An enhanced nonlinear iterative localization algorithm for DV_Hop with uniform calculation criterion
Introduction
Wireless sensor network (WSN) is a wireless multi-hop communication network system [1]. It is composed of a large number of sensor nodes with limited functions and battery power [2]. It has the characteristics of low cost, self-organization, and dynamic topology [3,4]. In recent years, with the rapid development of micro-electro-mechanical system, wireless communication technology, and electronic technology, the functions of sensor nodes have advanced significantly, and lead to the development of technologies such as Internet of things (IoT) and big data service [5]. In the meantime, WSN applications are further expanded, and play a vital role in industrial monitoring, environmental monitoring, military reconnaissance, disaster management and medical health.
When applying WSN, sensor nodes usually adopt random deployment, especially for large-scale networks. Hence location information of each sensor node is important and indispensable. One solution is to install a GPS or Beidou positioning module on each one to obtain their absolute location information, which is not only costly and also unpractical, as power consumption of sensor nodes would be greatly increased and the life cycle of each sensor node would be significantly shortened. Also, the performance of the positioning module will decline sharply when indoor or in a dense environment. One possible solution is to use a few sensor nodes with assembly positioning modules (called anchor nodes) and the already known information in WSN to compute the location of unknown nodes, namely node localization technology [6], which is highly feasible and widely employed by many scholars [6], [7], [8], [9], [10], [11], [12].
The existing localization algorithms can be divided into two categories: range-based and range-free. The range-based localization algorithms calculate the coordinates of unknown nodes using a multilateral positioning method after obtaining the distance or angle information between sensor nodes, but higher requirement for ranging hardware often leads to increase in cost in vulnerability to multipath fading, noise, and environmental factors. The range-free localization algorithm relies on the connectivity among sensor nodes and network topology to calculate the coordinates of unknown nodes [7]. Although the localization accuracy of range-free algorithms is lower than that of the range-based algorithm, it is low cost and simple to implement. Therefore, its practical application is more extensive, particularly for large-scale networks. It has attracted more attention from scholars to study ways to further improve their localization accuracy.
The representative range-free localization algorithms include centroid method [8], triangle inner point approximate detection method [9], bounding box method [10], multi-dimensional scaling method [11], and DV_Hop [12], etc. The first three range-free algorithms have strict requirements on the minimum number of adjacent anchor nodes for better localization accuracy [13], and the multi-dimensional scaling method has high calculation complexity [14]. The DV_Hop algorithm is one of the most popular localization algorithms, which has attracted more attention from scholars. The core principle of this algorithm is to approximate the distance from every pair of sensor node by the product of the average hop distance and the minimum hop number, therefore it is difficult to achieve accurate localization as required by some applications.
The calculation of the average hop distance has been improved for DV_Hop to reduce the estimated distance error. Guo [15] obtains the average hop distance of all anchor nodes to get the average hop distance of the whole network, and uses it to estimate the distance between sensor nodes. Liu [16] calculated the estimated distance error caused by the average hop distance of each anchor node, and use this error to correct the average hop distance of anchor nodes. Others utilized a different correction formula to obtain the estimated distance error [17], [18], [19]. Based on the estimated distance error, Mass-Sanchez [20] used a modified parameter to balance the average hop distance of the whole network. Kumar [21] added an improved term to the average hop distance of anchor nodes to calculate the average hop distance of the whole network. Another factor that affects the localization accuracy of the basic DV_Hop algorithm is the hop distance ambiguity. In other words, although the actual distance from different sensor nodes to the target node is inconsistent, the estimated distance will remain the same when the hop number is consistent. For this reason, Wu [22,23] proposed using the regular neighborhood distance to describe the proximity of adjacent sensor nodes, and Cui [24] transformed the discrete hop numbers into more accurate continuous ones. However, regular neighborhood distance is more suitable for node-intensive networks. For node sparse networks, the number of neighborhood node is small, which leads to inaccurate regular neighborhood distance. In the execution of the multilateral positioning step, the basic DV_Hop algorithm uses the least square method. Xiao [25] has pointed out that the least square method does not minimize the distance error directly, so the localization accuracy is poor. Tarrío [26] adopted the weighted least square method to improve the localization accuracy. Liu [27] has analyzed the circular positioning method, and it is iterative and needs to set the initial iteration value. If the initial iteration value is not close to the true value, the local minimum problem cannot be avoided.
The DV_Hop algorithm completes the final localization task through the sequential execution of multi-step calculations. If large error occurs at the initial step, it will inevitably lead to poor node localization accuracy. In this paper, an enhanced nonlinear iterative localization algorithm with uniform calculation criterion is proposed. The proposed algorithm improved the node localization performance in three aspects: correction for the average hop distance of anchor nodes; calculation for the average hop distance of unknown nodes; and optimization of the multilateral positioning. The main contributions of this paper are summarized as follows:
- i
In each step, the proposed algorithm adopts a uniform minimum mean square error criterion to avoid the conflict in the mathematical sense of the optimal calculation results in each step of the basic DV_Hop algorithm, and to reduce the error accumulation for the subsequent calculation.
- ii
The double weighted correction strategy for the average hop distance of anchor nodes is proposed. In the calculation for the average hop distance of anchor nodes, the double weighted correction strategy strengthens the influence of anchor nodes with smaller estimated distance error and gives them larger weight.
- iii
The calculation method for the average hop distance of the unknown nodes is designed. Under the minimum mean square error criterion, this method synthesizes influencing factors to deduce the calculation formula for the average hop distance of unknown nodes, and compares it with several typical estimation methods through simulation experiments, and then gives some suggestions for the number of surrounding anchor nodes involved in the calculation.
- iv
A nonlinear iterative optimization is used to execute the multilateral positioning process. The influence on the localization accuracy is compared and analyzed. The weight corresponding to the average per-hop distance error of each anchor node is set to further improve the localization accuracy.
The rest of this paper is organized as follows. Section 2 introduces the background of the study including the node localization problem, the basic DV_Hop algorithm, and some related work. Section 3 presents the proposed localization algorithm and its analysis. Section 4 demonstrates the large number of simulation experiments and the analysis and discussion of the localization performance. Finally, we conclude the paper in Section 5.
Section snippets
Problem description
Considering an m-dimensional WSN, m = 2 (or 3), the sensor nodes are randomly deployed in the monitoring area. There are two types of sensor nodes: anchor nodes and unknown nodes. Anchor nodes know their locations. They are in smaller number than unknown nodes, and generally account for no less than 10% of the total number of sensor nodes. To facilitate the description of node location problem easily, it is usually assumed that all sensor nodes have the same communication range, and the
Motivation
The basic DV_Hop algorithm completes the localization task through the sequential execution of multi-step calculations. If large error occurs at the initial step, it will inevitably lead to poor node localization accuracy. Hence, to improve the performance of the basic DV_Hop algorithm, it is essential to minimize the error accumulation using a uniform criterion, which should be used to evaluate the results from each step.
In the steps described in subSection 2.2, the calculation for the average
Simulation analysis and discussion
To evaluate the performance of the proposed algorithm, an in-depth comparative simulation study was carried out on the hardware platform (detailed configuration is: Windows 10 operating system, 16.0 GB memory, main frequency 3.40 GHz Intel Core i7 processor) using MATLAB R2015a simulation software. During the experiment, the improved strategy performance of the proposed algorithm at each step was analyzed separately, and the localization accuracy was compared with some typical algorithms,
Conclusions
This paper proposes an enhanced nonlinear iterative localization algorithm for DV_Hop with uniform calculation criterion. Under the uniform calculation criterion, the proposed algorithm adopts the minimum mean square criterion which can prevent the conflict of the optimal results of multi-step calculation in the mathematical sense; and the error accumulation can be reduced. The double weighted strategy is designed to obtain more accurate average hop distance of anchor nodes. The formula of the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to acknowledge the cooperation of all partners and the institutions that supported this work. The authors would also like to thank the handling associate editor and all the anonymous reviewers for their constructive comments. This work was supported in part by the National Natural Science Foundation of China [grant numbers 61973104, 61803146, 61704022, U1604151], in part by the Training Program for Young Backbone Teachers in Universities of Henan Province [grant number
Tianfei Chen was born in Henan, China in 1986. He received the B.S. degree in Automation, the M.S. and Ph.D. degrees in Control Theory and Control Engineering from Dalian Maritime University, Dalian, China, in 2008, 2010, and 2013, respectively. From 2014 to 2016, he was a Postdoctoral Researcher with Shenyang Institute of Automation, Chinese Academy of Sciences. He is currently an Associate Professor with the Key Lab of Grain Information Processing and Control, Ministry of Education, Henan
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Tianfei Chen was born in Henan, China in 1986. He received the B.S. degree in Automation, the M.S. and Ph.D. degrees in Control Theory and Control Engineering from Dalian Maritime University, Dalian, China, in 2008, 2010, and 2013, respectively. From 2014 to 2016, he was a Postdoctoral Researcher with Shenyang Institute of Automation, Chinese Academy of Sciences. He is currently an Associate Professor with the Key Lab of Grain Information Processing and Control, Ministry of Education, Henan University of Technology. His-research interests include wireless sensor networks and network simulations.
Lijun Sun received the B.S. degree from Xidian University, China, in 1989, the M.S. degree from the Hefei University of Technology, China, in 2001, and the Ph.D. degree from Northwestern Polytechnical University, China, in 2005. She is currently a Professor with the College of Information Science and Engineering, Henan University of Technology, Zhengzhou, China, where she is currently the executive director of the Key Laboratory of Grain Information Processing and Control, Ministry of Education. Her research interests include artificial intelligence, wireless sensor networks, computational intelligence, image processing, and robot application.