Anchor node path planning for localization in wireless sensornetworks

Ketan Sabale1 • S. Mini1

Published online: 10 June 2017

� Springer Science+Business Media, LLC 2017

Abstract Localization is one of the most important chal-

lenges of wireless sensor networks because the location

information is typically used in other domains such as

coverage, deployment, routing, and target tracking. There

exist some localization algorithms that facilitate the sensor

nodes to locate itself using the mobile anchor node posi-

tion. Some crucial attempts have been made in the past for

optimizing the mobile anchor node trajectory with good

accuracy. This paper presents a novel path planning

scheme, D-connect, which ensures the localization of all

the sensor nodes with minimum trajectory length. The

performance of the proposed scheme is evaluated through a

series of simulations. Experimental results reveal that the

shortest path for traversing the whole area can be traced

with the minimum localization error using this method. It

also shows that D-connect outperforms the existing meth-

ods in terms of the anchor node trajectory length as well as

the localization error.

Keywords Sensor network � Localization � Anchor node �Path planning mechanisms

1 Introduction

Wireless sensor networks (WSNs) are composed of large

collection of sensors that may be randomly deployed in a

certain geographical region. The sensor nodes collect

environmental data and forward that data to a remote

device where the data is analyzed and processed. If the

sensors cannot pass the information to the remote device

directly, some intermediate nodes have to forward the data

[8]. Sensor networks have a wide range of application areas

such as home, environment monitoring, military surveil-

lance, animal tracking, etc. WSNs can be used in the dis-

aster relief services where human operations are difficult.

Increased accuracy and minimizing time for location esti-

mation are the important factors to be considered in

emergency services. Sensor nodes have limited power

resources, computational power, and memory availability

[1]. Coverage, deployment, tracking and localization are

some challenges in WSNs. Since the location information

is used in other domains, it is necessary to determine the

origin of the information, prior to any information pro-

cessing. Localization can be defined as estimating the exact

physical location of the sensor node in a certain geo-

graphical area. Sensors can be located with the help of the

Global Positioning System (GPS). Due to the high cost and

poor performance of GPS indoors, it becomes inefficient to

equip all sensor nodes with GPS [3]. There have been some

localization algorithms that were proposed in the past, and

are still being used to locate unknown sensors. The clas-

sification of localization algorithms along several axes is

presented in Fig. 1.

In centralized algorithms, the sensor nodes send their

data to the central processing unit where the data is ana-

lyzed and processed to extract the positional information.

The approach in which each sensor node can locate itself is

& S. Mini

mini2min2002@yahoo.co.in

Ketan Sabale

ketansabale1@gmail.com

1 Department of Computer Science and Engineering, National

Institute of Technology Goa, Farmagudi, Goa, India

123

Wireless Netw (2019) 25:49–61

https://doi.org/10.1007/s11276-017-1538-6

known as distributed localization. The main advantages of

the centralized approach is accuracy, precision and the

ability to process greater amounts of data. The disadvan-

tages of these algorithms are poor scalability and a single

point of failure. The distributed algorithms do not require a

central base station. In the distributed localization

approach, localization is done through node-to-node com-

munication. Localization which is carried out with the help

of signal properties is known as Range-based localization

[13]. The common techniques used in range-based local-

ization are Angle of Arrival (AOA), Time of Arrival

(TOA), Time Difference of Arrival (TDOA) and Received

Signal Strength Indicator (RSSI). These localization algo-

rithms are based on time and distance dependent mea-

surements. In the Angle of Arrival (AOA) method, the

location is estimated with the help of the angle at which a

signal arrives at a sensor. Distance information is obtained

in the Time of Arrival (TOA) and Time Difference of

Arrival (TDOA) methods by computing the transmission

time of the wireless signal. These approaches give better

location accuracy but use extra hardware. Received Signal

Strength Indicator (RSSI) is a measurement of the power

present in a received signal. There is no requirement of

extra hardware for estimating the distance using RSSI

technique. Estimated distance travelled by the signal up to

the receiver point is calculated with effective path loss.

Range-free techniques do not need extra hardware but

localization depends on the connectivity of the network.

Localization based on range-free techniques in which the

anchor node moves along a hexagonal pattern is discussed

in [18]. Cost-effective ways of localization with less

accuracy are provided by range-free techniques. The

methods in which a sensor node can locate itself by using

the location information of some specific nodes is known

as Anchor-based approach. The position of Anchor nodes

is predefined or can be located with the help of GPS. An

anchor node is also referred to as a Beacon or a Reference

node. Anchor-free localization does not depend on the

anchor nodes. In this approach, each node computes the

relative coordinates by measuring the distance to its

neighboring nodes by using either range-free or range-

based techniques.

Usually WSN is used in remote geographical areas

where human operations are impossible. It is infeasible to

deploy beacons at known positions. So beacon nodes must

be equipped with GPS receivers. Cost effective WSN is

dependent on the minimum number of anchor nodes used.

So the motivation behind designing the D-connect trajec-

tory is to locate all the sensor nodes with the help of a

single beacon node. The beacon node broadcasts its loca-

tion information while travelling in the region of interest.

Beacons do not broadcast constantly. Advertising Interval

describes the time between each broadcast. Stability of the

signal depends on the Advertising Interval. The signal is

more stable for shorter intervals. It is very beneficial to use

such anchor nodes for localization. The fundamental issue

is to find an optimum path for a mobile beacon trajectory in

the region of interest. Before defining any path planning

mechanism, certain properties of optimum path planning

mechanisms should be investigated. Due to the poorly

designed trajectory, some sensor nodes may not be

localized.

The existing anchor node trajectories are different from

one another in the pattern they follow. The Mobile Anchor

Centroid Localization [8] traverses the region along a spiral

path. Due to the spiral nature of the path taken by the

anchor node, sensor nodes present in the corner of the

network do not get sufficient number of beacon positions,

which leads to an increase in the localization error. [9]

presents the Hilbert curve approach that solves the local-

ization and coverage problems. In this approach the

unknown sensor estimates its position by using h keys.

Scan and Double Scan [11] minimizes the anchor node

trajectory length but increases the localization time as the

Fig. 1 Classification of

localization algorithms

50 Wireless Netw (2019) 25:49–61

123

sensor has to wait for non collinear positions for location

estimation. The Z-curve [10] follows the path in a Z pattern

while LMAT [12] follows an equilateral triangle pattern.

All these trajectories differ in terms of construction and

work, but all try to achieve the same goal. To the best of

our knowledge, no literature provides a sufficient and

optimal trajectory to solve the problems of localization and

coverage.

In this paper, we propose a path planning scheme,

D-connect, for anchor-based localization using a range-

based technique. It guarantees the localization of all

unknown sensor nodes from a certain geographical region

with minimized localization error. It uses two signals with

two different transmitted signal powers which are required

to increase the accuracy while taking care of the

collinearity issue. For maximum accuracy, the anchor node

has to travel near the boundary of the region. In D-connect,

the increased power of the signal resolves this problem. For

locating any unknown sensor accurately, at least three non-

collinear beacon signals are required. If the sensor node

receives more than three beacon node positions, at least

one non-collinear position is required to eliminate any

collinear beacon.

The rest of the paper is organized as follows: Sect. 2

summarizes the related work on different existing local-

ization algorithms and path planning mechanisms with

more clarity. Section 3 defines the problem and describes

the D-connect method. The experimental results are

reported and discussed in Sect. 4. Sect. 5 concludes the

paper.

2 Related work

There have been several research efforts on tackling

problems related to localization in WSN. The various

hierarchical architectures of WSN are presented in [2].

Most existing localization schemes for WSNs are mainly

classified into two groups, computation based and range

based. A detailed classification is provided in [3]. Dis-

tributed computation based methods are discussed in [4, 5]

and [6]. The Monte-Carlo Localization algorithm is pre-

sented in [4]. The Monte-Carlo algorithm estimates the

position of an unknown sensor by considering the near and

the farther anchor node constraints. At first, the sensor node

constructs a possible location set which denotes the pos-

sible location of the sensor. In the filtering phase the

locations which are not satisfying the anchor node con-

straints are removed and the average of the remaining

location set gives the final estimated location of the

unknown node. The efforts for increasing the efficiency of

the Monte-Carlo algorithm are done in [5]. Drawing sam-

ples is a time consuming process, so Monte-Carlo

Localization Boxed algorithm constrains the area from

which the sensor draws samples. This method is known as

Monte-Carlo Localization Boxed (MCB) algorithm. The

increased accuracy and reduced localization time can be

obtained by using relay nodes. Self Localization

Scheme using relay nodes and anchor nodes is presented in

[6]. Relay nodes are also sensor nodes which get their

positional information from the anchor node. Sensor nodes

calculate their position by the received information about

the relay node position. The various conditions for relay

node selection are discussed in [6].

The efficiency of anchor based localization algorithms is

dependent on the trajectory of the anchor node. For

defining any new beacon node trajectory certain conditions

must be satisfied by the trajectory. First of all, trajectory

should pass closely to the unknown sensor for best position

estimation. Also each sensor node should have at least

three non-collinear anchor node positions to locate itself.

[7] illustrates the conditions that are to be satisfied by the

anchor node trajectory. The various schemes to reduce the

trajectory length of the anchor node are discussed in [8–11]

and [12]. [8] presents the trajectory in a spiral form. The

position estimation of sensor nodes is done with the help of

the range-free localization technique called Centroid

algorithm. The position of each sensor is calculated by

taking the average of the total received beacon messages in

the time interval t. The length of the Spiral trajectory is

more than all other trajectories. The localization algorithm

that uses the Spiral trajectory is known as the Mobile

Anchor Centroid Localization (MACL). The trajectory

based on the Hilbert space filling curve is presented in [9].

The Hilbert space filling curve is a one-dimensional curve,

which visits every point exactly once without crossing

itself within a two or three-dimensional space. The Hilbert

curve is generated recursively. A superior path planning

mechanism called Z-curve is explained in [10]. Z-curve

handles the collinearity issue occurring in the anchor node

trajectory by using the determinant of the matrix that

contains consecutive beacon positions received by the

sensor node. The received beacon positions are said to be

non-collinear if the determinant of the matrix is non-zero.

The Z-curve trajectory is tested for an obstacle presence

scenario. Scan and Double Scan methods are explained in

[11]. The Scan method has the disadvantage of collinearity.

In the Scan method, the mobile beacon node travels along

one dimension and when it reaches the end of the network

it travels along the second dimension where the length of

the path along the second dimension is equal to the reso-

lution. The procedure is repeated till the entire network is

traversed. The Double Scan method traverses the network

along both directions. The collinearity problem of the Scan

method is resolved by the Double Scan strategy up to some

extent. But the length of the Double Scan trajectory is

Wireless Netw (2019) 25:49–61 51

123

double, compared to the Scan mehod for the same reso-

lution. The Hilbert curve method overcomes the disad-

vantages of the Scan and Double Scan methods. Since the

Hilbert curve trajectory takes more turns, it gives better

position estimation compared to the Scan and Double Scan

trajectories. As Hilbert curve connects the centers of two

successive cells in the network, it will never move along

the border of the deployment area. This is a drawback of

the Hilbert curve method. Localization with a Mobile

Anchor node based on Trilateration (LMAT) is presented

in [12]. In LMAT trajectory, an anchor node moves along

the boundaries of the region based on an equilateral tri-

angle pattern.

After designing the optimum trajectory for an anchor

node, the next main task is to estimate the physical position

of the unknown sensor nodes using anchor node positions.

For estimating the position of an unknown node various

range-free and range-based methods can be used. The

range-free and range-based techniques are discussed in

[13]. The cost effective method in range-based localization

algorithm called RSSI is presented in detail in [14] and

[15]. Distance estimation using RSSI is dependent on path

loss. Various propagation models for mobile communica-

tion are discussed in [16]. Path loss and fading are the main

characteristics of the radio channel. The RSSI calculations

are basically influenced by path loss and fading. Free space

model, Two ray ground model and Log-normal shadowing

model are the RSSI propagation models used in wireless

sensor networks. When the transmitter and receiver have a

clear unobstructed line of sight between them, the free

space propagation model is used [16]. The Two ray ground

model is considered only when there exists a single direct

path between the transmitter and the receiver for the

propagation of the radio signal. The directed path and a

ground reflected propagation between the transmitter and

the receiver is considered in two ray propagation model.

The Log-normal shadowing model is the most suitable ra-

dio propagation model as it provides a number of param-

eters for configuration for different environments (indoor

and outdoor). This study mainly focuses on the develop-

ment of optimal anchor node trajectory for localization of

unknown sensors using the Log normal shadowing model.

3 Proposed work

3.1 Problem statement

Given a geographic region R, and a single anchor node A to

locate m sensor nodes S ¼ fS1; S2; S3; :::; Smg, the objectiveis to identify the minimum length trajectory for anchor

node A, such that all unknown sensor nodes are located

with minimum localization error.

If the mobile anchor node A, is at position ðx1; y1Þ andthe sensor node Si, ð1� i�mÞ is at location ðx2; y2Þ then A

can locate sensor Si iff sensor node Si lies within the

communication range r of A. That is,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðx1 � x2Þ2 þ ðy1 � y2Þ2q

� r ð1Þ

where r is the communication range of anchor node A.

Let (X, Y) and ðxi; yiÞ represent the estimated and orig-

inal coordinates of sensor Si, respectively. Then the

localization error is calculated by,

ErrorSi ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðX � xiÞ2 þ ðY � yiÞ2q

ð2Þ

The average localization error for all unknown sensors is

calculated by,

Erroraverage ¼X

n

i¼1

ErrorSim

ð3Þ

where m denotes the total number of unknown sensors

deployed throughout the region.

3.2 Mobile beacon node trajectory

The proposed strategy, D-connect, assumes that the anchor

node can transmit different signals with different power

from predefined points to overcome the collinear beacon

problem and creates an optimum path for traversing the

region in order to reduce the localization time. As D-con-

nect trajectory is deterministic and the anchor node posi-

tions for message transmission are already known, the

anchor node can send the signal with more power from

some fixed positions.

The basic curve of the trajectory is shown in Fig. 2. The

region is divided into sub-squares based on the level. The

concept of level is used in such a way that for level n, the

region is divided into 4n sub-squares. The mobile anchor

connects the centres of the sub-squares such that it will

form D-connect trajectory. The centres of the sub-squares

are c1; c2; c3. The sub-squares are named as Sq1, Sq2 and

Sq3 respectively. The level 3 and 4 are illustrated in Figs. 3

and 4 respectively. The resolution of a trajectory is equal to

the length of the side of each sub-square. The resolution is

given by l=2n, where l is the length of the geographical

region. The D-connect anchor node trajectory construction

is divided into 3 phases:

– Phase 1: Localizability relation

– Phase 2: Communication range definition

– Phase 3: Non-collinearity checking

Localizability Relation phase mainly focuses on deriv-

ing the relation for locating unknown sensors with the help

of anchor node positions. Communication Range phase

52 Wireless Netw (2019) 25:49–61

123

defines the communication ranges for different anchor

node positions. For estimating the sensor node position, at

least three non-collinear anchor node positions are

required. The obtained positions are checked for

collinearity in Non-Collinearity Checking phase.

– Localizability relation All unknown sensors are

localizable only if:

8siði¼1;::::;nÞ9fajðj ¼ 1; 2; 3Þjðdistðaj; siÞ� r1ÞVðdistðaj; siÞ� r2g

where si denotes unknown sensors and aj denotes the

anchor node messages which have been transmitted

from three different positions. r1 and r2 are communi-

cation ranges from two different positions. distðaj; siÞ

Fig. 2 D-connect travelling

mechanism

Fig. 3 D-connect travelling

mechanism

Fig. 4 D-connect travelling

mechanism

Wireless Netw (2019) 25:49–61 53

123

indicates the distance between the unknown sensor and

the anchor node position.

– Communication range definition To locate any

unknown sensor, the first requirement is that the

unknown sensor should receive an anchor node posi-

tion. The unknown sensor can receive a beacon position

only if it is within the communication range of the

beacon node. The communication range of the beacon

node should be adjusted in such a way that all unknown

sensors are covered. Each sub-square has resolution

d. To obtain three beacon node positions, it is required

that the unknown sensor should receive the beacon

node position from the same square or from adjacent

sub-squares whichever is nearer.

The sub-squares with centres at distance d from the con-

sidered sub-square are called adjacent sub-squares. For

example, c7 and c8 in Fig. 5 are the centres of adjacent sub-

squares.

This phase defines the communication range for differ-

ent anchor positions. In Fig. 5, let s1 denote the most dis-

tant sensor from c3 which is the centroid of the neighbor

sub-square. If s1 receives beacon message from c3 then s1can receive beacon messages from all adjacent sub-squares.

According to the Pythagoras theorem, in Fig. 5,

r21 ¼ ðd2Þ2 þ ð3d

2Þ2

r1 ¼ffiffiffi

5

2

r

d:

ð4Þ

c14

c2

c4 c

6

c5

c7

c8

c9

c10

c11

c12

c1

c3

d/2s1

3d/2

r1

r2

d

2d

s2

c13

Fig. 5 Communication range definition for an anchor node

r1 is the distance between c3 and s1. From this we can say

that the unknown sensor can receive the beacon position

from an adjacent sub-square centroid only if r1 �ffiffi

52

q

d.

Sometimes the beacon positions from adjacent sub-

squares are not sufficient. To receive three beacon mes-

sages and also to complete D-connect trajectory, we need

the third beacon position from another sub-square, other

than the same sub-square and the neighboring one. Let s2be the most distant sensor from c4 which is not in the

neighboring sub-square. If s2 receives beacon message

from c4 then s2 can receive beacon messages from sub-

squares other than adjacent sub-squares. Applying

Pythagoras theorem as shown in Fig. 5,

r22 ¼ðdÞ2 þ ð2dÞ2

r2 ¼ffiffiffi

5p

d:ð5Þ

r2 is the distance between c4 and s2. From this we can say

that an unknown sensor can receive a beacon position from

a sub-square other than the adjacent sub-squares only if

r2 �ffiffiffi

5p

d. The anchor node positions with communication

range r2 are fixed as the movement and beacon positions

for message transmission are already known and the

D-connect trajectory is deterministic.

The transmitted signal power is varied as a function of

distance. The transmitted signal power for the points using

r2 communication range increases as the ratio r1 to r2increases. Thus, the transmitted signal power for the

communication range r2 is 1.41 times transmitted signal

54 Wireless Netw (2019) 25:49–61

123

power of the communication range r1. The communication

range depends on the resolution d.

– Non-Collinearity Checking As shown in Fig. 5, any

unknown sensor can use the beacon message from the

intersection of sub-squares eg. c2; c4; :::. After receiving

three beacon messages collinearity condition should be

checked to eliminate the third collinear point. The three

coordinates are collinear if they lie on the same line.

Let MAT represent a matrix formed by the coordinates of

the three received beacons ðxc1 ; yc1Þ,ðxc2 ; yc2Þ,ðxc3 ; yc3Þ frompositions c1; c2 and c3.

MAT ¼ xc2 � xc1 yc2 � yc1xc3 � xc1 yc3 � yc1

� �

ð6Þ

The three received beacons are non-collinear, when

jMAT j ¼ ðxc2 � xc1Þðyc3 � yc1Þ � ðyc2 � yc1Þðxc3 � xc1Þ 6¼ 0

ð7Þ

where jMAT j represents the determinant of matrix MAT.

The total length of the trajectory is determined by

adding the length of the segments connecting the non

adjacent sub-square centres (c1 and c2 in Fig. 5) and the

length of segments connecting the adjacent sub-square

centres (c7 and c8 in Fig. 5). The total number of segments

connecting the non-adjacent sub-squares in one-side

traversing from c1 to c7 is ð2n � 1Þ. The total number of

such one-sided traversals in the whole region is ð2n�1Þ. Thelength of an individual segment connecting two non-adja-

cent sub-squares is ðffiffiffi

2p

� dÞ. The total number of seg-

ments joining adjacent sub-squares having length equal to

resolution (d) is ð2n�1 � 1Þ.Therefore the total length of the D-connect trajectory is

given by,

DD�connect ¼ ð2n � 1Þð2n�1 �ffiffiffi

2p

� dÞ þ ðð2n�1 � 1Þ � dÞð8Þ

where DD�connect represents the total length travelled by the

D-connect strategy for level n and resolution d.

3.3 Location estimation

After receiving three non-collinear beacon positions, the

location estimation is to be done using the RSSI technique.

In a realistic channel model like log normal shadowing, the

RSSI value at a distance d from the transmitter is given by

[15],

RSSIðdÞ ¼ PTrans � PLðd0Þ � 10g log10d

d0þ Xr ð9Þ

where PTrans is the transmission power of the signal at the

source, PLðd0Þ is the path loss at a reference distance (i.e.

d0), and g is the path loss exponent. The value of the path

loss exponent increases with obstructions in the environ-

ment. The path loss exponent value lies between 2 and 6.

The random variation in RSSI is modeled as a Gaussian

random variable Xr ¼ Nð0; r2Þ. The values of g and r can

be set depending on the propagation environment.

Table 1 lists path loss exponents for various mobile

radio environments. The value for shadowing deviation rdBis different for different environment. It ranges from 4 to

12 for outdoors. For every unknown sensor, after getting

sufficient distances between unknown sensor and beacon

positions, the triangulation method is used to obtain the

possible location for the unknown sensor.

In Fig. 6, let s be the unknown sensor to be localized.

a1; a2 and a3 are the three non-collinear anchor node

positions. Let d1; d2; d3 denote the euclidean distances

between anchor node positions a1; a2 and a3 and the sensor

node. ðx1; y1Þ; ðx2; y2Þ; ðx3; y3Þ are the known anchor node

positions. The possible coordinates for sensor s can be

obtained by [6],

X ¼ ðy2 � y1Þc� ðy3 � y2Þe2ððx2 � x1Þðy3 � y2Þ � ðx3 � x2Þðy2 � y1ÞÞ

Y ¼ ðx2 � x1Þc� ðx3 � x2Þe2ððx3 � x2Þðy2 � y1Þ � ðx2 � x1Þðy3 � y2ÞÞ

Table 1 Path loss exponents for different environments [17]

Environment Path loss exponent(g)

Free space 2

Urban area cellular radio 2.7–3.5

Shadowed urban cellular radio 3–5

In building line-of-sight 1.6–1.8

Obstructed in building 4–6

Obstructed in factories 2–3

Fig. 6 Localization of a sensor node using triangulation

Wireless Netw (2019) 25:49–61 55

123

where c ¼ ðx22 � x23 þ y22 � y23 � d22 þ d23Þ and

e ¼ ðx21 � x22 þ y21 � y22 � d21 þ d22ÞLet (X, Y) and ðxi; yiÞ represent the estimated and orig-

inal coordinates of sensor Si, respectively. Based on the

calculated position, the localization error is calculated by

(2). The average localization error for all unknown sensors

is calculated by (3).

4 Results and discussion

The performance of the proposed trajectory was evalu-

ated by a series of simulations using MATLAB. The

parameters are listed in Table 2. We consider a 100 m�100

m grid for experimentation. The number of sensors to be

localized are 100 with the help of a single anchor node. The

communication range of the anchor node varies with

respect to resolution (d). The resolution depends on the

level (n). For experimental results for all trajectories except

D-connect the communication range is set to r ¼ffiffi

52

q

d.

This communication range varies with resolution. D-con-

nect uses two communication ranges r1 and r2 from

equation 4 and equation 5 respectively. The transmitted

signal power for r2 is 1.41 times r1 as the transmitted signal

power is a function of distance. Other trajectories have

transmission power equal to the transmitted signal power

for r1. Path loss exponent is taken as 3.3 for shadowed

urban cellular radio network. The standard deviation for

noise is taken from 2 to 8. Path loss PLðd0Þ at a reference

distance 1 meter is considered as 55 dB. Results are

reported as an average of 50 different instances.

The length of geographical region is considered as 100

m. The communication range depends on the resolution

and level. The resolution corresponding to specified level is

shown in Tables 3 and 4. The results for trajectory length

have been evaluated for each level. The trajectory length

for an anchor node in LMAT, SPIRAL algorithms are

calculated respectively as [12]

DLMAT ¼ 2ffiffiffi

3p � L� dL

re þ ðLþ

ffiffiffi

3p

rÞ ð10Þ

DSpiral ¼X

dLre

t¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2 þ 4r2p2t2 þ 4r2t sin 4ptp

ð11Þ

where r is the communication range and L is the length of

the geographical region.

The Scan trajectory consists of ðLd� 1Þ segments of

length L parallel to the x axis and ðLd� 1Þ segments of

length d parallel to the y axis as shown in Fig. 7.

The trajectory length for the Scan algorithm is given by,

DScan ¼L

d� 1

� �

� Lþ L

d� 1

� �

� d ð12Þ

DScan ¼L

d� 1

� �

� ðLþ dÞ ð13Þ

Basically the Double Scan trajectory doubles the dis-

tance travelled by the Scan trajectory. The Double Scan

trajectory is presented in Fig. 8. The total length for

Double Scan trajectory is given by,

DDoubleScan ¼ 2L

d� 1

� �

� ðLþ dÞ� �

þ T ð14Þ

where T is the turn taken by the anchor node when it

completes one Scan trajectory. In this case T ¼ffiffiffi

2p

� d4.

A hybrid localization approach explained in [9] uses the

Hilbert curve mechanism for the anchor node trajectory as

shown in Fig. 9. In the Hilbert curve method, the region is

divided into 4n square cells. The anchor node connects the

Table 2 Simulations parameters

Parameter Value

Network size 100 m�100 m

Unknown sensors 100

Beacon nodes 1

Path loss exponent(g) 3.3

Standard deviation 2,4,6,8

PLðd0Þ 55 dB

d0 1 m

Transmission power -28–14.1 dBm

Simulation runs 50

Table 3 Trajectory length comparison for 100 m � 100 m region

Level (n) Res.(d) LMAT Spiral Scan D-connect

2 25 514.8 1495.9 375 237.1

3 12.5 827 2611.7 787.5 532.4

4 6.25 1387.3 4100.4 1593.8 1104.4

5 3.12 2533.4 7161.5 3196.9 2238.9

6 1.56 4838.5 13345 6398.4 4503.2

Table 4 Trajectory length comparison for 100 m � 100 m region

Level (n) Res. (d) Double scan Hilbert Z-curve D-connect

2 25 758.8 375 437.1 237.1

3 12.5 1579.4 787.5 911.7 532.4

4 6.25 3189.7 1593.8 1842.3 1104.4

5 3.12 6394.9 3196.9 3693.9 2238.9

6 1.56 12797 6398.4 7392.6 4503.2

56 Wireless Netw (2019) 25:49–61

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centres of these cells by using ð4n � 1Þ lines of length

equal to the resolution d. The travelling length of the

Hilbert trajectory is given by,

DHilbert ¼ ð4n � 1Þ � d ð15Þ

The total distance travelled by the anchor node using Z-

curve trajectory is given by [10],

DZ�curve ¼ dð58� 4nÞ � 1ed þ bð3

8� 4nÞc

ffiffiffi

2p

d ð16Þ

Table 3 shows the path length comparison for LMAT,

Spiral, Scan and D-connect strategies. Table 4 compares

the path length for Double Scan, Hilbert, Z-curve and

D-connect strategies. From Tables 3 and 4, we deduce that

when the level is 2, resolution i.e. the length of the sub-

square will be 25 m. At this resolution, the path length

travelled by an anchor node using LMAT strategy is 514.8

m whereas the Spiral strategy takes 1495.9 m to complete

the trajectory. Although the Scan method gives better

results as compared to the Spiral and LMAT methods, it

still suffers from the collinearity problem for high resolu-

tion. It gives three collinear beacon points for localization.

The Double Scan strategy resolves the collinearity problem

faced by the Scan method but it also increases the path

length. The Hilbert and Z-curve methods take 375 and

437.13 m to complete their trajectories respectively.

However, they also take more path length as compared to

the D-connect trajectory.

As the level increases, the resolution decreases. At level

3, resolution will be 12.5 m. The path length taken by the

D-connect method is still less compared to all other

strategies. Small resolutions result in more path length

which is unacceptable for a 100 m� 100 m area. The Spiral

trajectory length is always more than any other trajectory.

The results over other methods show the efficiency of

D-connect in terms of the trajectory length.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100Fig. 7 Scan travelling

mechanism

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100Fig. 8 Double scan travelling

mechanism

Wireless Netw (2019) 25:49–61 57

123

In a real time environment, the resolution for a grid is

considered by the power of a transmitted signal. For high

resolution, transmission power should be more.

Given a 100 m�100 m region, with small resolution, if

the trajectory length exceeds 2000 m then it will not be an

efficient trajectory. As we have power constraints, it is

always a good choice to keep resolution high with respect

to the power of the transmitted signal. While traversing the

region, the beacon node periodically transmits a position

message packet with its coordinates. In Scan, Double Scan

and Hilbert strategies, an unknown sensor node receives

three message packets that are transmitted from three dif-

ferent beacon positions and using those positions, the

unknown sensor node calculates the position using the

centroid method. We estimate the position of the unknown

sensor in the D-connect method using the RSSI technique.

Figure 10 represents the comparison of the localization

error for the Scan, Double Scan, Hilbert, Z-curve and

D-connect strategies. The localization error depends on the

environment and reliable wireless communication devices.

In a real time environment, various multipath fading fac-

tors cause large random signal variations. We have done

simulations to calculate the localization error for the

communication range 4.93–39.53 m for regular anchor

node positions. At the same time, the communication range

for special anchor node positions varies from 6.98 m to

55.90 m.

Figure 10 shows the localization error for different

strategies for standard deviation 2. The average localiza-

tion error produced by the D-connect trajectory after 50

simulation runs for level 2 is equal to 0.8315 m. The

localization error decreases as the level increases. Similarly

when the resolution of the grid is 12.5 m, the localization

error produced by the D-connect method is 0.3307 m. The

localization error produced by the D-connect strategy is

0.0698 m when the resolution is small (d\5 m). The

localization errors for Scan, Double Scan and Hilbert tra-

jectories are more than the D-connect trajectory error for

level 2. They are 9.16, 6.7157 and 9.15 m respectively. For

Z-curve, the error is less than D-connect and all other

trajectories but the length of the Z-curve trajectory is more

than the D-connect trajectory length. Z-curve gives 0.4256

m error for level 2 and gives 0.0430 m for level 5. The

difference between the errors produced by D-connect and

Z-curve decreases as the communication range increases.

Figure 11 presents the localization error comparison for

standard deviation 4. For r ¼ 4, the error produced by

D-connect is still less than Scan, Double Scan and Hilbert

trajectories. When standard deviation of noise is equal to 4,

the localization error for D-connect trajectory is 0.6738 m

and error for Scan, Double Scan and Hilbert trajectories are

3.6264, 2.9025 and 3.6377 m respectively. The error for

Scan, Double Scan and Hilbert strategies decreases as the

level increases. The Scan, Double Scan and Hilbert

strategies have collinearity problem. For large resolution an

unknown sensor may get collinear beacon node positions

for location estimation. The value of localization error

increases if the sensor gets collinear beacon positions. The

collinearity issue is handled by increasing the level and

decreasing the communication range. When the commu-

nication range is less, the sensor may get non-collinear

beacon positions as it may receive more number of beacon

node positions.

If any of the unknown sensors get the collinear beacon

positions for location estimation, it affects the average

localization error. The performance of the Scan, Double

Scan and Z-curve increases with reduction in communi-

cation range. D-connect and Z-curve methods resolve the

problem of collinearity before position estimation. Because

of the collinearity checking done by D-connect and

Z-curve trajectories, the performance of these trajectories

is always better than the others. The trajectories considered

for evaluation performs better for small resolution than for

large resolution.

Figure 12 gives the comparison for localization error

when r ¼ 8. The performance of Scan, Double Scan,

Hilbert strategies does not depend on the standard devia-

tion of noise. These trajectories estimate the position of an

unknown sensor by taking the average of the three received

beacon positions. Techniques which use RSSI calculations

for position estimation depend on the noise produced in the

environment. The accuracy of the position estimation

depends on the quality of the signal. The quality of the

signal degrades as noise in the environment increases. The

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Fig. 9 Hilbert travelling mechanism

58 Wireless Netw (2019) 25:49–61

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performance of D-connect decreases for standard deviation

of noise equal to 8. For communication range 39.53 m, D-

connect produces 3.3336 m error which is greater than the

error produced for small values of r for the same com-

munication range. With the same conditions Z-curve pro-

duces 1.7272 m error while Scan, Double Scan and Hilbert

trajectories gives 9.3990, 6.7174, 9.3924 m respectively. If

we increase the level, the communication range decreases.

This increases the performance of all trajectories. For level

3 with communication range 19.76 m, the errors produced

by D-connect, Scan, Double Scan, Hilbert and Z-curve

methods are 1.2947, 3.6095, 2.8867, 3.6043 and 0.7779 m

respectively. The Z-curve gives better performance in

terms of minimum localization error as compared to

D-connect and all other trajectories, but the length it takes

for completing the trajectory is 911.7 m which is almost

380 m more than that taken by the D-connect method. The

error produced by the following D-connect trajectory is

about 0.50 m more than the Z-curve trajectory, but the

length of trajectory decreases by about 380 m.

Fig. 10 Level versus

localization error (r ¼ 2)

Fig. 11 Level versus

localization error (r ¼ 4)

Wireless Netw (2019) 25:49–61 59

123

D-connect trajectory is susceptible to noise like other

methods. However it consistently gives better results in

terms of localization error. Figures 10, 11 and 12 show that

D-connect performs more efficiently than all other methods

in terms of length and localization error.

A relay node can be used to propagate beacon node

positions to sensors for minimizing the trajectory length.

But D-connect achieves the same goal by varying the

transmitted signal power. Simulations are done for regular

regions that can be divided in the grid. It is necessary to

partition the region in equal parts to fix the communication

range. For irregular regions, results may differ based on

how the regions can be divided. Thus, it is challenging to

adjust the power in irregular regions with multipath,

obstacles, etc.

5 Conclusion and future work

This paper presented D-connect, a strategy that gives three

non-collinear beacon node positions for the location esti-

mation of an unknown sensor while maintaining the

shortest trajectory. This paper also provides some existing

approaches for localization that are applied to WSN. The

proposed D-connect strategy is compared with other

existing strategies. The results show that D-connect out-

performs LMAT, Spiral, Scan, Double Scan, Hilbert and

Z-curve methods in terms of the length of its trajectory.

D-connect gives better results for localization error as

compared to the Scan, Double Scan and Hilbert trajecto-

ries. The results confirm that the D-connect trajectory is

efficient in terms of length of trajectory and localization

error. D-connect follows a different approach by varying

the power of the transmitted signal and ensures that the

sensor node will receive sufficient number of beacon

positions for location estimation. D-connect also solves the

coverage problem by providing beacon information to each

and every sensor which leads to the localization of all

sensors. We plan to test the D-connect strategy on networks

with sensors in the presence of obstacles and multipaths to

study real-time performance. We also plan to improve the

energy efficiency of the scheme by designing efficient

power transmission schemes in the future.

Acknowledgements The authors would like to thank Dr. Ankit

Dubey, Assistant Professor, Department of Electronics and Commu-

nication Engineering, National Institute of Technology Goa, India for

his valuable and constructive suggestions during the development of

this research work.

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Ketan Sabale received the B.E.

degree in Computer Engineer-

ing from University of Pune,

Maharashtra, India, in 2012 and

the M.Tech. Degree in Com-

puter Science and Engineering

from National Institute of

Technology, Goa, in 2016. He is

currently pursuing the Ph.D.

degree with the Department of

Computer Science and Engi-

neering, National Institute of

Technology, Goa. His research

interests include wireless sensor

networks, mobile ad hoc net-

works, and swarm intelligence.

S. Mini received the master’s

degree in Computer and Com-

munication from Anna Univer-

sity, Chennai, India, and the

Ph.D. degree in Computer Sci-

ence from University of Hyder-

abad. She is currently an

Assistant Professor in the

Department of Computer Sci-

ence and Engineering, National

Institute of Technology, Goa.

She is the principal investigator

of a project sanctioned under the

Early Career Research Award

Scheme of Science and Engi-

neering Research Board, Department of Science and Technology,

Government of India. Her research interests include wireless sensor

networks, internet of things, swarm intelligence, and combinatorial

optimization.

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