4.2 Weighted centroid Scheme:

In the weighted centroid based

localization algorithm 7 the distance between anchor nodes

and the unknown nodes are calculated same as centroid localization method but

weight of each nearby anchor node is multiplied. Using weighted centroid formula.In Fig. 7. A(x1,y1), A(x2,y2)

and A(x3,y3) represents anchor

nodes.w1,w2 and w3 represents weight of anchor

node and location of the blind node b (x,y)

can be calculated using eqution(2).

x=

; y=

———————————(2)

Fig.

7. Weighted Centroid Localization Scheme

4.3 Proposed Localization Algorithm:

The

proposed localization algorithm determines the location of unknown node using

the line of intersection method. In Fig.8. Four anchor nodes are present, they

are a (x1, y1), a (x2,y2), a(x3,y3)

and a(x3,y3) and unknown node p(x,y). In this method the first

nearest anchor node from unknown node p(x,y) is named as a (x1,y1),

second nearest node from unknown node p(x,y) is named as a (x2,y2),

third nearest node from unknown node p(x,y) is given as a (x3,y3) and fourth

nearest node from unknown node p (x,y) is named as a (x4,y4).

The nearest node is calculated using the

distance formula between two point.steps to calculate the unknown node location

as follows:

1)

Deploy

the sensor nodes randomly in the given sensor fields.

2)

Sensor

Field consits of anchor nodes and unkown nodes.

3)

Find

an anchor nodes location with the known location closer to the unknown node.

4)

Let

the co-ordinate of the first nearest anchor node to the unknown node is taken

as A(x1,y1) ,second nearest node is A(x2,y2),third

and fourth nearest node is A(x3,y3) and A(x4,y4).

5)

Find

the intersection of line passing through the midpoint of first nearest and second nearest anchor node

using the formula

——————–(3)

6)

Find

the mid point of first nearest and third nearest anchor node using the

formula

—-(4)

7)

Find the mid point of second nearest and third nearest anchor node

using the formula

–(5)

8)

Thus

it produces the required location of the unknown node. The emperical formula

for co-ordinates x & y of unknown

node is given by :

9)

10)

11) Find the average error of all the

nodes.

ig.

8. Proposed Localization Scheme

6 Implementation

Simulation

is done using Matlab. The performance

of proposed localization algorithm

is evaluated based on the localization error. In this work line of

intersection of mid point of nearest anchor nodes are computed.

6.1 Centroid Localization Simulation

In Centroid localization the

unknown nodes receive the beacon messages within the range of their

communication. The nodes then estimate

their position by taking the average of all the beacon positions using eqn

(1) and take the resulting centroid as

their estimated position. The simulation

is done within an area of 100

100m

with 40 unknown nodes and 40 beacons as shown in Fig. 9. The beacon nodes and unknown nodes are

randomly distributed inside the area.

The simulation is done for

different number of beacons varying from 20 to 80 in increments of 10 and the

localisation error is calculated for each node.

The localisation error is average over 50 iterations.

Fig.

9. Beacon nodes and

Unknown Nodes Distribution

Fig. 9 shows the localization results when centroid

localization is used. The average error

is in the range of 8m when there is 50 beacons with 40 unknown nodes are

simulated.

Fig. 10. Centroid Localization

6.2 Weighted Localization Simulation

In weighted localization the weights are

multiplied to the corresponding beacon position and average is taken. Usually distance between the beacon and

unknown node is taken as weights . Fig. 11 shows the localisation error between

the estimated and actual positions of the unknown nodes. The average localization error was found to

be in order of 6.5m which is better than the centroid localization.

Fig. 11. Weighted Localization Simulaltion

6.3

Proposed Localization Simulation

Fig. 12. Proposed Localization algorithm

In

proposed localization the beacons first communicate with each other nodes and

the mid points of each nearby anchor node and unkown node is calculated.The

line of intersection point is measured with the help of equations (3,4,5,6 and

7). The resulting localization error simulation is given in Fig. 12. The number of beacon nodes is 50 and 40

unknown nodes. The average localization error is around 5.5m which is better

than both weighted and centroid localization algorithms.

6.4 Comparison of Various Algorithms

Fig. 13. No of Beacons vs

Position Errors

Fig. 13 is

position error comparison of three algorithms, centroid algorithm, weighted centroid algorithm and improved

algorithm with beacon node numbers being ten, twenty, thirty, forty, fifty,

seventy and eighty respectively. From Fig. 13 we can intuitively discover that the

positioning error of three algorithms are gradually reduced along with the

increase of the number of beacon nodes. The simulation results show that the

positioning accuracy have been improved.

Improved algorithm thus reduces the environment factors and improves

positioning accuracy effectively by using line of intersection of mid point of

nearest anchor

nodes.

6.

Conclusion

In

this paperwe proposed new localiztioan algorithm

which estimates the locality information of a sensor node using the line of

intersection of midpoints of the nearest anchor of unknown node which is more

accurate and it does not require any extra hardware as like range-based

localization scheme.Proposed algorithm is easy to implement because computation

complexity and average location estimation error is low when compared with

traditional centroid and weighted centroid localization scheme.In the

simulation results the proposed algorithm gives location accuracy and less

average location estimation error than the centroid and weighted centroid

localization method. In future proposed localization algorithm can be applied

for Three dimensional space. In summary we say that the identification of exact

location of sensor node plays major role in many real-time research areas.

References:

1.

Chen, H. (2008). Novel centroid localization algorithm for three dimensional

wireless sensor networks. In Proc. About

the 4th international conference on IEEE wireless communications (pp.

1–4).

2.

Liu, K., Wang, S., & Zhang, F. (2005). Efficient localized localization

algorithm for wireless sensor networks. In Proc. 5th international conference on computer and information

technology (pp.21–23).

3.

Shu, J., Liu, L., & Chen, Y. (2009). A novel three-dimensional localization

algorithm in wireless sensor networks, wireless communications,networking and

mobile computing. In Proc. 5th

international conference on wireless communications (pp. 24–29).

4.

N. Bulusu, J. Heidemann and D. Estrin, “GPS-less Low Cost Outdoor Localization

for Very Small Devices,” IEEE Personal

Communication Magazine, newblock Vol. 7, No. 5, October 2000, pp. 28-34.

5.

T. He, C. Huang, B.M. Blum, J. A. Stankovic, and T. Abdelzaher, “Range-Free

Localization Schemes for Large Scale Sensor

Networks,” Proceedings of the

ninth annual international conference on Mobile computing and networking

(MobiCom 2003), San Diego, California, September 2003, pp. 81-95.

6.

Bachrach Jonathan and Taylor Christopher. Localization in Sensor

Networks.” In: Handbook of Sensor Networks. John Wiley and Sons, Inc.,

2005, pp. 277{310. isbn: 9780471744146. doi: 10.1002/047174414X.ch9. url:

http://dx.doi.org/10. 1002/047174414X.ch9.

7. J. Blumenthal et al.

Weighted Centroid Localization in Zigbee-based Sensor Networks.” In:

Intelligent Signal Processing, 2007. WISP

2007. IEEE International Symposium on. 2007, pp. 1{6. doi:

10.1109/WISP.2007.4447528.

8.

G. D. Stefano, F. Graziosi, and F. Santucci, “Distributed positioning algorithm

for ad-hoc networks,” in Proceedings of

IEEE Int. Workshop on UWB Systems, 2003.

9.

A. Harter, A. Hopper, P. Steggles, A.Ward, and P.Webster. The anatomy of a

context-aware application. In

Proceedings of the MOBICOM ’99, 1999.

10.

A. Savvides, C. Han, and M. Srivastava., Dynamic fine-grained localization in

ad-hoc networks of sensors. In proceedings of ACM MobiCom ’01, pages 166-179

2001.

11

D. Niculescu and B. Nath. Ad Hoc

Positioning Systems (APS). In

Proceedings of IEEE GLOBECOM ’01, 2001.

12

Meiling Sun. Research on GA based self-localization algorithm in wireless

sensor networks D.Dongying: China