Research Journal of Applied Sciences, Engineering and Technology 4(21): 4258-4264, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: December 20, 2011
Accepted: April 23, 2012
Published: November 01, 2012
Concentric Triple-Hop of Node Communication Range Location Discovery
Mantian Xiang, Chengzhi Long and Guicai Yu
Nanchang University, Nanchang, JiangXi 330047 China
Abstract: In order to locate the geographic positions of random distributed nodes in wireless sensor networks
more efficiently, a new localization algorithm C3HR (concentric triple-hop of node communication range) is
proposed in this study. C3HR aggressively extracts both positive and negative geographic constraints from the
wireless link layer. The algorithm then simultaneously sets up and solves these constraints to determine node
locations with the aid of a small number of anchor nodes. The result of analysis and simulation shows that the
proposed C3HR algorithm can optimize the constraints on nodes’ positions prominently, increase the estimation
accuracy and localization coverage significantly with sparse and non-uniform anchor distribution, decrease the
energy consumption of sensor nodes accordingly.
Keywords: Constraint optimization, localization, triple-hop cincture, wireless sensor network
INTRODUCTION
In Wireless Sensor Network (WSN) (Simic and
Sastry, 2002; Doherty et al., 2001; Vivekanandan and
Wong, 2006; Stupp and Sidi, 2004), the data that nodes
collect, receive or send would have real application value,
only when we can known the positional information of
every sensor node, in the most case. The aim of
localization is to evaluate the position of the rest other
nodes (called as unknown nodes) in the network,
according to some of nodes whose position are known
Whitehouse (2002) and Galstyan et al. (2004). In recent
years many localization algorithm and mechanism for
wireless sensor network were developed, which usually
used two kinds of network scenes: continuous and
discrete models (Wang et al., 2004; Xiang et al., 2007).
The discrete model is convenient to regulate modeling
and statistical analysis, reduce the algorithm complexity
(Savarese et al., 2002; Pathirana et al., 2005). Reference
(Simic and Sastry, 2002) introduced Bounding Box
algorithm (B-Box in short), which located unknown nodes
within the anchor nodes communication range in the
discrete network, approached these nodes real position
therefore. However, B-Box localization accuracy and
algorithm coverage are not high, which has very strict
requirement for anchor nodes distribution and density.
Furthermore, B-Box stability is not high because it is
easily influenced by the error propagation and noise
(Patwari and Hero, 2003; Liu and Wu, 2005). Other
similar methods can not improve accuracy and coverage
effectively and thoroughly, so it is necessary to study how
to solve the two problems.
CAB (Concentric Anchor-Beacons) localization
algorithm proposed concepts of ring, each anchor emits
beacon signals at different power levels, therefore
improved the location accuracy immediately
(Vivekanandan and Wong, 2006). In this study, we put
forward the concept of communication cincture in the
discrete network, reduce the amount of anchor nodes
which constraint the nodes location to their three hops
communication range and then propose a distributed
C3HR (concentric triple-hop of node communication
range) localization algorithm for wireless sensor
networks. Compared with traditional Bounding Box
algorithm, simulation results show that C3HR algorithm
effectively avoid the inherent limitations of Bounding
Box algorithm, improves the location accuracy and
algorithm coverage, reduces the network power
consumption.
In this study, we proposed the C3HR localization
algorithm for wireless sensor networks, which enables
nodes that are multiple hops away from anchors to
determine their position with high accuracy. C3HR is a
distributed range-free approach and do not require
information exchange between neighboring sensors. It has
a low computation overhead and is simple to implement.
C3HR uses anchors that broadcast beacon signals at
varying power levels consecutively and periodically. This
allows each sensor node to identify which concentric
cincture, centered at the anchor, the node resides in.
METHODOLOGY
Network model: As shown in Fig. 1, in the square
network area Q, it randomly distributes N nodes,
including K anchors. Assuming n is a even number, we
discompose Q to (n+1)2 square cells, Q = [!n/2, n/2]×
[!n/2, n/2]. The location of each node is represented by
the coordinate (i, j) of the unit division which it is located
in. Three kinds of beacon signal emitted by anchor nodes
Corresponding Author: Mantian Xiang, Nanchang University, Nanchang, JiangXi 330047 China
4258
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
There are several ways of generating nodes with
known positions. One is to equip a certain number of
nodes with GPS. Another is to a priori place a certain
number of anchors whose positions are known. They can
be equipped with some relatively sophisticated device
capable of localizing objects which lie at a distance within
the radio range of the anchor. Then, for the node lies
within the radio range from the anchor, its position will be
known to that anchor and can be communicated to the
node.
This study does not consider boundary effect and just
n
−ρ
discusses the unknown nodes within area Qρ = C(20,0) which
Fig. 1: C3HR network model
are D, 2 D, 3 D respectively and i, j, D are integer, !n/2#i,
j#n/2, 0<D#n/8. The corresponding communication range
of one hop, two hop, three hop for a node is a square area
centered it and the side length is 2D+1, 4D+1, 6D+1,
respectively.
Definition 1: Assuming node S’s coordinate is (x, y), its
communication cincture of one hop, two hop, three hop
respectively is:
CS = [ x − ρ , x + ρ ] × [ y − ρ , y + ρ ] − ( x , y )
ρ
[
]
[ x − ρ, x + ρ] × [ y − ρ, y + ρ] = C
CS2 ρ − ρ = x − 2 ρ, x + 2 ρ × [ y − 2 ρ , y + 2 ρ ] −
C
3ρ − 2 ρ
S
[
] [
]
− [ x − 2 ρ, x + 2 ρ] × [ y − 2 ρ, y + 2 ρ ] = C
2ρ
S
− CSρ
is far apart from Q boundary at least D and (0, 0) is the
original point. Assuming an unknown node S receives
three kind beacon signals from different anchor nodes,
respectively m1, m2, m3 and these signals’ emitting anchor
node S11, …, S1m1 , S21, …, S2m2 , S31, …, S3m3 constitute
linear constraints to S’s position. If m1 m2 and m3 are not
zero simultaneously, the anchor nodes which constraint
S’s position are all within CS3ρ . Otherwise, we need to
consider the constraints from all anchor nodes within Q
and such kind of evaluated area is usually very large, we
can conclude that this node is too sparse with anchor
nodes around to locate. Set IS1, IS2, IS3 represents the
communication range intersection of anchor nodes within
S’s one hop, two hop, three hop cincture range,
respectively:
⎧ m1 ρ
⎪⎪ I C m1 ≠ 0
I S1 = ⎨ i = 1 S1i
⎪
m1 = 0
⎪⎩ Qρ
= x − 3ρ, x + 3ρ × y − 3ρ, y + 3ρ
3ρ
S
− CS2 ρ
⎧ m2 2 ρ − ρ
⎪⎪ I CS
I S 2 = ⎨ j =1 2 j
⎪
⎪⎩ Qρ
In Fig. 1, S1, S2, S3 is anchor node which locates
within S’s one hop, two hop, three hop communication
cincture, respectively.
C3HR algorithm: In this section, we begin with a
discussion of the motivations and assumptions. It is
followed by the description of the C3HR localization
algorithm. We then discuss the advantages and limitations
of our proposed scheme.
C3HR algorithm principle: Each anchor broadcasts
three kinds of beacon signals, carries information
including the anchor’s position, its power level and the
estimated maximum distance the anchor can travel. Nodes
listen and record which anchors they can hear from and at
which power levels. From the information received by
each anchor heard, nodes determine which cincture they
are located within each anchor. Each node uses the
approximated center of intersection of the cinctures as its
position estimate.
m2 ≠ 0
m2 = 0
⎧ m3 3ρ − 2 ρ
⎪⎪ I C
m3 ≠ 0
I S 3 = ⎨ k =1 S 3 k
⎪
m3 = 0
⎪⎩ Qρ
Assume AS represents S’s all possible position sets, then:
⎧ Qρ I I S1I I S 2 I I S 3 m1 + m2 + m3 ≠ 0
⎪
⎪
⎛ K
⎞
AS = ⎨
3ρ ⎟
⎜
m1 + m2 + m3 = 0
⎪ Qρ I ⎜ U CSi ⎟
⎪⎩
⎝ i =1
⎠
Location performance analysis: AS is a random variable
with value between 1 and n2. In the remainder of this
section we address the following questions:
4259
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
C
C
What is the expectation of AS?
What is the probability that AS = 1 cell, i.e., that the
position estimate is perfect?
P ( i1 , i2 ) ,[ j1 , j2 ]
(
= Pr λij = 1||i1ρ < i < i2 ρ , j1ρ ≤ j ≤ j2 ρ
)
i= m∞, j= ± ∞
is, respectively corresponding to QD’s left, right, top,
lower boundary. Obviously P(", $) is symmetric with
P($, ").
Because the overlap of cinctures is multiple irregular
rectangular area which are not necessary adjacent, it is
difficult for C3HR algorithm to express the area AS
explicitly which is evaluated by node S and judge the
accuracy of the position estimation according to the
contained number of cell X = | AS |. The less X is, the less
possible position where unknown node exist in is, then the
lower the uncertainty of the location estimation is. For
easy to analysis and expression, assuming that we had
made the unknown node S locate in origin according to
Definition 4: The probability of a node exists outside of
3ρ
both CS3ρ and C( i. j ) at the same time:
χ = 1− 2 p +
{
}
{
}
max (6ρ + 1 − i ),0 .max (6ρ + 1 − j ),0
(n + 1)2
coordinate transformation. The probability p = (6ρ + 1)2 is that
And next we observe the probability that the cell
(i, j),AS located inside QD:
any node locates within the three hop range of one node
in the network and then we have the symbol definition
below.
C
2
(n + 1)
anchor nodes are located outside the range of
3ρ
both CS3ρ and C( i. j ) at the same time:
Definition 2: Indicator function:
⎧⎪ 1 (i , j ) ∈ AS
λij = ⎨
⎩⎪ 0 (i , j ) ∉ AS
P (6, ∞ ), = P , (6, ∞ ) = P ( − ∞ ,− 6) = P , ( − ∞ ,− 6)
= (1 − 2 p) = χ K
, − n / 2 ≤ i, j ≤ n / 2
K
C
Definition 3: Probability function:
C
As ( i , j ) ∈ Qρ I ⎛⎜⎝ CS6ρ ⎞⎟⎠ , for (i, j), AS, it requires all
As (i, j), CS6ρ , for different area, the probability
function in every cincture is different:
{
}
{
}, ⎤⎥ (1 − p) K − m
⎥
⎡ (6ρ + 1 − i )(6ρ + 1 − j ) − 2 max (5ρ + 1 − i ),0 .min (5ρ + 1 − j ), (4 ρ + 1)
∑ CKm3 ⎢⎢
(n + 1)2
m3 = 1
⎣
K
P (4,6],[ 0,6] = χ K +
{
C
P (2,4],[ 0,4] = χ K +
K
∑
m3 + m2
C
P (0,2],[ 0,2] = χ K
}
m3
3
⎦
{
} ⎤⎥
⎧
⎡ (4 ρ + 1 − i )(4 ρ + 1 − j ) − 2 max (3ρ + 1 − i ),0 . min (3ρ + 1 − j ), (2 ρ + 1)
⎪ m3 ( m3 + m2 ) !
CK
(1 − p) K − m3 − m2 ⎢⎢
m3 + m2 ⎪
m3 !. m2 !
(n + 1)2
⎪
⎣
⎨
∑
m3
= 1 m2 = 0 ⎪ ⎡ (6ρ + 1 − i )( 6ρ + 1 − j ) − 2(5ρ + 1 − i ) min (5ρ + 1 − j ), ( 4 ρ + 1) + ( 4 ρ + 1 − i )( 4 ρ + 1 − j ) ⎤
⎪• ⎢
⎥
⎪ ⎢
⎥
(n + 1)2
⎦
⎩ ⎣
{
m2
⎥
⎦
}
⎫
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎭
m
⎫
⎧
⎡
⎤ 1
⎪
⎪ C m3 + m2 + m1 (m3 + m2 + m1 )! (1 − p) K − m3 − m2 − m1 ⎢ ( 2 ρ + 1 − i )( 2 ρ + 1 − j ) ⎥
K
2
⎪
⎪
m3 !⋅ m2 !⋅ m1 !
( n + 1)
⎢⎣
⎥⎦
⎪
⎪
m2
⎪
m1 + m2 + m3 m1 + m2 ⎪ ⎡
⎤
K
⎪ ( 4 ρ + 1 − i )( 4 ρ + 1 − j ) − 2 min ( 3ρ + 1 − i ) , ( 2 ρ + 1) .min ( 3ρ + 1 − j ) , ( 2 ρ + 1) + ( 2 ρ + 1 − i )( 2 ρ + 1 − j ) ⎪
⎥ ⎬
+
⎨• ⎢
∑
∑
∑
2
( n + 1)
⎥ ⎪
m1 + m2 + m3 = 1 m1 + m2 = 1 m1 = 0 ⎪ ⎢
⎣
⎦
⎪
m3 ⎪
⎪ ⎡ ( 6ρ + 1 − i )( 6ρ + 1 − j ) − 2 min ( 5ρ + 1 − i ) , ( 4 ρ + 1) .min ( 5ρ + 1 − j ) , ( 4 ρ + 1) + ( 4 ρ + 1 − i )( 4 ρ + 1 − j ) ⎤ ⎪
⎥
⎪
⎪• ⎢
( n + 1) 2
⎥ ⎪
⎪ ⎢⎣
⎦ ⎭
⎩
{
}
{
}
{
}
{
}
Theorem: Let S be a node randomly picked from QD. C3HR estimates that the number of cell in localization estimation
area AS for S, is a function of network area side length and node communication distance, 1#X = |AS|#(n+1-2D)2 and its
expectation is:
E( X ) =
n/2− ρ
∑
n/ 2− ρ
∑
i = n/2+ ρ j = − n/2+ ρ
n/2− ρ
( ) ∑
E λij =
i = − n/2+ ρ
5ρ
5ρ
4ρ
5ρ
5ρ
ρ ⎞
⎛ 6 ρ 5ρ 6 ρ 6 ρ
Pr λij = 1 = 4⎜ ∑ ∑ + ∑ ∑ + ∑ ∑ + ∑ ∑ + 2 ∑ ∑ ⎟ P (4,6], [0,6]
⎝ i = 5ρ +1 j = 0 i = 0 j = 5ρ +1 i = 4 ρ +1 j = ρ +1 i = ρ +1 j = 4 ρ +1
j = − n/2+ ρ
i = 4 ρ +1 j = 0 ⎠
n/ 2− ρ
∑
(
)
{
4260
}
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
3ρ
4ρ
⎛ 4ρ 4ρ
+ 4⎜ ∑ ∑ + ∑ ∑ + 2
⎝ i = 3ρ +1 j = ρ +1 i = ρ + 1 j = 3ρ +1
4ρ
ρ
∑ρ ∑
3ρ
i = 3 +1 j = 0
3ρ
∑ρ ∑ρ
+
2ρ
i = 2 +1 j = +1
3ρ
ρ
∑ρ ∑
+2
i = +1 j = 2 +1
i = 2 +1 j = 0
⎞
⎟ P (2, 4 , 0, 4
⎠
{
][ ]}
] [ ] } + χ .[( n + 1 − 2ρ) − (12ρ + 1)
2ρ
ρ
ρ
ρ ⎞
⎛ 2ρ 2ρ
+ 4⎜ ∑ ∑ + 2 ∑ ∑ + ∑ ∑ ⎟ P (0, 2 , 0, 2
⎝ i = ρ +1 j = ρ +1
i = ρ +1 j = 0
i =1 j = 0 ⎠
{
Therefore, with n, D Wxed,
3ρ
∑ρ ∑ρ
+
2
K
2
]+ 1
lim E ( X ) = 1
K →∞
That is, the expectation of the size of the estimate tends to one, the perfect estimate, as the number of known nodes
tends to inWnity.
Inference: To every e>0, it exists a minimum K0, when K#K0 it meets the location accuracy requirement |E(X)-1| <e.
Anchor nodes’ minimal density (the proportion of anchor nodes’ number to the total discrete network cell) must satisfy:
K
(n + 1)2
>
(
)
log n2 + 148ρ 2 − 4 ρn + 40ρ + 2n − log e
(6ρ + 1)
Proof:
Obviously E(X)#E(X||i = 1, j = 0) and:
n
n
m =1
m= 0
∑ Cnma mbn −m = ∑ Cnma mbn −m − bn = (a + b)n − bn
1− 2
(6ρ + 1)2 ≤ 1 − (6ρ + 1) = 1 − (6ρ + 1)2 + 6ρ (6ρ + 1)
1− 2
(6ρ + 1)2 + 6ρ(6ρ + 1) = 1 − (6ρ + 1)2 − (6ρ + 1) ≤ 1 − (6ρ + 1)
1−
(6ρ + 1)2 + 6ρ(6ρ + 1) − 2 × 5ρ (4 ρ + 1) ≤ 1
−
thus
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(n + 1)2
(6ρ + 1)2 + 6ρ(6ρ + 1) = 1 − (6ρ + 1)
(n + 1)2
(n + 1)2
(n + 1)2
6ρ
6ρ
⎛ 6 ρ 5ρ
E ( X ) − 1 = 4⎜ ∑ ∑ + ∑ ∑ +
⎝ i = 5ρ + 1 j = 0 i = 0 j = 5ρ + 1
⎛ 4ρ 4ρ
+ 4⎜ ∑ ∑ +
⎝ i = 3ρ + 1 j = ρ +1
3ρ
4ρ
4ρ
∑ρ ∑ρ
+2
i = +1 j = 3 +1
5ρ
5ρ
∑ρ ∑ρ
i = 4 +1 j = +1
ρ
∑ρ ∑
5ρ
5ρ
∑ρ ∑ρ
+2
i = +1 j = 4 +1
3ρ
+
i = 3 +1 j = 0
3ρ
∑ρ ∑ρ
i = 4 +1 j = 0
3ρ
+2
i = 2 +1 j = 2 +1
ρ
∑ρ ∑
ρ
∑ρ ∑
i = 2 +1 j = 0
⎞
⎟ P (4, 6 , 0, 6
⎠
2
K
4261
{
] [ ]}
⎞
⎟ P (2, 4 , 0, 4
⎠
{
] [ ] } + χ ⋅ [( n + 1 − 2ρ) − (12ρ + 1)
2ρ
ρ
ρ
ρ ⎞
⎛ 2ρ 2ρ
+ 4⎜ ∑ ∑ + 2 ∑ ∑ + ∑ ∑ ⎟ P (0, 2 , 0, 2
⎝ i = ρ + 1 j = ρ +1
i = ρ +1 j = 0
i =1 j = 0 ⎠
{
4ρ
+
] [ ]}
2
]≤ ⎢⎢⎣1 − ((6nρ+ +1)1) ⎥⎥⎦
⎡
⎤
2
K
(n
2
+ 148ρ 2 − 4 ρn + 40ρ + 2n)
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
out that node communication distance has deeper
influence to the required amount of anchor nodes than the
network size (the total amount of cell). Once the
communication distance is too large, the requirement of
C3HR algorithm to anchor node density is almost
unchanged.
Relative position error:
Definition 5: Denote by (Xest, Yest) and (Xa, Ya)
respectively node’s estimation position and actual
position, then relative position error is:
Err =
Fig. 2: Experiment scene
( X est − X a + Yest − Ya )
2ρ
B-Box algorithm just can make effectively estimation
to the unknown nodes which have neighbor anchor nodes
within its one hop communication range, so when the
relative position error is more than 2, this node can not be
positioned by B-Box. While C3HR algorithm’s position
expends to 3D, therefore the effective relative estimation
error for some nodes is likely close to 6 and we conclude
that such nodes can not be located either.
SIMULATION RESULTS AND ANALYSIS
Fig. 3: The localization effect of B-box algorithm
Table 1: Anchor nodes’ minimal density with different n and D of
C3HR algorithm
Number of
Node’s communication distance of one hop
discrete
-------------------------------------------------------------------network cell 5
10
15
20
30
40
100×100
0.200
0.111
0.081
0.065
0.047
0.038
200×200
0.239
0.124
0.086
0.068
0.048
0.038
500×500
0.298
0.151
0.102
0.078
0.053
0.040
1000×1000
0.343
0.174
0.117
0.088
0.059
0.045
⎡
Since log ⎢1 −
⎢⎣
(6ρ + 1) ⎤⎥ ≤ − (6ρ + 1) ,
(n + 1)2 ⎥⎦
(n + 1)2
we obtain that to
achieve |E(X)-1| < e, it must satisfy:
K>
(
)
log n2 + 148ρ 2 − 4 ρn + 40ρ + 2n − log e
(6ρ + 1)
× (n + 1)
2
this completes the proof.
In Table 1, we assign e = 24, change n and the
required minimum anchor node density D. We can find
In order to evaluate and analyse C3HR algorithm’s
improvement to the localization accuracy and coverage of
B-Box algorithm, we implement multiple simulation
experiments using the NS2 network simulator. In
[1, 100]×[1, 100] square area, 200 nodes with the same
performance parameters are randomly distributed, among
which 50 are anchor nodes (Fig. 2), obviously in such
situation anchor nodes’ density is as very low as 25%.
The number of cells in discrete network model is
100×100. Below we use B-Box and C3HR algorithm
respectively to locate the rest 150 unknown nodes (Fig. 2)
and we don’t consider the nodes’ mobility in the
experiment.
First we set D = 12, the localization result of B-Box
algorithm is shown in Fig. 3. The line connects the nodes’
actual position and estimated position and the 12 solid
nodes represent those nodes which can not be estimated
by B-Box algorithm effectively, because their peripheral
anchor nodes are very too sparse. In Fig. 2, we can find
that some nodes’ position error is large. As Fig. 4, C3HR
algorithm reduces the position error, especially for the 12
nodes which can not be positioned by B-Box algorithm,
we can observe that the error reduces with 0.6 D~1.6 D in
general, showing that C3HR algorithm improves the
position accuracy.
To analyze the position performance completely, we
must make further comparison of the two algorithms’
4262
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
B-box
C3HR
3.5
Position error (p)
3.0
2.5
2.0
1.5
1.0
0.5
0
0
50
100
Unknown node number
150
Fig. 4: Two algorithm’s position error to all the network nodes
B-box
C3HR
Average position error (p)
7
6
CONCLUSION
5
4
3
2
1
0
4
6
18
8
14
16
10
12
Node communication range (p)
Fig. 5: Average position error comparison of the two algorithm
Ratio of nodes can be localized (n%)
than B-Box algorithm and so reduces the network nodes’
energy cost.
Figure 6 is the position coverage comparison of the
two localization algorithms. Since C3HR algorithm
expands the communication distance for the constraint of
the unknown nodes, so it expands the algorithm’s
coverage and the experiment results prove it well in
Fig. 6. When D is 4, B-Box algorithm can just locate 30%
nodes in the network, while C3HR algorithm can estimate
out 98% nodes’ position and reach to 100% coverage
soon. In the experiment, B-Box algorithm improves its
position coverage slowly, it can make position estimation
to all the nodes until D = 17. In comparision, C3HR
algorithm is more applicable to the complex sensor
network requirements for robustness and stability.
1.0
0.9
0.8
0.7
0.6
0.5
B-box
C3HR
0.4
4
6
8
14
16
10
12
Node communication range (p)
18
Fig. 6: Position coverage comparison of the two algorithms
estimation effect in different node’s communication
distance, as showing in Fig. 5. When D is little, 4 for
example, the average position error of C3HR algorithm is
less than 1.7D, while the error of B-Box algorithm reaches
as high as 6.1D. With the increase of communication
distance, the anchor nodes which enter the effective action
range of the two algorithms are also increasing, which
improves the accuracy of position estimation therefore.
When D = 10, the error of B-Box algorithm reduces to
0.95 D and C3HR algorithm reduces to 0.58 D. Since then,
the error of C3HR algorithm reduces by about 15%
compared with B-Box algorithm. It shows that in order to
get the same position accuracy, C3HR algorithm’s
dependence on the nodes’ communication distance is less
In this study, we proposed the C3HR localization
algorithm for wireless sensor networks, which enables
nodes that are multiple hops away from anchors to
determine their position with high accuracy. C3HR is a
distributed range-free approach and do not require
information exchange between neighboring sensors. It has
a low computation overhead and is simple to implement.
C3HR uses anchors that broadcast beacon signals at
varying power levels consecutively and periodically. This
allows each sensor node to identify which concentric
cincture, centered at the anchor, the node resides in. The
estimated position of the node is taken as the average of
all the valid intersection points. Simulation results show
that C3HR provides a lower position estimation error than
Bounding Box under a wide range of conditions and
improves the position estimation coverage of the
algorithm greatly, reduces the computational cost. At the
same time the position estimation performance of C3HR
has no relationship with the total network nodes and
distribution. Further study includes the implementation of
C3HR via testbed prototyping and the cutback of the
computation overhead beyond one hop cincture.
ACKNOWLEDGMENT
This study was supported by the Significant Scientific
Research Programs Foundation of the Education
Department of Jiangxi Province (No. GJJ11062); The
Main Technology Pathfinder Programs Foundation of
Jiangxi Province (070002); The Pillar Programs
Foundation of the Science and Technology Department of
Jiangxi Province (2007ZD03700).
REFERENCES
Doherty , L., K.S.J. Pister and L.E. Ghaoui, 2001. Convex
position estimation in wireless sensor networks.
Infocom. Anchorage Alaska, 3: 1655-1663.
4263
Res. J. Appl. Sci. Eng. Technol., 4(21): 4258-4264, 2012
Galstyan , A., B. Krishnamachari and K. Lerman, 2004.
Distributed online localization in sensor networks
using a moving target. The 3rd International
Symposium on Information Processing in Sensor
Networks (IPSN'04), Berkeley, California, USA, pp:
61-70.
Liu , C. and K. Wu, 2005. Performance evaluation of
range-free localization methods for wireless sensor
networks. Proceeding of IEEE IPCCC Phoenix, pp:
1304-1311.
Pathirana , P., N. Bulusu, A. Savkin and S. Jha, 2005.
Node localization using mobile robots in delaytolerant sensor networks. IEEE Trans. Mobile
Comput., 4: 285-296.
Patwari , N. and A. Hero, 2003. Using proximity and
quantized RSS for sensor localization in wireless
networks. Proceeding of ACM WSNA, pp: 714-722.
Savarese , C., J. Rabay and K. Langendoen, 2002. Robust
positioning algorithms for distributed ad-hoc wireless
sensor networks. Proceedings of USENIX Technical
Annual Conference Monterey, CA, pp: 317-327.
Simic , S.N. and S. Sastry, 2002. Distributed Localization
in Wireless Ad Hoc Networks. Technical Report
UCB/ERL M02/26, UC Berkeley.
Stupp , G. and M. Sidi, 2004. The expected uncertainty of
range free localization protocols in sensor networks.
Algorithmic Aspects of Wireless Sensor Networks:
First International Workshop, ALGOSENSORS,
3121: 85-97.
Vivekanandan , V. and V. Wong, 2006. Concentric
Anchor-Beacons (CAB) localization for wireless
sensor networks. IEEE International Conference on
Communications, ICC '06, University of British
Columbia, Vancouver, Canada, 9: 3972-3977.
Wang , H.B., L. Yip and K. Yao, 2004. Lower bounds of
localization uncertainty in sensor networks. In IEEE
ICASSP, Montreal, Canada, pp: 975-983.
Whitehouse , C.D., 2002. The design of calamari: An adhoc localization system for sensor networks. MA.
Thesis, University of California at Berkeley, pp: 173.
Xiang , M.T., H.S. Shi and L.H. Li, 2007. A node
localization algorithm based on connectivity in
wireless sensor networks. Chin. J. Sens. Actuat.,
20(10): 2308-2312.
4264