4.2 nearest node is calculated using the distance formula

4.2 Weighted centroid Scheme:  In the weighted centroid basedlocalization algorithm 7 the distance between anchor nodesand the unknown nodes are calculated same as centroid localization method butweight 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 anchornodes.w1,w2 and w3 represents weight of anchornode and location of  the blind node b (x,y)can be calculated using eqution(2).

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                              x=  ; y=           ———————————(2) Fig.7. Weighted Centroid  Localization Scheme4.

3 Proposed Localization Algorithm:Theproposed localization algorithm determines the location of unknown node usingthe line of intersection method. In Fig.8. Four anchor nodes are present, theyare a (x1, y1), a (x2,y2), a(x3,y3)and a(x3,y3) and unknown node p(x,y).

In this method the firstnearest 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 fourthnearest node from unknown node p (x,y) is named as a (x4,y4).The nearest  node is calculated using thedistance formula between two point.steps to calculate the unknown node locationas follows:1)    Deploythe sensor nodes randomly in the given sensor fields.2)    SensorField consits of anchor nodes and unkown nodes.3)    Findan anchor nodes location with the known location closer to the unknown node.4)    Letthe co-ordinate of the first nearest anchor node to the unknown node is takenas A(x1,y1) ,second nearest node is A(x2,y2),thirdand fourth nearest node is A(x3,y3) and A(x4,y4).5)    Findthe intersection of line passing through the midpoint of  first nearest and second nearest anchor nodeusing the formula          ——————–(3)6)    Findthe mid point of first nearest and third nearest anchor node using theformula     —-(4)7)    Find  the mid point of  second nearest and third nearest anchor nodeusing the formula   –(5)8)    Thusit produces the required location of the unknown node. The emperical formulafor co-ordinates x &  y of unknownnode is given by :9)     10)                          11)  Find the average error of all thenodes.

   ig.8. Proposed Localization Scheme 6 ImplementationSimulationis done using Matlab. The performanceof proposed localization algorithmis evaluated based on the localization error.

In this work line ofintersection of mid point of nearest anchor nodes are computed. 6.1 Centroid Localization Simulation                                  In Centroid localization theunknown nodes receive the beacon messages within the range of theircommunication.  The nodes then estimatetheir position by taking the average of all the beacon positions using eqn(1)  and take the resulting centroid astheir estimated position.  The simulationis done within an area of 100 100mwith 40 unknown nodes and 40 beacons as shown in Fig.

9.  The beacon nodes and unknown nodes arerandomly distributed inside the area.                 The simulation is done fordifferent number of beacons varying from 20 to 80 in increments of 10 and thelocalisation error is calculated for each node.

 The localisation error is average over 50 iterations.   Fig.9.  Beacon nodes andUnknown Nodes Distribution               Fig.

9  shows the localization results when centroidlocalization is used.  The average erroris in the range of 8m when there is 50 beacons with 40 unknown nodes aresimulated. Fig.

10. Centroid Localization6.2 Weighted Localization Simulation            In  weighted localization the weights aremultiplied to the corresponding beacon position and average is taken.

  Usually distance between the beacon andunknown node is taken as weights . Fig. 11 shows the localisation error betweenthe estimated and actual positions of the unknown nodes.  The average localization error was found tobe in order of 6.5m which is better than the centroid localization.

 Fig. 11.  Weighted Localization Simulaltion6.3Proposed Localization Simulation Fig.

12. Proposed Localization algorithm   Inproposed localization the beacons first communicate with each other nodes andthe mid points of each nearby anchor node and unkown node is calculated.Theline of intersection point is measured with the help of equations (3,4,5,6 and7). The resulting localization error simulation is given in Fig. 12.  The number of beacon nodes is 50 and 40unknown nodes.

The average localization error is around 5.5m which is betterthan both weighted and centroid localization algorithms. 6.4 Comparison of Various Algorithms Fig. 13. No of Beacons vsPosition Errors               Fig. 13 isposition error comparison of three algorithms, centroid algorithm,  weighted centroid algorithm and improvedalgorithm with beacon node numbers being ten, twenty, thirty, forty, fifty,seventy and eighty respectively.

From Fig. 13 we can intuitively discover that thepositioning error of three algorithms are gradually reduced along with theincrease of the number of beacon nodes. The simulation results show that thepositioning accuracy have been improved. Improved algorithm thus reduces the environment factors and improvespositioning accuracy effectively by using line of intersection of mid point ofnearest anchornodes.

6.ConclusionInthis paperwe  proposed new localiztioan algorithmwhich estimates the locality information of a sensor node using the line ofintersection of midpoints of the nearest anchor of unknown node which is moreaccurate and it does not require any extra hardware as like range-basedlocalization scheme.Proposed algorithm is easy to implement because computationcomplexity and average location estimation error is low when compared withtraditional centroid and weighted centroid localization scheme.In thesimulation results the proposed algorithm gives location accuracy and lessaverage location estimation error than the centroid and weighted centroidlocalization method. In future proposed localization algorithm can be appliedfor Three dimensional space. In summary we say that the identification of exactlocation of sensor node plays major role in many real-time research areas.  References:1.

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