A Sensor Positioning Scheme with High Accuracy in Nonuniform

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 507605 7 pageshttpdxdoiorg1011552013507605

Research ArticleA Sensor Positioning Scheme with High Accuracy inNonuniform Wireless Sensor Networks

Junho Park1 Hyuk Park1 Dong-ook Seong2 and Jaesoo Yoo1

1 School of Information and Communication Engineering Chungbuk National UniversityCheongju Chungbuk 361-763 Republic of Korea

2 BOAS Electronics Inc Industrial Technology Research Park Cheongju Chungbuk 361-763 Republic of Korea

Correspondence should be addressed to Jaesoo Yoo yjschungbukackr

Received 8 April 2013 Accepted 21 May 2013

Academic Editor James J Park

Copyright copy 2013 Junho Park et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In wireless sensor networks a geographical positioning scheme is one of core technologies for sensor applications such as disastermonitoring environment monitoring and military services For this reason the research for range-free positioning schemes hadprogressing actively And a density probability scheme based on the central limit theorem and normal distribution theory has beenproposed to improve the location accuracy in nonuniform sensor network environmentsThe density probability scheme estimates1-hop distance by using communication between nodes After that it estimates the final position of an unknown node But thedensity probability scheme has a problem thatit has equivalent 1-hop distance for all of nodes in the same area To overcome thisproblem we propose a novel sensor positioning scheme in non-uniformwireless sensor networks As a result the proposed schemeensures the high accuracy of sensor positioning in non-uniform networks To show the superiority of our proposed scheme wecompare it with the existing scheme such as DV-based position scheme Our experimental results show that the proposed schemeimproves by about 36 sensor positioning accuracy over the existing scheme on average even in non-uniform wireless sensornetworks

1 Introduction

By the remarkable development of computing technologiesthe ubiquitous environment has been served to providehuman beings with more convenient life This ubiquitousenvironment provides us with diverse and convenient ser-vices through the organic interaction among human beingscomputers and things The wireless sensor network one ofbasic technologies to detect the event and to control the exter-nal human environment in the ubiquitous environment hasbeen vigorously studied The ad hoc wireless sensor networkis constructed autonomously and collects diverse environ-ment information through the communication among sensornodes A sink node receives sensing values from sensor nodesin sensing area and transmits them to a user The collectedinformation is used for diverse purposes such as observa-tion of wildlifersquos habitat military affair fire detection envi-ronmentalmonitoringmedical service andU-City for appli-cation environment [1 2]

In the sensor network the positioning technology is oneof the most required and basic technologies In the position-ing scheme using the wireless devices every equipment isgenerally carrying the Global Positioning System (GPS) inorder to collect positioning information But it causes prob-lems such as excessive energy consumption due to GPSmod-ules and high costs for their construction in the large-scalesensor network environments [3 4] Therefore the position-ing schemes to reduce the energy consumption in the sensornetwork with limited energy have been actively studied

Typical positioning schemes are classified into the range-based schemes and range-free schemes The range-basedschemesmeasure the position of sensor nodes by using signalstrength or time difference between nodes and the range-free schemes measure the distance and estimate the positionthrough the connection information between nodes and theposition information of an anchor node without any subsid-iary hardware equipments [5] Recently range-free schemeshave been proposed [6ndash9] Unlikely range-based schemes

2 International Journal of Distributed Sensor Networks

range-free schemes measure the distance and estimate theposition through the connection information between nodesand the position information of an anchor node In additionit is efficient in the energy consumption and the cost to con-struct the network because only an anchor node is equippedwith GPS module Therefore the positioning schemesthrough the anchor nodes have been actively studied Theexisting schemes estimated the distance between nodes anddecided the position in the uniform sensor network environ-ments without considering density However in real applica-tions since sensors are distributed on the sensing fields ran-domly through aircrafts missile and so on the nonuniformsensor network environments are constructed in specificareas [10]Therefore the positioning schemes for the uniformsensor network environments are not suitable for the actualsituations since their error rates of density probability are veryhigh in the non-uniform sensor network environments

To solve the problem of the existing range-free schemeswe propose a novel positioning scheme by using the densityprobability model in the non-uniform network environmentIn the proposed scheme theminimumanchor nodes are usedand the distance is estimated according to the density in thenon-uniform sensor network environments By doing so thecost to construct the sensor network can be minimized andthe positioning precision can be improved

The remainder of this paper is organized as followsSection 2 overviews the existing positioning schemes in thewireless sensor networks and analyzes their problems InSection 3 we present our sensor positioning scheme usingdensity probability models in non-uniform wireless sensornetworks Section 4 shows the simulated experiments andcompares the existing scheme with the proposed schemeFinally we present concluding remarks in Section 5

2 Related Work

21 Range-Based Positioning Schemes Range-based schemesuse absolute point-to-point distance or angle informationto calculate positions between neighboring sensors usingextra communicationmodules After this the node estimatesposition of unknown nodes by trilateration algorithm [11]Common approaches for range-based schemes include Timeof Arrival (ToA) Time Difference of Arrival (TDoA) andAngle of Arrival (AoA) for this algorithm [3] ToA and TDoAmeasure signal arrival time or the difference of arrival timesto calculate distance based on transmission time and speedThey can be applied tomany different kinds of signals such asRF acoustic and ultrasound signals

Range-based positioning schemes such as ToA TDoAand AoA suffer from the positioning errors since wirelesschannels are very sensitive to the surrounding environmentwhen they use the strength and arrival time of each signalfor positioning ToA TDoA and AoA also have problemssuch as the usage of additional equipments additional costsand large energy consumption due to extra modules for asynchronization system among sensor nodes Therefore therange-based schemes in the wireless sensor network have adifficulty to positioning

L1

L2

A

L340 m

75 m

100 m

Figure 1 Example of DV-HOP estimated distance

22 Range-Free Positioning Schemes DV-HOP algorithm [7]and improved DV-HOP scheme [8 9] are range-free andmulti-hop routing positioning scheme in wireless sensornetworksThey measure the positions of the unknown nodesby using the average distance of 1-hop between anchor nodesDV-HOP algorithm is composed of steps as follows

Firstly each anchor node broadcasts a beacon framecontaining its position with a hop-count value initialized to0 to be flooded throughout the networkThen the nodes thatreceive the information of anchor nodes store the cumulatedhop counts from the anchor nodes to themselves and thepositions of the anchor nodes After that all of the nodescalculate average 1-hop distance through the hop count fromeach anchor node to themselves The average 1-hop distanceof anchor node 119894 is estimated using (1) Here ℎ

119894119895is the mini-

mum hop count of anchor nodes 119894 and 119895 and (119909119894 119910119894) and

(119909119895 119910119895) are their coordinates As a result 119862

119894119895is the calculated

average 1-hop distance In the example in Figure 1 nodes L1L2 and L3 are anchor nodes Consider

119862119894119895=

sumradic(119909119894minus 119909119895)2

+ (119910119894minus 119910119895)2

sumℎ119894119895

119894 = 119895(1)

In a similar manner the estimated average distances of1-hop of L2 and L3 are 1642m and 1590m respectivelyUnknown node A selects 1-hop distance of anchor node L2as the average 1-hop distance since node L2 has the shortestpath for the node A compared with nodes L1 and L3 Andthen node A calculates the estimated distance from threeanchor nodes anchor nodes 119894 119895 and 119896 as (2) Finally nodeA is assuming its position from three anchor nodes using tri-lateration Consider

119863119894= ℎ119886119894times 119862119894119895 (119894 = 1 2 3 119899) (2)

DV-HOP causes lower positioning error and uses feweranchor nodes than the existing schemes However in non-uniform environments where each area has a different den-sity DV-HOP causes higher positioning errors DV-HOPshould also distribute many anchor nodes to increase posi-tioning accuracyTherefore we propose the node density pro-bability model and the positioning scheme to overcome theproblems of DV-HOP

International Journal of Distributed Sensor Networks 3

Distribute location query(base station)

Broadcast location information(anchor nodes)

Store location informationof anchor nodes

Store shortest pathsto anchor nodes

Step 1

Store the basis datain all regular nodes

Step 2

Compute the positionin all regular nodes

Estimate 1-hop distancebased on CLT

Calculate error ratio

Re-estimate 1-hop distanceusing error ratio

Return the coordinatesof regular nodes

Figure 2 Flow chart of the proposed scheme

3 The Proposed Sensor Positioning SchemeBased on Neighbor Density

In this paper we propose a novel positioning scheme toreduce the positioning error and to decrease the constructioncosts in the non-uniform distributed sensor networks Theexisting schemes cause very large positioning errors in eacharea with a different density To reduce the positioning errorsit needs to distribute more anchor nodes in the networkHowever it significantly increases the construction cost dueto many anchor nodes To solve this problem the proposedscheme uses at least 4 anchor nodes placed at the boundary ofthe sensing fields Thereby the proposed scheme minimizesthe cost of construction of the sensor network Figure 2 showsthe process of the proposed positioning scheme First when aposition query is issued in the sensor network the unknownnodes assume their distances through the information of theanchor nodes Second the distances of the unknown nodesare refined with distances between the anchor nodes and

themWe explain steps 1 and 2 of Figure 2 in detail in Sections32 and 33

The proposed scheme is composed of the following foursteps

Step 1 The anchor nodes that exist in the boundary of thenetwork broadcast their positions

Step 2 The unknown nodes estimate the 1-hop distances oftheir neighbor nodes according to the densities of themselvesand their neighboring nodes

Step 3 Each node refines the estimated 1-hop distance bycalculating distance error ratio between the real distances ofanchor nodes and the relative distances through the shortestpaths between anchor nodes

Step 4 The unknown nodes estimate their positions by usingthe refined distance


Table 1 Shortest path and neighbor node list

Shortest path ID Shortest path hop Neighbor list119899119894

Cumulated hop 119899119894 119899119894+1 119899

119894+119899

120579 = 360998400

a

Figure 3 The estimated position of a sensor node

31 NetworkModel andCharacteristics Theanchor nodesA1A2 A3 and A4 are deployed in each corner of the sensingarea In the initial step anchor nodes broadcast their posi-tioning information messages (node ID hop coordinates) toall the nodes The normal sensor nodes save the informationof the anchor nodes and neighbor nodes like Table 1

32 Distance Estimation Considering Neighbor Density Prob-ability Each node estimates 1-hop distance by using CentralLimit Theorem [12 13] based on a normal probability distri-bution The normal distribution or Gaussian distribution isa continuous probability distribution that has a bell-shapedprobability density function If the number of trials or sam-ples objects increase it shows the normal distribution curveThe theory that sensor network environment is consistentwith the normal distribution model is the central limit theo-remThe average of normal distribution model approximatesto 120583 as the number of samples increases In the sensor net-work environment where thousands of sensors are deployedsamples are located in the center of the normal distributioncurveTherefore on the basis of the central limit theorem andthe normal distribution model each sensor node estimatesthe distances to the neighboring nodes For 1-dimensionthere is a point of the specific node that is an average of zeropoint In other words the point of 12 of the communicationradius is the probability that node exists

As shown in Figure 3 if the node draws a circle for thecommunication range and angle (120579 = 360∘) it is farther awaythan the estimated position of 1-dimension Therefore theestimated position for 2-dimension unlike the position of 1-dimension is a point in the circle that the area of its innercircle is equal to the area of its outer circle As a result it ispossible to estimate the distance between nodes through thevalues of the normal distribution table

Equation (3) is the distance calculation equation betweenneighbor nodes based on the values of the normal distribu-tion table 119877 is a communication range of a sensor node and

25 m 23 m 21 m 14 m17 m 17 m

21 m

148 m

100 m

Anchor node

Refining node

Neighbor node

A1

A2

Figure 4 Correction of error rate for an estimated distance

119899 is the number of its neighbor nodes And then the entiresensor nodes estimate the distance between them and theirneighbor nodes through (3) It makes it possible to estimatemore real distance in the non-uniform sensor network wherethe areas have different densities Consider

119889Est(119896) =radic12058711990323

120587= radic1199032

3 119899 = 2

119889Est(119896) =radic1199032

119899 + 1 119899 ge 3

(3)

33 Error Correction of an Estimated Distance If the positionof a node is localized using the estimated distance it has anerror for shorter or longer than the real distance since thesize of the whole network is not considered As a result theproposed scheme needs the correction to reduce the errorrate of the estimated distance Figure 4 shows the error rateof an estimated distance A real distance between anchornode A2 and anchor node A3 is 100m However the esti-mated distance through (3) is 148m Therefore in order tocorrect the error between the real distance and the estimateddistance each node through (4) calculates an error rate forthe accumulated distance of the two anchor nodes throughtheir shortest path and their real linear distance

And then each unknown node refines the estimateddistance through the error rate Finally the unknown nodesthrough 4 anchor nodes measure their positions with tradi-tional trilateration Consider

119889estminusAll(119896) =119894

sum

Node ID(119896)=0119889Est(119896) +

119895

sum

Node ID(119896)=0119889Est(119896) 119894 = 119895

119889Real(119894119895) = radic(119909119894 minus 119909119895)2

+ (119910119894minus 119910119895)2

error (119896) =119889Real119889EstminusAll(119896)

119889ref(119896) = 119889Est(119896) times error(4)


DV-HOP (random) Proposed (random)

DV-HOP (Gaussian) Proposed (Gaussian)

Figure 5 Comparison of localization results

Table 2 Evaluation environment

Parameter ValueSize of sensor networks (m timesm) 200 times 200

Number of distributed normal nodes 100sim500Number of distributed anchor nodes 4Radius of communication (m) 10sim30

4 Performance Evaluation

41 Network Environment We have developed a simulatorbased on JAVA to evaluate our proposed scheme and theexisting scheme DV-Hop The sensor network is based onrandom and non-uniform (Gaussian) models by consideringthe real distribution characteristics of sensors Table 2 showsthe evaluation environments The size of the sensor networkis a square area of 200m times 200m Four anchor nodes aredeployed at each corner of the sensing field and the num-ber of sensor nodes is varied from 100 to 500 The commu-nication ranges for sensor nodes and anchor nodes are 10m15m 20m 25m and 30m The performance evaluation isperformed based on J-Sim v060 [14]

A positioning error rate is difference between a real coor-dinate and an estimated coordinate Therefore we evaluatethe accuracy as the distance error rate between the real

coordinate of a node and the coordinate of its estimated posi-tion Equation (5) for a real distance and a positioning coordi-nate is used

Position Error (119877) =radic(1199091015840 minus 119909)

2+ (1199101015840 minus 119910)

2

119903maxtimes 100

(5)

42 Performance Evaluation Results Figure 5 shows the loca-lization results of DV-HOP and the proposed scheme Asshown in Figure 5 our proposed scheme achieves better per-formance than the DV-HOP In Figure 5 black points areanchor nodes and white points are unknown nodes And ablack line is the distance between a real position and an esti-mated position Simulation calculated the average error ratesevery ten times for the proposed and DV-HOP algorithmswhen the communication range is varied from 10m to 30m

Figure 6 shows the average positioning error rate accord-ing to the communication range With the same communi-cation range the position error rate of our proposed schemeis smaller than that of DV-HOP In the case of DV-HOPsince the hop distance is proportional to the communicationrange the accuracy of its positioning is low In the randommode the proposed scheme achieves about 30performanceimprovements over DV-HOP in terms of the positioning

6 International Journal of Distributed Sensor NetworksAv

erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30

Communication range (m)

DV-HOP (random) DV-HOP (Gaussian)Proposed (random) Proposed (Gaussian)

Figure 6 Average positioning error according to the communica-tion range


Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0

Network size (m)50 100 200 500

Figure 7 Average position error according to the network size

accuracy In the non-uniformmodel that has very large devi-ation of density the proposed scheme achieves about 36higher accuracy than DV-HOP The reason is that the pro-posed scheme measures the positions of the nodes by con-sidering their densities As a result our scheme improves theaccuracy of positioning over the existing scheme

Figures 7 and 8 show the average positioning error rateaccording to the network size and the number of sensornodes Figure 7 shows similar positioning error ratio for ourscheme and DV-Hop in the small 50 times 50 scale networkHowever the proposed scheme in the large 500 times 500 scalenetwork improves the accuracy of positioning over DV-HopFigure 8 shows the average positioning error according to thenumber of total nodes Our scheme improves the accuracy ofpositioning by about 49 over DV-Hop on average UnlikeDV-Hop the proposed scheme shows the high position accu-racy as each node has a different 1-hop distance As a resultour scheme has an advantage that it can be applied to variousenvironments because it has high accuracy in the large scalenetwork as well as the small scale network


Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0

Number of distributed sensor nodes (EA)50 100 200 500

Figure 8 Average positioning error according to the sensor nodes

5 Conclusion

In this paper we have proposed the sensor positioningscheme using density probability models in non-uniformwireless sensor networks that considered characteristics ofthe sensor node deploymentThe proposed scheme estimatesthe distance between nodes using the characteristics of den-sity in non-uniform sensor network environments The pro-posed scheme performs error correction between the esti-mated distance and the real distance Therefore it is possibleto reduce the positioning error As the results of performanceevaluation the proposed scheme showed that the position-ing accuracy was significantly improved over the existingscheme In the future work we plan to extend our work toestimate the positions of sensor nodes in the case of network-hole occurrence

Acknowledgments

This research was supported by Basic Science Research Pro-gram through the National Research Foundation of Korea(NRF) funded by the Ministry of Education Science andTechnology (2012R1A1A2A10042015) and Technology Devel-opment Program for ldquoAgriculture and Forestryrdquo or ldquoFoodrdquo orldquoFisheriesrdquo and Ministry for Food Agriculture Forestry andFisheries Republic of Korea

References

[1] G Chatzimilioudis D Zeinalipour-Yazti and D GunopulosldquoMinimum-hot-spot query trees for wireless sensor networksrdquoin Proceedings of the 9th ACM International Workshop on DataEngineering forWireless andMobile Access (MobiDE rsquo10) pp 33ndash40 June 2010

[2] J Yick B Mukherjee and D Ghosal ldquoWireless sensor networksurveyrdquoComputerNetworks vol 52 no 12 pp 2292ndash2330 2008

[3] G Mao B Fidan and B D O Anderson ldquoWireless sensor net-work localization techniquesrdquo Computer Networks vol 51 no10 pp 2529ndash2553 2007

[4] E Schlecht C Hulsebusch F Mahler and K Becker ldquoThe useof differentially corrected global positioning system to monitor


activities of cattle at pasturerdquoApplied Animal Behaviour Sciencevol 85 no 3-4 pp 185ndash202 2004

[5] J J Caffery Jr ldquoNew approach to the geometry of TOA loca-tionrdquo inProceedings of the 52ndVehicular TechnologyConference(VTC rsquo00) vol 4 pp 1943ndash1949 September 2000

[6] T He C Huang BM Blum J A Stankovic and T AbdelzaherldquoRange-free localization schemes for large scale sensor net-worksrdquo in Proceedings of the 9th Annual International Confer-ence on Mobile Computing and Networking (MobiCom rsquo03) pp81ndash95 September 2003

[7] D Niculescu and B Nath ldquoDV based positioning in Ad Hocnetworksrdquo Telecommunication Systems vol 22 no 1ndash4 pp 267ndash280 2003

[8] W-W Ji and Z Liu ldquoAn improvement of DV-Hop algorithmin wireless sensor networksrdquo in Proceedings of the Interna-tional Conference onWireless Communications Networking andMobile Computing (WiCOM rsquo06) pp 1ndash4 September 2006

[9] H Chen K Sezaki P Deng and H C So ldquoAn improved DV-Hop localization algorithmwith reducednode location error forwireless sensor networksrdquo IEICE Transactions on Fundamentalsof Electronics Communications and Computer Sciences vol E91-A no 8 pp 2232ndash2236 2008

[10] P-H Huang J-L Chen Y T Larosa and T-L Chiang ldquoEsti-mation of distributed fermat-point location for wireless sensornetworkingrdquo Sensors vol 11 pp 4358ndash4371 2011

[11] F Thomas and L Ros ldquoRevisiting trilateration for robot local-izationrdquo IEEE Transactions on Robotics vol 21 no 1 pp 93ndash1012005

[12] O Johnson InformationTheory and the Central Limit TheoremWorld Scientific 2004

[13] A William Central Limit Theorem International Encyclopediaof the Social Sciences 2008

[14] J-Sim httpwwwj-simzcucz

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



range-free schemes measure the distance and estimate theposition through the connection information between nodesand the position information of an anchor node In additionit is efficient in the energy consumption and the cost to con-struct the network because only an anchor node is equippedwith GPS module Therefore the positioning schemesthrough the anchor nodes have been actively studied Theexisting schemes estimated the distance between nodes anddecided the position in the uniform sensor network environ-ments without considering density However in real applica-tions since sensors are distributed on the sensing fields ran-domly through aircrafts missile and so on the nonuniformsensor network environments are constructed in specificareas [10]Therefore the positioning schemes for the uniformsensor network environments are not suitable for the actualsituations since their error rates of density probability are veryhigh in the non-uniform sensor network environments

To solve the problem of the existing range-free schemeswe propose a novel positioning scheme by using the densityprobability model in the non-uniform network environmentIn the proposed scheme theminimumanchor nodes are usedand the distance is estimated according to the density in thenon-uniform sensor network environments By doing so thecost to construct the sensor network can be minimized andthe positioning precision can be improved

The remainder of this paper is organized as followsSection 2 overviews the existing positioning schemes in thewireless sensor networks and analyzes their problems InSection 3 we present our sensor positioning scheme usingdensity probability models in non-uniform wireless sensornetworks Section 4 shows the simulated experiments andcompares the existing scheme with the proposed schemeFinally we present concluding remarks in Section 5

2 Related Work

21 Range-Based Positioning Schemes Range-based schemesuse absolute point-to-point distance or angle informationto calculate positions between neighboring sensors usingextra communicationmodules After this the node estimatesposition of unknown nodes by trilateration algorithm [11]Common approaches for range-based schemes include Timeof Arrival (ToA) Time Difference of Arrival (TDoA) andAngle of Arrival (AoA) for this algorithm [3] ToA and TDoAmeasure signal arrival time or the difference of arrival timesto calculate distance based on transmission time and speedThey can be applied tomany different kinds of signals such asRF acoustic and ultrasound signals

Range-based positioning schemes such as ToA TDoAand AoA suffer from the positioning errors since wirelesschannels are very sensitive to the surrounding environmentwhen they use the strength and arrival time of each signalfor positioning ToA TDoA and AoA also have problemssuch as the usage of additional equipments additional costsand large energy consumption due to extra modules for asynchronization system among sensor nodes Therefore therange-based schemes in the wireless sensor network have adifficulty to positioning

L1

L2

A

L340 m

75 m

100 m

Figure 1 Example of DV-HOP estimated distance

22 Range-Free Positioning Schemes DV-HOP algorithm [7]and improved DV-HOP scheme [8 9] are range-free andmulti-hop routing positioning scheme in wireless sensornetworksThey measure the positions of the unknown nodesby using the average distance of 1-hop between anchor nodesDV-HOP algorithm is composed of steps as follows

Firstly each anchor node broadcasts a beacon framecontaining its position with a hop-count value initialized to0 to be flooded throughout the networkThen the nodes thatreceive the information of anchor nodes store the cumulatedhop counts from the anchor nodes to themselves and thepositions of the anchor nodes After that all of the nodescalculate average 1-hop distance through the hop count fromeach anchor node to themselves The average 1-hop distanceof anchor node 119894 is estimated using (1) Here ℎ

119894119895is the mini-

mum hop count of anchor nodes 119894 and 119895 and (119909119894 119910119894) and

(119909119895 119910119895) are their coordinates As a result 119862

119894119895is the calculated

average 1-hop distance In the example in Figure 1 nodes L1L2 and L3 are anchor nodes Consider

119862119894119895=

sumradic(119909119894minus 119909119895)2

+ (119910119894minus 119910119895)2

sumℎ119894119895

119894 = 119895(1)

In a similar manner the estimated average distances of1-hop of L2 and L3 are 1642m and 1590m respectivelyUnknown node A selects 1-hop distance of anchor node L2as the average 1-hop distance since node L2 has the shortestpath for the node A compared with nodes L1 and L3 Andthen node A calculates the estimated distance from threeanchor nodes anchor nodes 119894 119895 and 119896 as (2) Finally nodeA is assuming its position from three anchor nodes using tri-lateration Consider

119863119894= ℎ119886119894times 119862119894119895 (119894 = 1 2 3 119899) (2)

DV-HOP causes lower positioning error and uses feweranchor nodes than the existing schemes However in non-uniform environments where each area has a different den-sity DV-HOP causes higher positioning errors DV-HOPshould also distribute many anchor nodes to increase posi-tioning accuracyTherefore we propose the node density pro-bability model and the positioning scheme to overcome theproblems of DV-HOP






Step 1


Step 2


















Cumulated hop 119899119894 119899119894+1 119899

119894+119899

120579 = 360998400

a






25 m 23 m 21 m 14 m17 m 17 m

21 m

148 m

100 m

Anchor node

Refining node

Neighbor node

A1

A2



119889Est(119896) =radic12058711990323

120587= radic1199032

3 119899 = 2

119889Est(119896) =radic1199032

119899 + 1 119899 ge 3

(3)



119889estminusAll(119896) =119894

sum

Node ID(119896)=0119889Est(119896) +

119895

sum

Node ID(119896)=0119889Est(119896) 119894 = 119895

119889Real(119894119895) = radic(119909119894 minus 119909119895)2

+ (119910119894minus 119910119895)2















2+ (1199101015840 minus 119910)

2

119903maxtimes 100

(5)




erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30





Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0






Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0



5 Conclusion


Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Step 1


Step 2


















Cumulated hop 119899119894 119899119894+1 119899

119894+119899

120579 = 360998400

a






25 m 23 m 21 m 14 m17 m 17 m

21 m

148 m

100 m

Anchor node

Refining node

Neighbor node

A1

A2



119889Est(119896) =radic12058711990323

120587= radic1199032

3 119899 = 2

119889Est(119896) =radic1199032

119899 + 1 119899 ge 3

(3)



119889estminusAll(119896) =119894

sum

Node ID(119896)=0119889Est(119896) +

119895

sum

Node ID(119896)=0119889Est(119896) 119894 = 119895

119889Real(119894119895) = radic(119909119894 minus 119909119895)2

+ (119910119894minus 119910119895)2















2+ (1199101015840 minus 119910)

2

119903maxtimes 100

(5)




erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30





Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0






Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0



5 Conclusion


Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Cumulated hop 119899119894 119899119894+1 119899

119894+119899

120579 = 360998400

a






25 m 23 m 21 m 14 m17 m 17 m

21 m

148 m

100 m

Anchor node

Refining node

Neighbor node

A1

A2



119889Est(119896) =radic12058711990323

120587= radic1199032

3 119899 = 2

119889Est(119896) =radic1199032

119899 + 1 119899 ge 3

(3)



119889estminusAll(119896) =119894

sum

Node ID(119896)=0119889Est(119896) +

119895

sum

Node ID(119896)=0119889Est(119896) 119894 = 119895

119889Real(119894119895) = radic(119909119894 minus 119909119895)2

+ (119910119894minus 119910119895)2















2+ (1199101015840 minus 119910)

2

119903maxtimes 100

(5)




erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30





Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0






Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0



5 Conclusion


Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















2+ (1199101015840 minus 119910)

2

119903maxtimes 100

(5)




erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30





Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0






Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0



5 Conclusion


Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










erag

e pos

ition

ing

erro

r (

) 100908070605040302010

010 15 20 25 30





Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0






Aver

age p

ositi

onin

g er

ror (

) 100

908070605040302010

0



5 Conclusion


Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









A Sensor Positioning Scheme with High Accuracy in Nonuniform

Documents

Transcript of A Sensor Positioning Scheme with High Accuracy in Nonuniform