A localization algorithm based on anchor-free wireless sensor network

Chen Liu1,a,Jianlin Mao1,b,Zicheng Chi1.c,Lixia Fu1,d,Fenghong Xiang1,e

Faculty of Information Engineering and Automation , Kunming University of Science and

Technology, Kunming 650500, China a340026346@qq.com, bkm_mjl@aliyun.com, c26068951@qq.com, d905771625@qq.com,

e1718473881@qq.com

Keywords：：：：Anchor-free；Cumulative error；SAAPSO algorithm；Taylor algorithm；Co-location

Abstract：：：：The localization of anchor-free wireless sensor network’s serious cumulative error leads

to low positioning accuracy. To solve this problem, this paper proposed a co-located positioning

method based on asynchronous change of learning factor adaptive weights particle swarm

optimization algorithm(SAAPSO) and Taylor algorithm. The first phase of localization is building

relative coordinate system. The second phase is estimating the node’s initial position with SAAPSO

algorithm and using Taylor algorithm to iterative calculate in the node’s initial position to obtain

accurate result. In the third stage, the node with precise coordinates takes part in the localization of

rest nodes. Simulation results show that: this positioning algorithm has smaller cumulative error and

higher accuracy.

1. Introduction

Wireless sensor network(WSN) is a hot field nowadays. For WSN, get relative positions or

absolute positions of nodes is critical. So locate nodes is the chief problem of WSN need to be

solved.

Anchor-free WSN[1,2] has advantages such as low cost and easy to deploy in large-scale, but

generates error accumulation during localization, leading to low localization accuracy. In order to

solve this problem, this paper proposes a co-location method based on asynchronous change

learning factor’s adaptive weight PSO algorithm(SAAPSO) and Taylor algorithm. Firstly a relative

coordinate system is built and the nodes which established relative coordinate system are regarded

as virtual anchor nodes[3]. Secondly, an initial estimate value is get by locating unknown node

using SAAPSO. Thirdly, the initial estimate value is regarded as Taylor algorithm’s initial value to

proceed iterative refinement to get the node’s calculate coordinates. Ultimately, the node will be

regarded as virtual anchor node and locates next unknown node. Simulation results show that: this

algorithm has small localization accumulative error and high precision.

Definition 1: node connection degree.

The number of neighbor nodes within the scope of node’s communication.

2. The improved Particle Swarm Optimization algorithm

This paper proposed a kind of particle swarm optimization algorithm based on asynchronous

change learning factor's adaptive weights(SAAPSO). It combines the PSO algorithm[4,5] based

on asynchronous learning factor and the PSO algorithm based on adaptive weighted[6,7], not only

improves the convergence speed and precision of the algorithm, but also balances the global search

ability and local improvement ability of the algorithm.

Advanced Materials Research Vol. 1056 (2014) pp 221-226 Submitted: 03.09.2014Online available since 2014/Oct/27 at www.scientific.net Accepted: 28.09.2014© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.1056.221

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.194.20.173, Monash University Library, Clayton, Australia-06/12/14,19:29:56)

SAAPSO algorithm steps

1) Initialize the position and velocity of each particle in the population randomly;

2) Evaluate the fitness of each particle. The current position and adaptive value of each particle are

stored in each particle's “pbest”. The optimal individual adaptive value's position and adaptive value

of “pbest” is stored in “gbest”;

3) Update the particle's velocity and displacement using the type below;

( )( ) ( )

=++=+

−+−+=+

Djtjivtjixtjix

tjixjgprctjixjiprctjivwv

...2,1),1(,)(,)1(,

)(,,*2*2,,*1*1)(,*)1t(i.j (1)

4) Update the learning factor;

−

+=

−

+=

tt

inic

finc

inicc

tt

inic

finc

inicc

*

max

,2,2

,22

max

,1,1

,11

(2)

5) Update the weight;

;

,max

,)

min(

)min

(*)minmax

(

min

>

≤−

−−

−

=

avgffw

avgff

favgf

ffww

w

w (3)

6) For each particle, the adaptive value is compared with the best position, if it is better, the

adaptive value will be served as the current best position. Then all "pbest" value and "gbest" value

will be made a comparison and finally "pbest" will be updated;

7) If operation precision or iterations meets the reset, search stop, output the result, otherwise,

return to step 3 to continue to search.

3. The anchor-free localization algorithm process

1) Deploy WSN, give each node a unique ID number.

2) Nodes acquire neighbor nodes lists and range values.

3) The node which has the smallest ID number is served as virtual coordinate system's original point

( )0,00N and inform neighbor nodes.

4) The original point receives connectivity from its neighbor nodes and chooses the neighbor node

which has maximum connectivity as the reference node 1N . ( )0,011 rN

is determined according to

their range value. So the x axis of relative coordinates is determined.

5) 0N and 1N inform their respective neighbor nodes of relative coordinate positions. While a

node is the neighbor node of two nodes at the same time and has maximum connectivity in the

222 Machine, Manufacturing, Materials and Information Technology II

neighbor nodes of these two nodes, this node will be the reference node 2N . 02r is supposed as

the range value between 0N and 2N . 12r is supposed as the range value between 1N and 2N .

The coordinates of 2N can be figured out:

−

−+ 2

2

2

02

01

2

12

2

02

2

01 ,2

xrr

rrr and

−−

−+ 2

2

2

02

01

2

12

2

02

2

01 ,2

xrr

rrr.

−

−+= 2

2

2

02

01

2

12

2

02

2

012 ,

2xr

r

rrrN

is taken, so the relative coordinate

system of the network is confirmed.

6) 0N , 1N and 2N are regarded as virtual anchor nodes.

7) Acquire the virtual anchor nodes' number of unknown nodes' neighbor nodes. The node which

has maximum connectivity and the virtual anchor nodes' number of neighbor nodes is equal or

greater than 3 will be chosen to estimate the initial position by using SAAPSO algorithm. 8) Iterate and refine the node's estimate position with Taylor algorithm to get a precise position. The

node which has got precise coordinate value will be regarded as virtual anchor node to participate in

other nodes' localization in the network.

9) Repeat steps 7 and 8 until all the unknown nodes in the network are identified. (assuming that the

connectivity of all the nodes in the network are equal or greater than 3)

Figure 1 is the algorithm flow chart:

Figure 1 Algorithm flow chart

4. The experimental simulation analysis

4.1 Experimental parameters Settings

The simulation area is set as 40m*40m. 15 nodes are deployed randomly within the area and

node communication radius is 15m. After the confirmation of nodes' real coordinates, I determine

Advanced Materials Research Vol. 1056 223

neighbor relations according to node communication radius, calculate the distance between adjacent

nodes, and makes random node coordinates to ensure the connection degree of random nodes'

coordinates is equal or greater than 3. SAAPSO parameters: the number of particles "N" = 40; the

initial value of c1 and c2 "c1, ini" = 2.5, "c2, ini" = 0.5; the final iteration value of c1 and c2 "c1,

fin" = 0.5, "c2, fin" = 2.5; "wmax" = 0.9, "wmin" = 0.5; the maximum number of iterations "M" =

1000. The threshold value of Taylor algorithm 002.0=ε , the maximum number of iterations is 20. A

noise obey Gaussian distribution ( )randnN * is added in the range value between nodes. The unit is

m.

4.2 Algorithm's validity

Figure 2 is the real positions and algorithm's estimate position contrast graph of 15

nodes under the condition of noise index N = 1m. The communication radius of nodes is 15m. We

can see in the figure that error between two coordinates of each node is small. It reflects the

algorithm is effective.

-20 -15 -10 -5 0 5 10 15 20-20

-15

-10

-5

0

5

10

15

20

distance/m

dis

tanc

e/m

real position

estimate position of the improved algorithm

Figure 2 Contrast of nodes real positions and improved algorithm's estimated positions

4.3 Algorithms performance comparison

Under the same simulation environment, Min-max + Taylor algorithm[3,8], SAAPSO algorithm,

SAAPSO + Taylor algorithm are compared in average position error and mean square error of each

node.

4.3.1 Average position error

The performance reflects the localization accuracy rating of WSN and shows the estimated

positions' average deviation of all nodes in network, namely:

M

yyxxM

i

iiii∑=

−+−

= 1

2'2' )()(

δ

Among them, "M" means the number of wireless sensor network nodes. In this paper, "M"=15;

( )ii yx , , ( )'' , ii yx respectively means algorithm's estimated position and real position of node 'i'. The

average position errors are got when it simulates respectively under the condition of noise figure

N=0.2m, 0.4m, 0.6m, 0.8m, 1.0m, shown in figure 3.

224 Machine, Manufacturing, Materials and Information Technology II

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

noise figureN/m

the

av

era

ge p

ositio

n e

rror/

m

SAAPSO+Taylor algorithm

Min-max+Taylor algorithm

SAAPSO algorithm

Figure 3 SAAPSO +Taylor, Min-max +Taylor, SAAPSO-comparison of this three

algorithms’ average position error value

The simulation results show that under different noise figure influence, the average position

error of SAAPSO +Taylor algorithm is much less than Min-Max +Taylor algorithm's. Through the

experiment we also find that, the average position error of Min-max +Taylor algorithm increases

rapidly. This is because when the noise is bigger, the accuracy of estimate nodes' initial position

with Min -max algorithm gets lower. When the error between initial estimate position and real

position is too large, it's easy to lower the localization accuracy of Taylor algorithm and lead to

Taylor algorithm misconvergence.

4.3.2 Mean square error

This performance shows the dispersion degree of node's localization error distribution, namely:

2)

0(

2)

0( yyxxRMSE −+−=

( )yx, , ( )00 , yx respectively show average estimated position coordinates and real coordinates of

node. Simulation operates in the case of noise figure is "N" = 0.5m and get each node's mean square

error "RMSE", as shown in figure 4.

4 5 6 7 8 9 10 11 12 13 14 150.05

0.1

0.15

0.2

node number

RM

SE

/m

SAAPSO+Taylor algorithm

Min-max+Taylor algorithm

SAAPSO algorithm

Figure 4 SAAPSO +Taylor, Min-Max +Taylor, SAAPSO-comparison of this three algorithms'

node estimated position "RMSE"

Due to the first phase of localization-establish relative coordinate system are the same,

estimated coordinates and "RMSE" of node 1, 2, 3, respectively are the same.

Advanced Materials Research Vol. 1056 225

The simulation results show that the SAAPSO +Taylor algorithm's nodes localization "RMSE"

is smaller than SAAPSO algorithm's and Min -max +Taylor algorithm's. On account of the number

of virtual anchor nodes is few, Min -max +Taylor algorithm's localization error is obviously bigger

than SAAPSO algorithm's and SAAPSO +Taylor algorithm's when locating the node 4 and 5. Along

with the number of virtual anchor nodes in network increases, localization accuracy of Min -max

+Taylor algorithm increases slightly and localization accuracy of these three algorithm are rarely

different when locating the node 6, 7, 8. But due to error accumulation effect, the three algorithm's

localization accuracy decrease. Among them, localization accuracy of Min -max +Taylor algorithm

decreases fastest while SAAPSO +Taylor algorithm's localization error is obviously smaller than

the other two algorithms'.

5. Conclusion

To solve the problem of low localization accuracy caused by error accumulation during

localization in network without anchor nodes, this paper proposed a localization based on SAAPSO

algorithm and Taylor algorithm and introduced the concept of virtual anchor nodes and node

connection degree. Simulation experiments show that compared with co-localization based on Min

-max algorithm and Taylor algorithm, SAAPSO algorithm, co-localization based on SAAPSO

algorithm and Taylor algorithm reduces the localization error accumulation and has higher

localization accuracy, is suitable for WSN without anchor nodes.

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226 Machine, Manufacturing, Materials and Information Technology II

Machine, Manufacturing, Materials and Information Technology II 10.4028/www.scientific.net/AMR.1056 A Localization Algorithm Based on Anchor-Free Wireless Sensor Network 10.4028/www.scientific.net/AMR.1056.221

DOI References

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http://dx.doi.org/10.3724/SP.J.1087.2010.01736