NONLINEAR MODELING AND ANALYSIS OF WSN NODE LOCALIZATION METHOD

International Journal of Wireless & Mobile Networks (IJWMN) Vol. 10, No. 1, February 2018
DOI: 10.5121/ijwmn.2018.10106 61
NONLINEAR MODELING AND ANALYSIS OF WSN
NODE LOCALIZATION METHOD
Xiaoyang Liu1,2
,Ya Luo1
, Chao Liu1
,Hengyang Liu1
1
School of Computer Science and Engineering, Chongqing University of Technology,
Chongqing, 400054, China
2
College of Engineering, The University of Alabama, Tuscaloosa, Alabama,35401,USA
Correspondence author: Ya Luo; E-mail:158010342@qq.com
ABSTRACT
In this paper, node localization algorithms in wireless sensor networks are researched, the traditional
algorithms are studied, and some meaningful results are obtained. For the localization algorithm and route
planning of WSN exists a big localization error in wireless communication. WSN communication system is
researched. According to the anchor nodes and unknown nodes, a new localization algorithm and route
planning method of WSN are proposed in this paper. At the same time, a new genetic algorithm of route
planning of WSN is proposed. The performance of the node density and localization error is simulated and
analyzed. The simulation results show that the performance of proposed WSN localization algorithm and
route planning method are better than the traditional algorithms.
KEYWORDS
wireless sensor network;anchor node; localization algorithm; route planning
1. INTRODUCTION
So far, in the process of studying and developing of wireless sensor networks(WSN), security has
been concentrated less. As a new network,the wireless sensor network is a multi-discipline,
highlyintersecting researched hot field, which is of both military and business values.Topology
control is one of the most fundamental problems in wireless sensor networks.[1-2]
. WSN,which are
the newest technology of information collecting and processing, have a wide range of application
including military and business. But the node localization information has a key role in the
application of wireless sensor network.Research of the wireless sensor network gradually gets the
focus from the industrial and academe[3-4]. It has a great application future in the military and
civil area. Reducing power consumption to extend network lifetime is one of the most important
challenges in designing wireless sensor networks. In order to improve the positioning accuracy of
wireless sensor networks, references [5-7] proposed a localization algorithm DAC-ND based on
aggregation, collinearity and connectivity of anchors. The relationship between the positioning
accuracy and the distribution of anchors were studied. The experimental shows that the anchor
nodes in collinear or concentration distribution can lead to poor positionig accuracy for WSN
localization algorithms based on distance measurement. References [8-15] prolonged network
lifetime, good scalability and proper load balancing are important requirements for many sensor

62
network applications. Clustering sensor nodes is an effective technique for achieving these goals.
Clustering Algorithm based on Node Correlation (CANC) is proposed.CANC utilizes received
signal strength, residual energy and connectivity to choose cluster-heads. It takes the node
correlation into account to determine cluster members. Analysis and simulation results show
preliminarily that, the new CANC algorithm can make cluster-heads well distributed and achieve
good performance in terms of system lifetime, scalability and LBF (load balancing factor).
Classi`c clustering algorithms in wireless sensor networks are studied ,which are fixed operation
periods and too much information exchanged in cluster-heads selection. Then an Energy-Efficient
Clustering Algorithm (EECA) is proposed, whose kernels are adaptive operation period model
and a new cluster-heads selection method[16-18]
. Simulation results show that the proposed
protocol can adjust operation period adaptively and reduce the information exchanging in
choosing cluster-heads, is more energy-efficient and suitable for wireless sensor network. A new
localization algorithm and route planning for use in wireless sensor network are studied in
References[19-20].References[21-22]presents the analytic and simulation results of the
performance of UWB relative localization estimation in wireless sensor networks. References
[23-24]propose resolving schemes of data collection in wireless sensor networks of both plane
model and linear and nonlinear mathematics model,and proposed a new node route planning
method.
The main contributions of this paper are listed as follows.(1) A new WSN node localization
algorithm is proposed to reduce the localization error and and the number of anchor nodes.(2) A
new genetic algorithm of route planning of WSN is proposed Some novel synchronization results
are proposed.These results are more practical.(3) The novel route planning method is proposed
for prolonging network lifetime and obtaining shortest path in WSN.
The rest of this paper is organized as follows. In Section 2,the wireless sensor network system
model node route planning is researched. In Section 3,the localization algorithm and route
planning is built up for the wireless sensor network communication system. In Section
4,simulation results are presented.Finally,conclusions are drawn in Section 5.
II. TRADITIONAL WSN NODE ROUTE PLANNING
Wireless sensor network network includes an anchor nodes and unknown nodes. It can be
implemented with a laser or microwave communication between them.It is a challenging problem
about the localization algorithm. The traditional localization algorithm of SCAN[25-26]
for
wireless sensor network can be described as follows:
The beacon node’s position can be noted as 1 1( , )x y ,A is the unknown node, the position is
( , )x y ,We suppose 1d=AB ,so we can get:
The traditional localization algorithm of CIRCLES[27-28]
for wireless sensor network [20-21]
is noted
as follows.The relationship of multilateral localization of the unknown node is shown in Fig.1.

63
p
1p
2p
3p
4p
X
Y
Z
Fig.1. Multilateral localization of the unknown node
There are two beacon nodes in the wireless sensor network system. The position of beacon node
C 2 2 2( , , )x y z , 2AC d= , the mathematics model can be denoted as[28-29].
There are three beacon nodes in the wireless sensor network system, the mathematics model can
be expressed as
The distance of anchor nodes can be calculated as follows:
III. WSN NODE LOCALIZATION ALGORITHM
For wireless sensor network node localization, due to the Localization of the mobile node insert
uncertain nodes, so the inserted into the virtual anchor nodes, which helps to limit the

64
localization error. The node system model is shown in Fig.2.
( , )x y
1 1( , )x y
2 2( , )x y
3 3( , )x y
Anchor node
Unknown node
Fig.2. The node system model
The node movement route plan are obtained.So we can get:
0
0
cos(2 )
sin(2 )
x x r t t
y y r t t
π ϕ
π ϕ
= + × × +

= + × × +
(6)
Similarly,in the triangle ,we can get:
21
2
0
2
1
2
2 )4/(
cos
dd
ddd −+
=θ (7)
Combined with formula (6) and (7),d0 can be expressed as:
2
22 2
2
2
3
2
1
0
ddd
d
−+
= (8)
The total path length can be expressed as
20
2 2 2 2 2 2
t=1
4 4 sin(4 ) 4 cos(4 )D r r t r t t r t tπ π π= + + +∑ (9)
Node relative positioning and the radial error can be expressed respectively:
( ) ( ) ( )
2 2 2' ' '
1
100%
n
i i i i i i
i
avg
x x y y z z
error
n R
=
− + − + −
= ×
×
∑
(10)
%100
)(
1
'
×
×
−
=
∑=
Rn
xxabs
error
n
i
ii
x
(11)

65
IV. WSN NODE ROUTE PLANNING
In WSN, the uneven distribution of nodes and the different amount of perception data will lead to
the imbalance of energy consumption and hotspot problem.To solve this key problem of WSN,a
route planning algorithm of mobile WSN sink node is proposed to prolong network lifetime and
travel shorter route in wireless sensor networks. By defining the grids in the network area, several
candidate sites of mobile sink are distributed in each grid, and then sink node select a site for
sojourning and collecting data of nodes in each grid. Based on the relationship between network
lifetime and the selection of sink sites, the network model is proposed in Fig.3.
Network grid
Sink Station Node of high amount data
Node of low amount data
Fig.3. The network model
As can be seen from Fig.4.The monitoring area is divided into multiple same grid size. The
length of grid is L ( L R< , R is the communication radius of WSN). Wireless sensor nodes
( n ) are distributed randomly in the monitoring area. gridV denotes the grid set. nodeV is the sensor
node set. According to the actual circumstance of the network. Sink station nodes ( m ) are
distributed in each grid. siteV m G= × and sel siteV G− = .
The sensor nodes to send data to a node of one hop routing is considered. The energy
consumption of node i send 1 bit data to the sink node is as follows:
( )
( )
2
0
4
0
,
,
else fs i MS i ms
i
else mp i MS i ms
f E d d d
E
f E d d d
ε
ε
→ →
→ →
 × + <
= 
× + ≥
(12)
Where, f is the sensor node data transmission rate.
The network life cycle netT can be defined by Network began to run into any one node energy
exhausted by the time. survival time of network nodei can be expressed as

66
, 1,2, ,
i i
e data
i i
i i
S S
T t i n
E t f
  
= = = 
  
K (13)
Where, i
eS is residual energy of node i . i
dataS is the sense data
volume of node i . it is the consuming time by accessing sink nodes.
Based on the above analysis. Purpose is to maximize the network life cycle, and to minimize sink
moving path length.
The optimization model can be formulated as
( )max min /
node
i TSP
i V
T d
∈
(14)
( )2
. . i
i i else fs i MS es t T t E d S iε →× + ≤ ∀ (15)
i
i dataft S i= ∀ (16)
0, 0, 1,2,i i MST d i n→> ≥ = K (17)
Where, formula (14) is the ratio of min
node
i
i V
T
∈
(maximize the network lifetime) and TSPd (The only site
selection in each grid node traversal path length in their wake).Constraint formula (15) ensures
that each sensor node in the network life cycle energy consumption is less than the initial energy
of data transmission. Constraint formula (16) ensure that each sensor node in the mobile sink to
access data transmission time is equal to the volume of the data of perception. Constraint formula
(17) ensures the network life cycle and the distance of the sensor nodes to the mobile sink node is
not negative.
3 1 6 4 5 2
1 00 1 1 00 1
Network grid
Sink node
Combination
0
1
1
1
0
1
1
6
0
1
1
4
0
1
1
5
0
1
1
2
0
1
1
3
Gene
Sub-chain 1
Sub-chain 2
Chromosome
Fig.4. The relationship between the sub-chain and the chromosome
The optimization model can be solved by the following steps:
Step 1: Initialization
Initializes a double-stranded chromosomes,the number of chromosomes is C .The number of
iterations g is equal to 0.Chromosome operands 0c = , 1 2a a= .

67
Step 2: Chromosome assessment
Calculate all the fitness of chromosomes, those have biggest fitness will be selected to the next
generation of populations.
Step 3: Selection
According to the roulette strategy, select two chromosomes which need to cross.
Step 4: Cross
Generate a random number between0 1 .If it is greater than the value of 1a .Crossover operation
was carried out on the selected two chromosomes. Crossover operation is used by using partial
matches the crossover. First randomly generated two intersections, definition of these two areas
as the matching area. And the exchange of two elder matching area.As can be seen from Fig.9.
0
1
1
1
0
1
1
6
0
1
1
4
0
1
1
5
0
1
1
2
0
1
1
3
0
1
1
3
1
0
1
1
1
0
0
5
0
1
1
2
0
1
1
4
1
0
1
6
0
1
1
1
0
1
1
1
0
1
1
5
0
1
1
5
0
1
1
2
0
0
1
3
0
1
1
3
0
0
1
6
1
1
0
4
0
1
1
2
0
1
1
2
0
1
0
6
Elder A
Elder B
TEMP A
TEMP B
Fig. 5. The exchange of parental matching regions
The TEMP A,TEMP B of matching area in digital duplication. According to match the location
of the area one by one to replace.Matching relationship is{ }3 2,1 4↔ ↔ .Generation individual A
and B.
Step 5: Mutation
Generate a random number between0 1 .If it is greater than the value of 1a .Crossover operation
was carried out on the selected two chromosomes.Randomly generated two variants. Exchange of
chromosome two variants of genes, Variation of pair to sub-chain 2(sink station chain) a
corresponding value for a variable.
Step 6: Return (End)
1c c= + ,if 1c C< − , skip to step 3.Otherwise 1g g= + and 0m = .If maxg g< , return to step 2.
Otherwise, double chain of genetic algorithm is termination. Obtain largest fitness of
chromosomes. The chromosome decoding available mobile sink node traverses the entire optimal

68
path grid to collect data.
The congestion prediction of WSN is defined as:
1 1
2 2
j j jfc α β= ⋅ + (18)
Where, jα is cache utilization of the node j , jβ is the congestion factor of the node j . /j jl Lβ = . L
indicates the total number of links in the current network.
Node forwarding goodness is defined as:
( )
2
1
1 j
j
j
fc
fs
e
ε−
−
=
−
(19)
Where, jε denotes the minimum number of hops from the node to the target node.
In order to evaluate the quality of the path calculated by the multipath routing algorithm, the path
fitness function from the source node s to the destination node d is defined based on the
parameters defined as follows:
( ) ( ),
1
/
n
s d ij ij
j
fitness i fcµ ε
=
= ⋅∑ (20)
Subject to:
{ } ( )
( )
, 1, 2,... ..., ,
0,1 1,2,...,ij
s i i ij d path s d i
j nµ
 ∈ →

= =
(21)
V. SIMULATION ANALYSIS
A. Main parameters setting
Main simulation parameters setting of WSN node localization and route planning are shown in
Table 1.
Table 1. Main simulation parameters setting

69
B.Simulation results analysis
To verify the convergence of the proposed algorithm, the largest fitness value and the average
fitness is simulated and calculated. Its convergence speed, the optimization results are shown in
Fig.6.
Fig.6. The convergence of proposed algorithm
As can be seen from Fig.8,the proposed algorithm has good convergence by comparing the
optimal solution and the average solution.
In order to compare network life cycle performance of the proposed algorithm and the traditional
algorithms(MS-LEACH-RN algorithm and LEACH algorithm).Sensor
nodes(50,100,150,100,250,300) are distributed randomly in the area of WSN.
Fig.7. Network lifetime
As shown in Fig.7, the proposed algorithm of the network life cycle is 1~2 times the traditional
algorithm of MS-LEACH-RN, it is 8 times of the LEACH algorithm. It is proved that the
proposed algorithm can extend the network survival time considering the 150 nodes to be
mounted on the random uniform topology. The relation between node radius and localization
error is shown in Fig.8.
0 100 200 300 400 500 600 700 800 900 1000
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
Evolution generations
Fitnessvalue
Max fitness value
Average fitness value
50 100 150 200 250 300
0
100
200
300
400
500
600
700
800
900
The number of sensor nodes
Networklifecycle(rounds)
Proposed
MS-LEACH-RN
LEACH

70
Fig.8. Relation between node density and localization error
As can be seen from Fig.8.It shows different changing tendency along with different localization
error.In all,the proposed algorithm is better than the traditional SCAN and CIRCLES methods.
When the number of nodes n is equal 50.The relation between average localization error and
ranging radius is shown in Fig.9.
Fig.9. The average localization error under different ranging radius
In Fig.9.The ranging radius is increased from 30 to 70.The average localization error of the
algorithms with the increase of ranging radius is becoming less.Compared with traditional
methods(SCAN and CIRCL), the proposed node localization algorithm was 21.5 % and 11.6%
decreased, respectively.
VI. SUMMARY
Based on the analysis of the wireless sensor network,some conclusions are obtained.First of all,
the wireless sensor network communication system is set up.Then,localization algorithm and
node route planning of wireless sensor network are proposed. Some mathematics model is built
according to the wireless sensor network communication system, a new genetic algorithm of
route planning of WSN is proposed.Last,WSN node localization algorithm and route planning
method are simulated. The performance of the proposed localization algorithm and route
planning method is better than the traditional methods.
2 4 6 8 10 12 14 16 18 20
0.8
1
1.2
1.4
1.6
1.8
2
Node density
Locationerror(m)
Proposed algorithm
Traditional SCAN
Traditional CIRCLES
30 35 40 45 50 55 60 65 70
0
1
2
3
4
5
6
7
8
Ranging Radius(m)
AverageLocalizationError(s)
Proposed algorithm
Traditional SCAN
Traditional CIRCL

71
Though this work is targeted at the node localization of WSN, the methods presented here could
be applied for other applications such as the localization of nodes through Internet of Things
(IOT) and Internet of Vehicles (IOV).
In the future,we intend to study the spatial localization of nodes in WSN, which is an active area
of research,with many applications in sensing from distributed systems,such as micro aerial
vehicles, smart dust sensors, and mobile robotics.
ACKNOWLEDGEMENT
The paper was supported by science and technology research program of chongqing municipal
education commission(kj1600923,kj17092060),young fund project of humanities and social
sciences research of ministry of education of china (16yjc860010),national social science fund of
china west project(17xxw004),social science of humanity of chongqing municipal education
commission(17skg144),natural science foundation of china (61571069,61501065,61502064,6150
3052).2017 annual open project of chongqing university network public opinion and ideological
dynamic research center of consultation (kfjj2017024).the author xiaoyang liu thanks for the
financial support from csc(china scholarship council)(no.201608505142).
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