Rangefree localization using expected hop progress in anisotropic wireless sensor networks
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Abstract
Accurate localization of nodes is one of the key issues of wireless sensor network (WSN). A localization algorithm using expected hop progress (LAEP) has been successfully applied in isotropic wireless sensor networks. However, rangefree LAEP cannot be directly used for anisotropic WSNs because anisotropic problems limit the applicability of multihop localization. In order to solve the problem, an improved localization algorithm is proposed to reduce the localization error. In this paper, we adapt the expected hop progress to anisotropic WSNs by considering both hop count computation and anchor selection. Then, particle swarm optimization algorithm is introduced to improve the positioning accuracy. The experimental results demonstrate that our algorithm has better higher precision than do stateoftheart algorithms. Even for isotropic WSNs, our algorithm always outperforms its counterparts.
Keywords
Anisotropic wireless sensor networks Rangefree Multihop Expected hop progress Particle swarm optimizationAbbreviations
 2D
Twodimensional
 ANs
Anchor nodes
 AWSN
Anisotropic wireless sensor network
 CDF
Cumulative distribution function
 DER
Distance estimation error
 DOI
Degree of irregularity
 EHP
Expected hop progress
 GPS
Global positioning system
 LAEP
Localization algorithm using expected hop progress
 MDE
Mean distance error
 NRMSE
Normalized rootmeansquare error
 PSO
Particle swarm optimization
 UNs
Unknown nodes
 WSN
Wireless sensor network
1 Introduction
Wireless sensor networks (WSNs) are an emerging technology that has potential applications in various fields, such as healthcare, surveillance, astronomy, military and agriculture [1, 2, 3, 4]. Most of these applications require knowledge of the exact locations of the sensor nodes used to sense the data. In the absence of such information, data may not be useful for users. Therefore, the precise localization of sensors is a critical requirement in WSNs [5].
The localization issue in WSNs can be resolved by using the global positioning system (GPS) with each sensor node, but this is not favourable due to energy, cost and size issues. An efficient and better alternative is required to localize the sensor nodes. Various nonGPSbased localization algorithms have been used, which are categorized into rangebased [6, 7] and rangefree [8, 9] algorithms. Although the rangebased algorithms are more accurate than the rangefree localization algorithms, they require a very high cost. Unlike rangebased algorithms, rangefree algorithms, which rely on the network connectivity to estimate the positions of regular nodes without any extra hardware supporting, are more powerefficient and do not require additional hardware. At present, most researchers focus on isotropic WSNs. Wireless sensor networks are mostly applied to complex environments where there are obstacles and holes, in which case they are called anisotropic wireless sensor networks (AWSNs). In this case, when the line connecting two nodes passes these obstacles, the shortest paths between anchor nodes and regular nodes are likely to be curved and its length may be estimated much larger than corresponding Euclidean distance. Therefore, position estimation is inaccurate.
DVHop [10], Amorphous [11], MDSMAP [12] and APIT [13] are examples of early rangefree localization schemes that are well suited for isotropic wireless networks (i.e. where obstacles do not exist). However, the distance estimation accuracy of these methods is severely degraded in anisotropic networks, resulting in unacceptable overall localization errors. To solve this problem, a few new rangefree algorithms are proposed for tolerating erroneous distance estimates in AWSNs. The proximity distance mapping (PDM) [14] algorithm replaces the average hop distance with a proximitydistance mapping matrix in estimating the distances between nodes and anchors. Substantial topological information can be preserved by the mapping matrix. The patterndriven scheme (PDS) [15] algorithm applies various distance estimation algorithms for anchors based on their exhibited patterns. Next, the anchor supervised [16] algorithm is presented. In this approach, every anchor selects a set of reliable anchors for which distance estimates can be accurately obtained. Later, a location algorithm that uses the expected hop progress (EHP) was proposed in [17, 18]. A modified EHP approach is obtained by redefining a new cumulative distribution function (CDF) and achieves satisfactory localization results [19]. The algorithm depends not only on the communication radius of the anchors, but also on the communication radius of the internodes, which is closer to the real Euclidean distance between any two nodes. Recently, Farrukh Shahzad proposed a scheme, called DVmaxHop [20], that can achieve similar or better performance by just introducing a control parameter MaxHop in the first phase of the DVHop algorithm. However, most of these methods do not achieve better positioning accuracy or achieve better accuracy at the expense of high computational or communication overheads. Therefore, a lowcost and highprecision algorithm for anisotropic WSNs is necessary.
In this paper, we propose a novel rangefree localization algorithm based on the modified EHP and a particle swarm optimization algorithm (PSO) [21] that is tailored for anisotropic WSNs. First, we assume that the degree of irregularity (DOI) of the communication radius is equal to zero. Then, the distance from regular nodes to reliable anchors can be estimated precisely by introducing a control parameter, MaxHop. The reliable anchors are properly chosen following a new reliable anchor selection strategy. Next, we use the mathematical expectation of CDF to estimate the distances between the regular nodes and the reliable anchors. Finally, the PSO algorithm is used for localization optimization.
The organization of this paper is as follows. Section 2 presents the localization model of multihop AWSN. Then, the proposed rangefree localization algorithm and PSO algorithm are proposed in this section. The simulation results and performance evaluations are analysed in Section 3. Finally, Section 4 concludes the paper.
2 Methodology
2.1 Network model and overview

N = the total number of all nodes;

N_{a} = the number of anchor nodes (ANs);

N_{u} = the number of unknown nodes (UNs);

R = the communication range or radius of each node (m);

λ = the node density in the monitoring area;

area(k, R) = the kth node’s coverage area with the kth sensor as the centre and radius R.
In multihop AWSN localization, the goal is to estimate the locations of all UNs by using ANs and partial information of the distances between various pairs of ANs and UNs. We suppose that the ith anchor node broadcasts data packet containing its position and the jth regular node receives the data packet through multihop communication. Then, we employ the shortest path method to obtain a possible path between a source sensor and a destination sensor with the minimum number of hops. Let n_{ij} be the number of hops between the ith anchor and the jth regular node. The distance \( {\widehat{d}}_{ij} \) from the jth regular node to the ith anchor is estimated as follows [24]:
Although heuristic and analytical algorithms are proven to be sufficiently accurate in isotropic WSNs, their accuracies are not optimal in anisotropic WSNs. It is very likely that the shortest path between an anchor node and a regular node is curved in an AWSN, thereby resulting in an overestimation of the hop count between these two nodes. According to Fig. 1, the hop size between nodes A_{1} and U_{1} is six hops; however, the number of hops between them is far smaller due to obstacles. The larger the hop size estimation errors are, the greater the distance estimation errors are, and consequently, the less accurate the localization is. To solve this problem, we propose a novel localization algorithm that is based on new reliable anchor selection strategy. We introduce a parameter MaxHop in the first phase of our algorithm. The algorithm ignores the information if the hop count is greater than MaxHop. In the anisotropic network, when two nodes locate at two ends of an obstacle group, we ignore the farther anchor which will cause a detoured path, and consequently, the shortest path between two nodes will not be curved. Then, the EHP method is adopted to calculate the average hop distance. In Fig. 1, regular node U_{1} will select A_{4} and A_{3} as reliable anchors. We can use the average hop distance to make the distance calculation among regular node U_{1} and reliable anchors more precise in AWSNs. In the next section, we derive the expression for \( {\overline{h}}_s \) that is exploited later in our algorithm.
2.2 The proposed algorithm and its analysis
2.2.1 Hop distance derivation using the EHP approach
where α = x−R and f_{X}(x) is the pdf of X, which can be substituted by 1/R, because f_{X}(x) is a uniform random variable over [R,2R]. If R is fixed, it is very likely that the perhop distance increases if the number of nodes located inside Q increases. According to formula (8), \( {\overline{h}}_s \) can be derived if the node density and the transmission range are given. In this way, a more accurate average hop distance can be easily obtained in AWSNs through finite integrals.
2.2.2 Anchor selection strategy
In general, the greater the hop count between two nodes, the higher the distance estimation error in the AWSN. To solve this problem, we propose a new reliable anchor selection strategy in which a hop size threshold is set; we call this parameter MaxHop [20]. When a node receives the position of any anchor with its hop count, the algorithm ignores the information if the hop count is greater than MaxHop; consequently, the information is not propagated further. This algorithm reduces the superposition of this cumulative error, improves the positioning accuracy, and reduces the network traffic. To obtain better positioning accuracy and low overheads, the threshold MaxHop should be set as close as possible to the smallest integer value on the basis of the successful positioning of all nodes.
The size of the hop threshold MaxHop is mainly determined by the connectivity and anchor node density of the network. Its expression can be derived as follows [27]:
2.2.3 Particle swarm optimization
 1.
Initialize M particles. The particle iteration number is expressed as t. In the search space, the position and velocity are expressed as formula (11).
 2.
Select a suitable fitness function. It is used to judge the individuals in the population.
 3.
Update the velocity and position of the particle. At each iteration number (t + 1), the velocity and position of particle (a) are updated according to the following two equations:
 4.
Judge whether the termination conditions are satisfied. If the conditions are satisfied, the cycle is terminated; otherwise, step 2 and step 3 are repeated.
 5.
Select the global extremum. When the maximum number of iterations is reached, the value of gbest that is selected by the fitness function is used as the estimated coordinates of the unknown nodes.
Pseudo code of localization algorithm
3 Experimental results and discussions
Simulation parameters
Parameter  Value 

S  100 × 100 m^{2} 
N _{ a}  20 or 15:5:45 
λ  0.01:0.01:0.06 
r _{ i}  20 m 
M  50 
t _{max}  100 

Localization error

Distance error
The size of the distance error directly affects the localization error. The distance error is the difference between the actual distance and the estimated distance between the two nodes, which can be represented by the mean distance error (MDE) and the distance estimation error (DER), as defined in formula (15) and formula (16), respectively.

Localization percentage
Due to the hop threshold limit, the percentage of unknown nodes for successful positioning cannot be 100% because this would result in the absence of anchor nodes. However, the percentage of positioning nodes is an important index for evaluating the localization algorithm. The localization percentage can be expressed as follows:
3.1 Select the appropriate value of MaxHop
3.2 Comparison of MDE and NRMSE with various node densities
3.3 Influence of the number of anchor nodes and iteration times
3.4 Comparison of localization NRMSE CDFs of various localization methods
3.5 Precision analysis of the algorithms in an isotropic WSN
4 Conclusion
In this paper, a novel rangefree localization algorithm for multihop anisotropic wireless sensor networks is presented. The simulation result demonstrates that our modified algorithm has higher localization precision compared with stateoftheart algorithms. In addition, our algorithm has achieved good results in isotropic WSNs, especially in the middle of the location area. In general, whether applied with or without the PSO algorithm, our proposed algorithm always outperforms the most representative WSN localization algorithms. However, if the optimization algorithm is added, the energy consumption will increase while increasing the localization accuracy. As a future work, we plan to study the heterogeneous wireless sensor networks where all nodes’ communication ranges are different and we are also planning to study the influence of the irregular communication range in AWSN.
Notes
Acknowledgements
Not applicable.
Funding
This work is supported by National Natural Science Foundation of China (No. 61472278 and 61102125), Key project of Natural Science Foundation of Tianjin University (2017ZD13), the Research Project of Tianjin Municipal Education Commission (No. 2017KJ255).
Availability of data and materials
Not applicable.
Authors’ contributions
WW proposed the main idea and performed the simulation and manuscript writing. XW provided guidance for the algorithm design and helped revise the manuscript. All authors read and approved the final manuscript.
Authors’ information
Wu Wen received his bachelor’s degree in communication engineering from Liaoning University of Technology in 2016. He is pursuing her master’s degree in communication and information engineering at Tianjin University of Technology, China. His research interests include anisotropic wireless sensor networks, wireless sensor networks localization and performance evaluation and optimization.
Xianbin Wen received his PhD from the Northwestern Polytechnical University, Xi’an, China, in 2005. He is currently a professor with the School of Computer and Communication Engineering, Tianjin University of Technology, Tianjin, China. His research interests include image interpretation, machine learning, and information hiding.
Liming Yuan received the PhD degree in computer science and technology from Harbin Institute of Technology, China, in 2014. He is currently working as a lecturer in the School of Computer Science and Engineering at Tianjin University of Technology, China. His research interests are mainly in machine learning and image processing.
Haixia Xu received her MSc degree in applied mathematics from the Northwestern Polytechnical University, China, in 2006, and a PhD in computer science and technology from the same university in 2009. She is currently an associate professor at the School of Computer and Communication Engineering, Tianjin University of Technology, China. Her main research interests include image analysis, signal processing, and pattern recognition.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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