) do6. For allxi do7.Compute the step size forLe′vy flight according to the Equation (11)8.Generate a new cuckooxj from the nest xi randomly by taking Lévy flight using the Equation (12)9.If (xj>Xmax)then10.xj⟵Xmax11.End If12.If (xj<Xmin)then13.xj⟵Xmin14.End If15.Calculate the fitnessFj using the Equation (10)16.Choose a random nest (xk) among n nest randomly17.If (Fj>Fk) then18.xj⟵xk19.Fj⟵Fk20.End If21.End For22.Keep the current global optimal fitness:fmin23.Compute the probabilityPa using the Equation (16)24.A fraction (Pa) of worse nests abandoned and new ones/solutions are built/generated correspondingly25.For all the nests(say,xi) to be built/generated do26.If (xi>Xmax)then27.xi⟵Xmax28.End If29.If (xi<Xmin)then30.xi⟵Xmin31.End If32.Calculate the fitness using the Equation (10) and evaluate its quality/fitness Fi33.Keep best solutions (or nests with quality solutions)34.End For35.Rank all the solutions and find the current best36.End While


## 4.1. Identifying and Classifying Unknown Sensor Nodes

In the first step, the proposed method identifies and classifies the unknown sensor nodes. Each unknown node can measure a set of RSS values from anchor nodes within its communication range according to Equation (5) in Section 3, for example, RSS1,RSS2,⋯,RSSNr,0≤Nr≤N. Considering that the farther the distances between the unknown node and anchor nodes are, the smaller the RSS will be likely. In addition, no matter anchor nodes are deployed on the perimeter of sensor area or deployed randomly in the sensor area, the difference between measured RSS values will be larger when the unknown node is deployed around the edge of the sensor area. On the contrary, if the unknown node is located near the inner part of sensor area, the difference between measured RSS values will be relatively smaller. Based on the above idea, we propose the Equation (7) to identify and classify unknown sensor nodes.
(7)i∈boundarysensornodeDIFi≥Td,non‐boundarysensornodeotherwise,whereDIFi=RSSmaxi−RSSmini, which represents the difference between measured RSS values for ith unknown node; RSSmaxi and RSSmini, respectively, represent the maximum and minimum RSS from anchors. In addition, Td is the threshold to identify whether the unknown node is a boundary node; in this paper, it is defined as Equation (8).
(8)Td=l∗RSSmaxi.The scale factorl in Equation (8) is set to be 0.25 in this paper. From Equation (7), it can be seen that if the difference between measured RSS values is greater than the threshold Td, the ith unknown node is identified to be a boundary node, and conversely, it is a nonboundary node.


## 4.2. Anchor Node Selection

Research has proved that it is usually not the best choice to calculate the locations of unknown nodes using all the anchor nodes within communication range [22]. Therefore, in the second step, a new anchor selection strategy is proposed. The main goal of the anchor selection strategy is to reduce the noise level of the selected anchor nodes, which is more favorable to improve localization accuracy, given that the measured RSS from different anchor nodes is different due to the different noise level caused by the temporal and spatial changes of the environmental conditions affecting the transmission of radio signal. The measured RSS at an unknown node is a function of its distance to the anchor node and the farther anchor node makes the RSS measurements affected more serious. According to the above analysis, the main idea of anchor selection strategy is that if the unknown sensor node is a boundary node, the proposed method will sort the received RSS values and select a fraction of anchor nodes with higher RSS. Conversely, if it is a nonboundary node, the proposed method will select all the anchors within its communication range. The proportional value for the boundary node is set to 0.75 through extensive experiments and the comprehensive consideration of localization accuracy and computational consumption. The advantage for such an anchor node selection is that it can reduce the influence of ranging error caused by farther distance measurements on location accuracy.


## 4.3. Enhancing Localization Accuracy

The real distance between sensor nodes is seriously influenced by RSS ranging error and the estimated location often deviates from the actual location. In addition, the larger the distance measurement is, the more serious the RSS ranging error is and finally the worse the location result is. Therefore, if the number of the selected anchors is greater than or equal to three, in order to enhance the contribution of those anchors from the distance measurements which are likely accurate, in this step, we assign a different weight to each selected anchor node, and the normalized weight can be modeled using Equation (9):
(9)wj=1/dij′k∑j=1Ns1/dij′kj=1,2,3,⋯,Ns,wherewj denotes the weight factor for the jth selected anchor node and is derived from the distance measurements between ith unknown node and selected anchor nodes, where Ns denotes the number of the selected anchor nodes and dij′ represents the measured distance between the ith unknown node and jth anchor node. Extensive experiments are conducted to derive the reasonable k value in Equation (9). In our experiments k is set to be 1. As shown in Equation (9), the weight wj is determined by the size of distance measurements between unknown node i and the anchor nodes belonging to the selected anchor node set. We can see that the farther the distances between the unknown node and anchor nodes are, the smaller the contribution of the anchor nodes in localization process will be.


## 4.4. Location Estimation

Location estimation in WSN is always treated as multidimensional optimization problem and can be solved through metaheuristic algorithms [35, 36]. Once the anchors are selected according to the proposed strategy described in the above subsections, each localizable unknown node locates itself through running the modified cuckoo search algorithm [19].This algorithm estimates the coordinates by minimizing the objective function which represents the mean of square of ranging error defined in Equation (10):
(10)fxi,yi=1Ns∑j=1Nswj∗dij−dij′2,whereNs denotes the number of selected anchor nodes and wj is the weight of the selected anchor node j, which is defined in Equation (10). As it can be noticed, the above Equation (10) is very similar to Equation (1) which is introduced in Section 3, apart from the weighting factor that mainly enhances the contribution of those selected anchor nodes from which the measured RSS value is higher. When the objective function is minimized, the corresponding xi,yi will be the coordinate of the ith unknown node.In the modified cuckoo search algorithm, the initial values for all the nests (solutions) are generated randomly and each solution is evaluated by calculating the objective function in Equation (10) to find the corresponding fitness of the solution. The fitness depends on the quality of the solution. The smaller the value of objective function is, the higher the quality of the solution is, and consequently, the closer the solution is to the real location of the unknown node. If the fitness of the current solution is better than that in previous generation, the previous solution will be updated by the current solution with better fitness. To find the global optimal location for each localizable unknown node as efficiently as possible, the modified cuckoo search algorithm adopts three schemes to control the generation of the new random solutions.First, the modified cuckoo search algorithm computes the step sizeα for Lévy flight using the Equation (11):
(11)α=αmax−N_iterN_itertotal∗αmax−αmin,whereamax and amin denote the maximum and minimum of step size, respectively; N_iter and N_itertotal denote the current iteration number and total number of iterations, respectively. Once we get the step size α, for a cuckoo (solution) i, the new solution xit+1 is generated by Lévy flight using the following Equation (12):
(12)xit+1=xit+α⊕Le′vyλ,where⊕ represents entry-wise multiplications, and the Lévy flight is a random walk that is characterized by a series of instantaneous jumps chosen from a probability density function which has a power law tail. And the step length of random walk formed by Lévy flight can be calculated by using Equation (13):
(13)Le′vyλ=uv1/λ,whereλ is a constant, 1<λ≤3, and u and v are drawn from normal distributions as Equation (14):
(14)u~N0,σu2,v~N0,σv2,where(15)σu=Γ1+λsinπλ/2Γ1+λ/2λ2λ−1/21/λ,σv=1.Briefly speaking, the step sizeα decreases as the increasing of the iteration numbers. The modification of the step size can make the population promote the global search ability at the beginning of iterations and enhance the local search by decreasing the step size. Based on the modification of the step size, some new solutions generated by Lévy flight will tend to the global optimum solution gradually as the iterations proceed.Second, the modified cuckoo search algorithm employs the fitness of the solution to build the mutation probabilityPa (a fraction Pa of n solutions replaced by new random solutions) using Equation (16):
(16)Paj=Pamin+Pamax−Pamin∗K,K<1PamaxN_iter,otherwisej=1,2,3,⋯,n,whereK=fitnessj−fmin, which depends on the quality of the jth solution. fitnessj and fmin denote the current fitness of the jth solution and current global best fitness of the population, respectively; Pamax and Pamin represent the maximum and minimum of the mutation probability Pa, respectively. In brief, when the quality of current jth solution is close to the current global optimum solution, the higher the quality of the solution is, the smaller the mutation probability Pa is. In contrast, the mutation probability Pa will decrease with the increasing of iterations. Based on the modification about Pa, the modified cuckoo search algorithm enhances the population diversity and thus can avoid the local convergence.Finally, each solution generated is restricted in the certain range so that the modified cuckoo search algorithm can reduce energy computation caused by meaningless search. What is more, the global optimum solution can be found at a faster rate.Based on the above three aspects, new solutions are generated and evaluated depending on Equation (10). Global optimum solution is updated as the iterations proceed. Once the global optimum solution stops updating or the termination conditions are reached, the current solution is the best location of the unknown node xi,yi. Otherwise, the modified cuckoo search algorithm continues to the next generation. For each unknown node, step 4.1~step 4.4 are conducted repeatedly unless no unknown nodes can be localized or the termination conditions are reached.The detailed experimental process of the proposed localization algorithm is described in Algorithm1.Algorithm 1: The proposed localization algorithm based on anchor node selection scheme.
1.Begin2.For each unknown node do3.Indentifying the unknown node and performing anchor selection according to the different types of the unknown node4.Calculating the weight for each selected anchor node5.Building the objective function using the Equation (10)6.Generate initial population of n nests(solutions)xixi,i=1,2…n7.Set the range ofα and Pa: amin, amax, Pamin, Pamax8.Set the range of the nest(solution):Xmin, Xmax9.Set the maximum number of iterations:N_itertotal10.Calling Algorithm211.EndAlgorithm 2: The modified cuckoo search algorithm.
1.For allxi do2.Calculate the fitnessFi using the Equation (10)3.End For4.N_iter=15.While (N_iter<N_itertotal) do6. For allxi do7.Compute the step size forLe′vy flight according to the Equation (11)8.Generate a new cuckooxj from the nest xi randomly by taking Lévy flight using the Equation (12)9.If (xj>Xmax)then10.xj⟵Xmax11.End If12.If (xj<Xmin)then13.xj⟵Xmin14.End If15.Calculate the fitnessFj using the Equation (10)16.Choose a random nest (xk) among n nest randomly17.If (Fj>Fk) then18.xj⟵xk19.Fj⟵Fk20.End If21.End For22.Keep the current global optimal fitness:fmin23.Compute the probabilityPa using the Equation (16)24.A fraction (Pa) of worse nests abandoned and new ones/solutions are built/generated correspondingly25.For all the nests(say,xi) to be built/generated do26.If (xi>Xmax)then27.xi⟵Xmax28.End If29.If (xi<Xmin)then30.xi⟵Xmin31.End If32.Calculate the fitness using the Equation (10) and evaluate its quality/fitness Fi33.Keep best solutions (or nests with quality solutions)34.End For35.Rank all the solutions and find the current best36.End While


## 5. Simulation Experiments and Performance Evaluation

### 5.1. Simulation Setting

In this paper, all simulation experiments are implemented in Matlab platform. To verify the effectiveness of the proposed algorithm, we compared the localization performance of the proposed method with that of the localization technique without special anchor selection scheme [19] which selects all anchors’ information received and the localization technique selecting nearest anchors within communication range [23]. For each localization technique, the localization result is estimated based on the modified cuckoo search algorithm. Extensive simulation experiments are conducted to study the effects of anchor node ratio, ranging error factor and node density on the localization methods in terms of average localization error and cumulative distribution function (CDF) of localization error. The average localization error is defined as the average Euclidean distance between the real and estimated locations of sensor nodes, and it can be computed using the following Equation (17):
(17)Averagelocalizationerror=∑i=1NLXi−xi2+Yi−yi2NL,whereXi,Yi is the real location coordinate and xi,yi is the estimated location coordinate and NL represents the number of localized node. The smaller the average localization error is, the better the localization performance is. CDF represents the distribution of average localization error. When several localization algorithms are compared, the average localization error takes a certain value, the greater the value of CDF is, and the better the localization performance is.In our simulation, we set the simulation scenario as follows: all sensor nodes are randomly deployed in a50∗50 m sensor field using a continuous uniform distribution pseudorandom generator. The ratio of anchor nodes varies from 10% to 60%, the node density, namely, the number of all sensor nodes is set to be 50, 100, 150, 200, 250, and 300. The ranging error factor for all sensor nodes varies from 0.05 to 0.25. To eliminate the effects of randomness of topology generation and bioinspired algorithm, each data point is averaged over 10 different test network and each result for a kind of network topology is averaged by running 30 times repeatedly. The parameter settings of the modified cuckoo search algorithm are as follows: αmin and αmax are set to 0.9 and 1.0, respectively, Pamin and Pamax are set to 0.05 and 0.25, respectively, Xmin and Xmax are set to 0 and 50, respectively, and the value of nest number is 25. The iteration threshold for each algorithm is 100 times.


### 5.2. Simulation Results and Evaluation

#### 5.2.1. Effects of Anchor Node Ratio

The ratio of anchor nodes has an important influence on localization performance and cost in WSN. In this subsection, the effects of anchor node ratio on localization performance are evaluated. The anchor node ratio varies from 10% to 60%. The node density is set to be 100, and ranging error factor is 0.1. Figure2 shows the average localization error versus anchor node ratio in WSN by adopting three different localization schemes. It can be clearly observed that the localization accuracy increases significantly for the proposed method and the localization technique selecting the information received from all anchors, especially when anchor ratio increases gradually from 10% to 40%. This is because that with the increasing number of anchor nodes, more available anchors participate in the localization. However, when anchor node ratio increases to a certain extent, the advantage of increasing the number of anchor nodes to improve the localization accuracy becomes less obvious. It means that in actual WSN applications, there is no need to deploy too many anchors. This will undoubtedly benefit WSN applications in terms of the energy consumption and cost. Besides that, for the localization technique selecting four nearest anchors within communication range, the average localization error does not decrease with the increase of the number of anchor nodes. The reason is that this approach only employs four nearest anchor nodes, and even when the number of anchor nodes is increased, most of increased anchor nodes do not contribute to improve the localization accuracy. What is more, the simulation results show that the proposed method can yield the smallest average localization error. This attributes to the fact that the proposed method overcomes the influences of ranging error on positioning accuracy to a certain extent.Figure 2
Effects of anchor node ratio on average localization error.It is shown in Figure3 that the CDF of three different localization schemes for a WSN with 100 sensor nodes and 20% anchor nodes. From Figure 3, it can be seen that the probability for a localization error less than 0.94 m is 100% by using the proposed algorithms. However, it is impossible for the other localization algorithms. More specifically, 100% of localization accuracy is at about 1.24 m for the localization technique selecting the information received from all anchors, and 100% of localization accuracy is at about 4.22 m for the localization technique selecting four nearest anchors within communication range. This suggests that the improvement in localization accuracy for the proposed algorithm is considerable. Figure 4 shows the CDF of different localization algorithms for a WSN with 100 sensor nodes and 30% anchor nodes. From Figure 4, we can see that as the number of anchor nodes increases, the localization accuracy is improved for the proposed algorithms and the localization technique selecting all the anchors’ information received. The conclusion is identical with Figure 2. Besides that, the probability to locate the unknown nodes with localization error less than 0.74 m is 100% for the proposed algorithm, while 100% of localization accuracy is at about 0.98 m and 4.66 m, respectively, for the localization technique selecting all the anchors’ information received and the localization technique selecting four nearest anchors within communication range. As a whole, this also proves the effectiveness of the proposed algorithm in reducing localization error from another perspective.Figure 3
CDF of average localization error for 100 sensor nodes and 20% anchor nodes.Figure 4
CDF of average localization error for 100 sensor nodes and 30% anchor nodes.


#### 5.2.2. Effects of Ranging Error Factor

The ranging error factor represents the noise level associated with the range measurement and is an important parameter affecting the localization accuracy. The number of anchor nodes is set to be 30% of all sensor nodes, and the node density is set to be 100. The ranging error factor varies from 0.05 to 0.25. Figure5 shows the effects of ranging error factor on the localization accuracy of several localization algorithms. As illustrated in Figure 5, the localization accuracy decreases as the ranging error factor increases. This is because ranging error in distance measurements grows with the ranging error factor. For the proposed method, the location error also increases with the ranging error factor, but in a slower trend. In fact, the proposed scheme outperforms especially the other two localization techniques. For the localization technique selecting four nearest anchors, the localization error is always largest among the three localization techniques under all noise levels of ranging error factor. The reason behind this is that it increases the probability to abandon some good anchor nodes which can improve the localization accuracy. Figure 6 plots the CDF of different localization algorithms when the ranging error factor is 0.05. It can be seen that for a localization error of 0.34 m (0.5 m and 2.5 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. Figure 7 plots the CDF of different localization algorithms when the ranging error factor is 0.15. Comparing the CDF in Figure 6 with the CDF in Figure 7, we can see that with the increase of ranging error factor, localization error increases for all the localization algorithms. Besides that, for a localization error of 1.12 m (1.44 m and 4.36 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. From the simulation results, we can conclude that the proposed method is superior in reducing localization error under all ranging error levels.Figure 5
Effects of ranging error factor on average localization error.Figure 6
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.05.Figure 7
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.15.


#### 5.2.3. Effects of Node Density

Node density is another important parameter impacting the localization performance and cost for WSN. Thus, in the subsection, the effects of node density on localization error in terms of average localization error are shown in Figure8. The variation of node density is from 50 to 300.The ratio of anchor nodes is set to be 30% of all the sensor nodes. The ranging error factor equals to 0.1. As depicted in Figure 8, when the node density increases from 50 to 200, the average localization error decreases evidently for the proposed method and the localization technique selecting all the anchors’ information received. This is due to the fact that as the node density increases, the number of anchors available increases too. However, when the node density continues to increase, the effects of node density on the localization accuracy are not obvious. This suggests that in practical applications, we can deploy the WSN node density according to the corresponding requirement. It is also worth noting that the average localization error of the localization technique selecting four nearest anchors increases gradually with the growth of node density. This is because that most of the increased anchors are not involved in the localization process. The results are in line with the conclusion in the Section 5.2.1. Figures 9 and 10 illustrate the CDF of three localization algorithms when the node density is 50 and 150, respectively. For a localization error of 1.16 m (1.38 m,3.82 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range when node density is 50. In addition, when node density is 150, for a localization error of 0.6 m (0.78 m and 5.12 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting the information received from all anchors, and the localization technique selecting four nearest anchors within communication range. The simulation results indicate that the proposed method can achieve the best localization performance under different node density. This further proves the validity of the proposed method.Figure 8
Effects of node density on average localization error.Figure 9
CDF of average localization error for 50 sensor nodes and 30% anchor nodes.Figure 10
CDF of average localization error for 150 sensor nodes and 30% anchor nodes.


## 5.1. Simulation Setting

In this paper, all simulation experiments are implemented in Matlab platform. To verify the effectiveness of the proposed algorithm, we compared the localization performance of the proposed method with that of the localization technique without special anchor selection scheme [19] which selects all anchors’ information received and the localization technique selecting nearest anchors within communication range [23]. For each localization technique, the localization result is estimated based on the modified cuckoo search algorithm. Extensive simulation experiments are conducted to study the effects of anchor node ratio, ranging error factor and node density on the localization methods in terms of average localization error and cumulative distribution function (CDF) of localization error. The average localization error is defined as the average Euclidean distance between the real and estimated locations of sensor nodes, and it can be computed using the following Equation (17):
(17)Averagelocalizationerror=∑i=1NLXi−xi2+Yi−yi2NL,whereXi,Yi is the real location coordinate and xi,yi is the estimated location coordinate and NL represents the number of localized node. The smaller the average localization error is, the better the localization performance is. CDF represents the distribution of average localization error. When several localization algorithms are compared, the average localization error takes a certain value, the greater the value of CDF is, and the better the localization performance is.In our simulation, we set the simulation scenario as follows: all sensor nodes are randomly deployed in a50∗50 m sensor field using a continuous uniform distribution pseudorandom generator. The ratio of anchor nodes varies from 10% to 60%, the node density, namely, the number of all sensor nodes is set to be 50, 100, 150, 200, 250, and 300. The ranging error factor for all sensor nodes varies from 0.05 to 0.25. To eliminate the effects of randomness of topology generation and bioinspired algorithm, each data point is averaged over 10 different test network and each result for a kind of network topology is averaged by running 30 times repeatedly. The parameter settings of the modified cuckoo search algorithm are as follows: αmin and αmax are set to 0.9 and 1.0, respectively, Pamin and Pamax are set to 0.05 and 0.25, respectively, Xmin and Xmax are set to 0 and 50, respectively, and the value of nest number is 25. The iteration threshold for each algorithm is 100 times.


## 5.2. Simulation Results and Evaluation

### 5.2.1. Effects of Anchor Node Ratio

The ratio of anchor nodes has an important influence on localization performance and cost in WSN. In this subsection, the effects of anchor node ratio on localization performance are evaluated. The anchor node ratio varies from 10% to 60%. The node density is set to be 100, and ranging error factor is 0.1. Figure2 shows the average localization error versus anchor node ratio in WSN by adopting three different localization schemes. It can be clearly observed that the localization accuracy increases significantly for the proposed method and the localization technique selecting the information received from all anchors, especially when anchor ratio increases gradually from 10% to 40%. This is because that with the increasing number of anchor nodes, more available anchors participate in the localization. However, when anchor node ratio increases to a certain extent, the advantage of increasing the number of anchor nodes to improve the localization accuracy becomes less obvious. It means that in actual WSN applications, there is no need to deploy too many anchors. This will undoubtedly benefit WSN applications in terms of the energy consumption and cost. Besides that, for the localization technique selecting four nearest anchors within communication range, the average localization error does not decrease with the increase of the number of anchor nodes. The reason is that this approach only employs four nearest anchor nodes, and even when the number of anchor nodes is increased, most of increased anchor nodes do not contribute to improve the localization accuracy. What is more, the simulation results show that the proposed method can yield the smallest average localization error. This attributes to the fact that the proposed method overcomes the influences of ranging error on positioning accuracy to a certain extent.Figure 2
Effects of anchor node ratio on average localization error.It is shown in Figure3 that the CDF of three different localization schemes for a WSN with 100 sensor nodes and 20% anchor nodes. From Figure 3, it can be seen that the probability for a localization error less than 0.94 m is 100% by using the proposed algorithms. However, it is impossible for the other localization algorithms. More specifically, 100% of localization accuracy is at about 1.24 m for the localization technique selecting the information received from all anchors, and 100% of localization accuracy is at about 4.22 m for the localization technique selecting four nearest anchors within communication range. This suggests that the improvement in localization accuracy for the proposed algorithm is considerable. Figure 4 shows the CDF of different localization algorithms for a WSN with 100 sensor nodes and 30% anchor nodes. From Figure 4, we can see that as the number of anchor nodes increases, the localization accuracy is improved for the proposed algorithms and the localization technique selecting all the anchors’ information received. The conclusion is identical with Figure 2. Besides that, the probability to locate the unknown nodes with localization error less than 0.74 m is 100% for the proposed algorithm, while 100% of localization accuracy is at about 0.98 m and 4.66 m, respectively, for the localization technique selecting all the anchors’ information received and the localization technique selecting four nearest anchors within communication range. As a whole, this also proves the effectiveness of the proposed algorithm in reducing localization error from another perspective.Figure 3
CDF of average localization error for 100 sensor nodes and 20% anchor nodes.Figure 4
CDF of average localization error for 100 sensor nodes and 30% anchor nodes.


### 5.2.2. Effects of Ranging Error Factor

The ranging error factor represents the noise level associated with the range measurement and is an important parameter affecting the localization accuracy. The number of anchor nodes is set to be 30% of all sensor nodes, and the node density is set to be 100. The ranging error factor varies from 0.05 to 0.25. Figure5 shows the effects of ranging error factor on the localization accuracy of several localization algorithms. As illustrated in Figure 5, the localization accuracy decreases as the ranging error factor increases. This is because ranging error in distance measurements grows with the ranging error factor. For the proposed method, the location error also increases with the ranging error factor, but in a slower trend. In fact, the proposed scheme outperforms especially the other two localization techniques. For the localization technique selecting four nearest anchors, the localization error is always largest among the three localization techniques under all noise levels of ranging error factor. The reason behind this is that it increases the probability to abandon some good anchor nodes which can improve the localization accuracy. Figure 6 plots the CDF of different localization algorithms when the ranging error factor is 0.05. It can be seen that for a localization error of 0.34 m (0.5 m and 2.5 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. Figure 7 plots the CDF of different localization algorithms when the ranging error factor is 0.15. Comparing the CDF in Figure 6 with the CDF in Figure 7, we can see that with the increase of ranging error factor, localization error increases for all the localization algorithms. Besides that, for a localization error of 1.12 m (1.44 m and 4.36 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. From the simulation results, we can conclude that the proposed method is superior in reducing localization error under all ranging error levels.Figure 5
Effects of ranging error factor on average localization error.Figure 6
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.05.Figure 7
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.15.


### 5.2.3. Effects of Node Density

Node density is another important parameter impacting the localization performance and cost for WSN. Thus, in the subsection, the effects of node density on localization error in terms of average localization error are shown in Figure8. The variation of node density is from 50 to 300.The ratio of anchor nodes is set to be 30% of all the sensor nodes. The ranging error factor equals to 0.1. As depicted in Figure 8, when the node density increases from 50 to 200, the average localization error decreases evidently for the proposed method and the localization technique selecting all the anchors’ information received. This is due to the fact that as the node density increases, the number of anchors available increases too. However, when the node density continues to increase, the effects of node density on the localization accuracy are not obvious. This suggests that in practical applications, we can deploy the WSN node density according to the corresponding requirement. It is also worth noting that the average localization error of the localization technique selecting four nearest anchors increases gradually with the growth of node density. This is because that most of the increased anchors are not involved in the localization process. The results are in line with the conclusion in the Section 5.2.1. Figures 9 and 10 illustrate the CDF of three localization algorithms when the node density is 50 and 150, respectively. For a localization error of 1.16 m (1.38 m,3.82 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range when node density is 50. In addition, when node density is 150, for a localization error of 0.6 m (0.78 m and 5.12 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting the information received from all anchors, and the localization technique selecting four nearest anchors within communication range. The simulation results indicate that the proposed method can achieve the best localization performance under different node density. This further proves the validity of the proposed method.Figure 8
Effects of node density on average localization error.Figure 9
CDF of average localization error for 50 sensor nodes and 30% anchor nodes.Figure 10
CDF of average localization error for 150 sensor nodes and 30% anchor nodes.


## 5.2.1. Effects of Anchor Node Ratio

The ratio of anchor nodes has an important influence on localization performance and cost in WSN. In this subsection, the effects of anchor node ratio on localization performance are evaluated. The anchor node ratio varies from 10% to 60%. The node density is set to be 100, and ranging error factor is 0.1. Figure2 shows the average localization error versus anchor node ratio in WSN by adopting three different localization schemes. It can be clearly observed that the localization accuracy increases significantly for the proposed method and the localization technique selecting the information received from all anchors, especially when anchor ratio increases gradually from 10% to 40%. This is because that with the increasing number of anchor nodes, more available anchors participate in the localization. However, when anchor node ratio increases to a certain extent, the advantage of increasing the number of anchor nodes to improve the localization accuracy becomes less obvious. It means that in actual WSN applications, there is no need to deploy too many anchors. This will undoubtedly benefit WSN applications in terms of the energy consumption and cost. Besides that, for the localization technique selecting four nearest anchors within communication range, the average localization error does not decrease with the increase of the number of anchor nodes. The reason is that this approach only employs four nearest anchor nodes, and even when the number of anchor nodes is increased, most of increased anchor nodes do not contribute to improve the localization accuracy. What is more, the simulation results show that the proposed method can yield the smallest average localization error. This attributes to the fact that the proposed method overcomes the influences of ranging error on positioning accuracy to a certain extent.Figure 2
Effects of anchor node ratio on average localization error.It is shown in Figure3 that the CDF of three different localization schemes for a WSN with 100 sensor nodes and 20% anchor nodes. From Figure 3, it can be seen that the probability for a localization error less than 0.94 m is 100% by using the proposed algorithms. However, it is impossible for the other localization algorithms. More specifically, 100% of localization accuracy is at about 1.24 m for the localization technique selecting the information received from all anchors, and 100% of localization accuracy is at about 4.22 m for the localization technique selecting four nearest anchors within communication range. This suggests that the improvement in localization accuracy for the proposed algorithm is considerable. Figure 4 shows the CDF of different localization algorithms for a WSN with 100 sensor nodes and 30% anchor nodes. From Figure 4, we can see that as the number of anchor nodes increases, the localization accuracy is improved for the proposed algorithms and the localization technique selecting all the anchors’ information received. The conclusion is identical with Figure 2. Besides that, the probability to locate the unknown nodes with localization error less than 0.74 m is 100% for the proposed algorithm, while 100% of localization accuracy is at about 0.98 m and 4.66 m, respectively, for the localization technique selecting all the anchors’ information received and the localization technique selecting four nearest anchors within communication range. As a whole, this also proves the effectiveness of the proposed algorithm in reducing localization error from another perspective.Figure 3
CDF of average localization error for 100 sensor nodes and 20% anchor nodes.Figure 4
CDF of average localization error for 100 sensor nodes and 30% anchor nodes.


## 5.2.2. Effects of Ranging Error Factor

The ranging error factor represents the noise level associated with the range measurement and is an important parameter affecting the localization accuracy. The number of anchor nodes is set to be 30% of all sensor nodes, and the node density is set to be 100. The ranging error factor varies from 0.05 to 0.25. Figure5 shows the effects of ranging error factor on the localization accuracy of several localization algorithms. As illustrated in Figure 5, the localization accuracy decreases as the ranging error factor increases. This is because ranging error in distance measurements grows with the ranging error factor. For the proposed method, the location error also increases with the ranging error factor, but in a slower trend. In fact, the proposed scheme outperforms especially the other two localization techniques. For the localization technique selecting four nearest anchors, the localization error is always largest among the three localization techniques under all noise levels of ranging error factor. The reason behind this is that it increases the probability to abandon some good anchor nodes which can improve the localization accuracy. Figure 6 plots the CDF of different localization algorithms when the ranging error factor is 0.05. It can be seen that for a localization error of 0.34 m (0.5 m and 2.5 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. Figure 7 plots the CDF of different localization algorithms when the ranging error factor is 0.15. Comparing the CDF in Figure 6 with the CDF in Figure 7, we can see that with the increase of ranging error factor, localization error increases for all the localization algorithms. Besides that, for a localization error of 1.12 m (1.44 m and 4.36 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range. From the simulation results, we can conclude that the proposed method is superior in reducing localization error under all ranging error levels.Figure 5
Effects of ranging error factor on average localization error.Figure 6
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.05.Figure 7
CDF of average localization error for 100 sensor nodes and 30% anchor nodes. In addition, the ranging error factor is 0.15.


## 5.2.3. Effects of Node Density

Node density is another important parameter impacting the localization performance and cost for WSN. Thus, in the subsection, the effects of node density on localization error in terms of average localization error are shown in Figure8. The variation of node density is from 50 to 300.The ratio of anchor nodes is set to be 30% of all the sensor nodes. The ranging error factor equals to 0.1. As depicted in Figure 8, when the node density increases from 50 to 200, the average localization error decreases evidently for the proposed method and the localization technique selecting all the anchors’ information received. This is due to the fact that as the node density increases, the number of anchors available increases too. However, when the node density continues to increase, the effects of node density on the localization accuracy are not obvious. This suggests that in practical applications, we can deploy the WSN node density according to the corresponding requirement. It is also worth noting that the average localization error of the localization technique selecting four nearest anchors increases gradually with the growth of node density. This is because that most of the increased anchors are not involved in the localization process. The results are in line with the conclusion in the Section 5.2.1. Figures 9 and 10 illustrate the CDF of three localization algorithms when the node density is 50 and 150, respectively. For a localization error of 1.16 m (1.38 m,3.82 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting all the anchors’ information received, and the localization technique selecting four nearest anchors within communication range when node density is 50. In addition, when node density is 150, for a localization error of 0.6 m (0.78 m and 5.12 m), the probability to estimate the locations of unknown nodes is 100% with the proposed method, the localization technique selecting the information received from all anchors, and the localization technique selecting four nearest anchors within communication range. The simulation results indicate that the proposed method can achieve the best localization performance under different node density. This further proves the validity of the proposed method.Figure 8
Effects of node density on average localization error.Figure 9
CDF of average localization error for 50 sensor nodes and 30% anchor nodes.Figure 10
CDF of average localization error for 150 sensor nodes and 30% anchor nodes.


## 6. Conclusions

In this paper, we propose a new anchor node selection strategy for improving RSS-based localization in WSN. The approach first utilizes the difference of the maximum and minimum RSS from anchors to identify whether an unknown node is a boundary node, in addition, each selected anchor node is assigned to a different weight which is determined by the size of distance measurements between the unknown node and anchors belonging to the selected anchor node set, which can reduce the influence of ranging error on localization accuracy to a certain extent. Finally, a modified cuckoo search algorithm is used to compute the coordinates of unknown nodes. Extensive simulation experiments are conducted to study the effects of anchor node ratio, ranging error factor and node density on the proposed method in terms of average localization error and cumulative distribution function (CDF) of localization error. The effectiveness of the proposed algorithm is compared with other methods, and the results show that the proposed method can perform better in improving localization accuracy. In the future, we are planning to demonstrate the proposed method in practical application scenarios.



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*Source: 2611329-2022-05-24.xml*