Localization is one of the key technologies in wireless sensor networks (WSNs), since it provides fundamental support for many locationaware protocols and applications. Constraints of cost and power consumption make it infeasible to equip each sensor node in the network with a global position system (GPS) unit, especially for largescale WSNs. A promising method to localize unknown nodes is to use several mobile anchors which are equipped with GPS units moving among unknown nodes and periodically broadcasting their current locations to help nearby unknown nodes with localization. This paper proposes a mobile anchor assisted localization algorithm based on regular hexagon (MAALRH) in twodimensional WSNs, which can cover the whole monitoring area with a boundary compensation method. Unknown nodes calculate their positions by using trilateration. We compare the MAALRH with HILBERT, CIRCLES, and SCURVES algorithms in terms of localization ratio, localization accuracy, and path length. Simulations show that the MAALRH can achieve high localization ratio and localization accuracy when the communication range is not smaller than the trajectory resolution.
Wireless sensor networks (WSNs) consist of a large number of sensor nodes deployed in a given region of interest (ROI) to fulfill tasks such as area surveillance, biological detection, home care, object tracking, and sending information to sink nodes via multihop communication [
In WSNs, determining unknown nodes’ locations is a critical task since it provides fundamental support for many locationaware protocols and applications, such as locationbased routing protocol; the location information is critical for sensor nodes to make optimal routing decisions [
The problem of localization is a process of finding location information of the unknown nodes in a given coordinate system [
Constraints of cost and power consumption make it infeasible to equip each sensor node in the network with a GPS unit, especially for largescale WSNs. A promising method to localize unknown nodes is to use several mobile anchors which are equipped with GPS units moving among unknown nodes and periodically broadcasting their current locations (beacon points) to help nearby unknown nodes with localization [
Mobile anchor assisted localization.
Generally, mobile anchor assisted localization algorithm involves three stages: (i) mobile anchor traverses the ROI while periodically broadcasting beacon packets which include their current positions; (ii) unknown nodes within the communication ranges of the mobile anchors receive the beacon packets and estimate distances to the anchors by using physical properties of communication signal when needed; and (iii) unknown nodes calculate their positions if they fall inside the overlapping communication ranges of at least three (four) noncollinear (noncoplanar) anchor nodes by using appropriate localization schemes in twodimensional (2D) (threedimensional (3D)) WSNs.
In this paper, we propose a mobile anchor assisted localization algorithm based on regular hexagon (MAALRH) with objectives of maximizing localization ratio and localization accuracy. To cover the entire ROI, we present a boundary compensation method (BCM) to ensure that the unknown nodes could fall inside the overlapping communication ranges of at least three noncollinear beacon points.
The rest of this paper is organized as follows. Section
A fundamental research issue of mobile anchor assisted localization algorithm is to design path planning scheme that mobile anchor should move along in a given ROI in order to minimize the localization error as well as the time required to localize the whole network.
Path planning schemes can be either static or dynamic. Static path planning scheme designs movement trajectory before starting execution; mobile anchor follows the predefined trajectory during the localization process. Dynamic path planning scheme designs movement trajectory dynamically or partially according to the observable environments or deployment situations and so forth.
Koutsonikolas et al. [
A large amount of dynamic path planning schemes were proposed to consider the real distribution of unknown nodes in the given ROI.
Li et al. [
Another research issue of mobile anchor assisted localization algorithm is to design localization scheme by which unknown nodes calculate their positions based on beacon points received from mobile anchors.
Ssu et al. [
Network architecture of this paper is shown in Figure
Network architecture.
Two assumptions are made.
The mobile anchor has sufficient energy for moving and broadcasting anchor packets during localization. The speed of the mobile anchor is adjustable and uniform in the process of localization.
The communication model is perfect spherical radio propagation and there exists measurement errors. The mobile anchor has identical communication range
In a twodimensional ROI, suppose that the unknown node
Unknown node calculates its coordinates by using of the trilateration. Thus, the localization error is defined as
When the measurement error
Analysis of localization error.
Note that
Since
The equality holds when
In other words, the localization error is the smallest when three anchor nodes form a regular triangle.
The problem of path planning for mobile anchor is to design movement trajectory satisfying the following properties: (i) it should pass closely to as many potential node positions as possible, aiming at localizing as many unknown nodes as possible; (ii) it should provide each unknown node with at least three (four) noncollinear (noncoplanar) anchor points in a 2D (3D) WSN to achieve unique estimation of known node’s position; (iii) it should be as short as possible to reduce the energy consumption of mobile anchors and time for localization.
The performances of mobile anchor assisted localization algorithm are influenced by the following factors.
Communication range: a larger communication range of the mobile anchor covers more unknown nodes. Thus, the unknown nodes have more choices to select appropriate anchor points to calculate their coordinates.
Movement trajectory: a well designed movement trajectory can eliminate collinearity (coplanarity) problem and make full use of the realtime information, that is, the distribution of unknown nodes, environment information, and so forth.
Broadcast interval: a shorter broadcast interval means that the mobile anchor would broadcast its location more frequently, which may bring about a better localization performance.
Path length: a longer path length means that the mobile anchor has more opportunities to broadcast its location and pass by more unknown nodes; however, it will consume more energy.
Thus, we should solve the above four problems when designing a mobile anchor assisted localization algorithm.
The general procedure of MAALRH consists of four steps, as shown in Algorithm
anchor is equal to the resolution, that is,
trajectory is depicted in Figures
denotes the sending time,
by using the RSSI technique;
triangle and if it is within the regular triangle. If so, the unknown node calculates its location by using the trilateration.
We assume that the ROI is a square. We divide the ROI into several subrectangles according to the length of the square. The communication range of mobile anchor nodes can be adjusted according to the length of subrectangles. The distance between two successive segments of the subrectangles is defined as the resolution (
An example of network segmentation.
Assume that the ROI is a square with the area of
The mobile anchor traverses the entire ROI following the regular hexagon trajectory at the speed of
Movement trajectory of MAALRH without a boundary compensation method.
A rectangular coordinate system is constructed with the origin at
Thus, for a given ROI, the total path length depends on the
Since the regular hexagon movement trajectory leaves four corners of ROI uncovered, to improve localization ratio, we present a boundary compensation method to enhance the MAALRH. In BCM, mobile anchor travels in the sensing area which is larger than the ROI, as shown in Figure
The relation of sensing area and ROI.
We choose
Movement trajectory of MAALRH with a boundary compensation method.
Thus, path length of the MAALRH with a boundary compensation method can be calculated by using
An example of the trilateration is shown in Figure
An example of the trilateration.
Hence,
Various path planning schemes have been proposed for single mobile anchor assisted localization. We choose HILBERT, CIRCLES, and SCURVES to be compared with our proposed MAALRH.
HILBERT can reduce the collinearity without significantly increasing the path length compared with SCAN and DOUBLESCAN. A
CIRCLES consists of a sequence of concentric circles centered within the ROI [
SCURVES is based on the SCAN, which progressively scans the ROI from left to right. However, SCURVES takes an “
We evaluate the localization accuracy by using average and standard deviation of localization errors of unknown nodes, which are defined as
Our simulations are performed using Matlab. Suppose that the ROI is a square. Table
Parameters used in the simulation.
ROI size  480 m × 480 m 
Communication range  60–140 m 
Resolution  60 m, 80 m, and 120 m 
Movement speed  10 m/s 
Number of unknown nodes  100–500 
We evaluate performances of five movement trajectories under three resolutions: 60 m, 80 m, and 120 m in terms of localization ratio, localization accuracy, path length, and scalability.
Figure
Localization ratio with different resolutions.
From the simulation, we can conclude that the localization ratio depends on the communication range of the sensor nodes and the resolution of the movement trajectory which determines the amount and the distance interval of the anchor points.
Figure
Average deviation with different resolutions.
Figure
Standard deviation with different resolutions.
For each of the five movement trajectories, the path length is a function of
Path length with different resolutions.
We vary the number of the unknown nodes from 100 to 500 with the step of 100, communication range of 80 m, and resolution of 80 m to test the scalability of the MAALRH_BCM. Table
Scalability of MAALRH_BCM.
100  200  300  400  500  


100%  100%  100%  100%  100% 

0.1324  0.1538  0.1454  0.1459  0.1397 

0.0237  0.0264  0.0193  0.0240  0.0204 
In this paper, we propose a mobile anchor assisted localization algorithm based on regular hexagon in twodimensional WSNs, which can cover a square ROI entirely with a boundary compensation method. Simulations indicate that compared with HILBERT, CIRCLES, and SCURVES algorithms, the MAALRH_BCM can achieve higher localization ratio and localization accuracy when the communication range is not smaller than the resolution. In summary, a carefully designed movement trajectory can significantly improve localization performances.
The future research issues in the area of mobile anchor assisted localization possibly are as follows.
In real applications, obstacleresistant mobile anchor assisted localization algorithms are needed to deal with the obstacles in a given ROI. Movement trajectories of mobile anchors should be designed dynamically or partially according to the observable environment or deployment situations to make full use of the realtime information during localization.
Single mobile anchor assisted localization algorithm takes a long time to locate all the unknown nodes in a ROI, especially for a largescale WSN. Thus, collaborative mobile anchor assisted localization algorithm which uses several mobile anchors should be specifically designed to reduce localization time and improve localization accuracy.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work is supported by the Natural Science Foundation of Jiangsu Province of China, no. BK20131137; the Applied Basic Research Program of Nantong Science and Technology Bureau, no. BK2013032; and the Guangdong University of Petrochemical Technology’s Internal Project, no. 2012RC0106. Jaime Lloret’s work has been partially supported by the “Ministerio de Ciencia e Innovacion,” through the “Plan Nacional de I+D+i 2008–2011” in the “Subprograma de Proyectos de Investigacion Fundamental,” Project TEC201127516. Joel J. P. C. Rodrigues’s work has been supported by “Instituto de Telecomunicações,” Next Generation Networks and Applications Group (NetGNA), Covilhã Delegation, by national funding from the Fundação para a Ciência e a Tecnologia (FCT) through the PestOE/EEI/LA0008/2013 Project.