Research ArticleA Game-Based Secure Localization Algorithm forMobile Wireless Sensor Networks

Tianyue Bao12 Jiangwen Wan1 Kefu Yi1 and Qiang Zhang1

1School of Instrumentation Science and Optoelectronics Engineering Beijing University of Aeronautics andAstronautics (Beihang University) Beijing 100191 China2Northeast Petroleum University Daqing 163318 China

Correspondence should be addressed to Jiangwen Wan jwwanbuaaeducn

Received 25 March 2015 Revised 23 June 2015 Accepted 3 August 2015

Academic Editor Feng Hong

Copyright copy 2015 Tianyue Bao 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

The issue of node localization is a fundamental problem in wireless sensor networks Recently the localization problem for mobilesensor networks in hostile environment has received significant attention Due to the mobility of the sensor nodes it is morechallenging to achieve node localization in attacked sensor networks than in static ones To address these challenges the paperpresents a novel game-based secure localization algorithm The nodesrsquo strategy level can be indicated through the results of trustevaluation and then by means of constructing reasonable strategy space and payoff function using game theory all kinds ofnodes within the network can achieve the optimal payoffs The performance of our algorithm is evaluated by extensive simulationexperiments The simulation results show that the localization error of our proposed algorithm is lower than those of the existingones in attacked environment

1 Introduction

With the development of microcomputer technology mobilewireless sensor networks (MWSNs) are widely used in manyfields such as underwater sensor border detection andanimal tracking [1 2] Location awareness is very importantbecause many applications of MWSNs depend on the infor-mation of locations of sensor nodes Localization is to obtainthe nodes position [3 4]

In most existing sensor networks nodes are static How-ever in some modern applications localizations become adifficulty when nodes are moving and being attacked [5] Amobile node is unable to receive location information rapidlyand accurately when it is attacked [6] The false coordinatesor distance estimationwill cause amajor localization error fornormal sensor nodes In this case some methods should beexplored to eliminate or reduce the adverse influence causedby malicious beacon nodes and ensure safe localization inmobile WSNs

In this paper we propose a game-based security local-ization (GSL) algorithm for solving the mobile node self-localization problem with the existence of malicious node

Firstly node in multiple hop transmission decides the behav-ior grade according to the time and space informationSecondly according to the behavior grade the completemultirisk level strategy space is constructed and is updatedover time Finally node selects a behavior grade to obtainoptimal benefits Simulation experiment results show that thealgorithm can effectively restrain nodersquos malicious behaviorsand boost the cooperation ability of the network The local-ization error with GSL is lower than those without GSL inmobile and attacked environment

The remainder of this paper is organized as followsSection 2 introduces related works on secure localizationalgorithms Section 3 presents the network model attackmodel and game model Section 4 provides the detail ofGSL algorithm Section 5 presents the simulation results andSection 6 concludes the paper

2 Related Works

The research in security localization algorithm for wirelesssensor networks is mainly divided into two methods Thefirst method is based on sensor nodes It can prevent nodes

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 642107 8 pageshttpdxdoiorg1011552015642107

2 International Journal of Distributed Sensor Networks

from being affected by the attack through the establishmentof protection mechanisms (Verifiable Multilateration SeR-Loc etc) or removing malicious nodes from the networkusing the effective detection and filtering methods (DRBTSARMMSE and a voting-based algorithm etc) The secondmethod is based on security equipment It can improvethe defense capability of the network by adding securityequipment in the physical layer

Lazos et al [7] present a robust positioning system calledROPE which utilizes a location verification technique toidentify the location claims of the sensor nodes before datacollection

Yang et al [8] analyze the outlier data detection problemand design a stray monitoring algorithm based on generalcycle bilateration which reduced to data from the group toimprove localization accuracy

Yu et al [9] propose a BRS-based robust secure local-ization (BRSL) algorithm aiming at reducing the impact ofthe malicious attackers in the network The BRSL methodincludes two phases the setup trust evaluation frameworkand the localization stage

Wei and Guan [10] introduce a novel scheme calleda lightweight positioning verification algorithm (LPVA) itdoes not rely on dedicated hardware equipment under thecondition of network attack resistance and can be used in thelow-cost network

Xiao et al [11] propose a robust network localizationalgorithm call RobustLoc based on a robust patch mergingoperation that can reject outliers for both multilateration andpatch merging

The above studies mainly eliminate the fake beacon infor-mation (ROPE RobustLoc etc) or detect malicious nodes(LPVA BRSL etc) or increase equipment to improve local-ization accuracy but seldom deal with action information ofsensor nodes when nodes are mobile Our proposal utilizedan improved game theory and the sensor nodesrsquo pluralisticbehavior in the network to establish a trust-preferentialstrategy which make the beacons cooperate effectively

3 Network Model

31 Network Environment In an environment under attacka mobile wireless sensor network consists of anchor nodesunknown nodes and malicious nodes nodes with knowncoordinates are called anchor nodes nodes whose coordi-nates are unknown are called unknown nodes and nodeswhich are captured and possibly attack are called maliciousnodes All nodes are randomly distributed in the two-dimensional space of the network and on the move

As shown in Figure 1 the communication radius of eachnode in the network is represented by 119903 and the maximummoving speed is represented by119881max Each node has a uniqueID and the coordinates of unknown nodes are estimatedby obtaining the coordinate information of adjacent anchornodes

32 AttackModel In the sequentialMonte-Carlo localizationalgorithm coordinates of unknown nodes are calculated

b1

b2

b3b4

b5

b6

b7 b8

b9

b10

N

d1

d2

d3d4

d5

d6

d8

d7d10

d12

d9

d11

Attack channel

a1

a2

2r

2r

Figure 1 Attack model with long attack distance

N

a1

a2

2r2r

b1

b2

b3b4

b5

b6

b7 b8

b9

b10

d1

d7d2

d3d4

d5

d6

d9d8

d10

d11

d12

Attack channel

Figure 2 Attack model with short attack distance

through sample set [12] The unknown node will selectlocations of anchor nodes within single hop and two hopsas members of the sample set and therefore the accuracyof location information of anchor nodes within this scopedetermines the accuracy of positioning [13] The attackmodels used in this paper are shown in Figures 1 and2 The unknown node 119873 can monitor the informationof anchor nodes (1198871ndash1198876) Meanwhile it may be attackedby the malicious node 1198861 The malicious node 1198861 obtainsthe information of anchor nodes (1198877ndash11988710) provided by 1198862(from the region of 1198862) through the attack channel andtransmits this information to the unknown nodes Nodesto be positioned will mistakenly take such beacon nodesas reference information within its two-hop range causinglocalization errors of unknown nodes We assume that theattack channel between malicious nodes is independent ofdistance Potential cases of attacks are shown in Figure 1where the distance between malicious nodes is long andestimation of coordinates of unknown nodes based oncoordinates transmitted by malicious nodes will cause largeerrors In Figure 2 the distance between malicious nodesis relatively short and the two-node scopes of maliciousnodes have an area of intersection in which the node 1198876 islocated

In a multihop network we use 119879 to represent the timeof each hop For the unknown node119873 the distance betweenit and 1198891ndash1198896 is one hop and the communication time is 119879

International Journal of Distributed Sensor Networks 3

To obtain data 1198897 channel has to cover three hops so itscommunication time is 3119879

33 Game Model

331 Game Participants In the process of mobile position-ing every unknown node will obtain the information of bea-con nodes within one hop or two hops [14] For attacks whichmay exist in data transmission links all nodes involved in thetransmission of information are gameparticipantsThereforeparticipants in the game model include information sender119879 information recipient 119877 and 119899 information forwarders 119864Throughout information transmission the data sent by thesending nodemay travel through 119899 forwarding nodes to reachthe receiving node so the number of participants of the gameis 119899 + 2

332 Strategy Space In this paper we define the strategyspace according to the different behaviors of nodes Nodebehaviors include cooperative uncooperative and attackbehavior According to the different attack effect the attackbehavior is divided into 119899 level and the attack level isdetermined by the attack effect For example the influenceof the attack in Figure 1 is much greater than that in Figure 2so the attack level in Figure 1 is higher than in Figure 2 Wedivide node actions into multiple levels according to theireffects We call the behaviors taken by nodes which areshown in Table 1 strategy space

In the strategy space set of nodes 119866 = 119862119880 1198601

1198602 119860

119899 119862 119880 represent cooperative behaviors and

uncooperative behaviors respectively Cooperative behaviorsrefer to the cooperative response of nodes such as receiv-ing or forwarding after listening to signals Uncooperativebehaviors refer to the fact that the nodes do not deal with theinformation which needs receiving or forwarding that is noresponse will be carried out where the set 119860

1 1198602 119860

119899

represents a collection of different levels of attacks Attacklevel depends on the degree of influence of reference coordi-nates on the positioning accuracy In the positioning processfor example different attacks have different effects on theaccuracy of positioning The longer the distance betweenfalse coordinates and actual coordinates (Figure 1) is thestronger the attackrsquos destructive power will be the bigger thepositioning error will be and the higher the attack level willbe The false coordinate information (Figure 2) with shortdistance can help localization when anchor nodes are sparseso its attack level is low

333 Game Payoff In the game process of transmission ofpositioning information the payoff of a participant afterchoosing a strategy at the moment of 119905 can be 119906

119896(119905) where

119896(119905) isin 119866 For the attack nodes and each informationsender every gamer who participates in the informationtransmission will choose a behavior mode in the strategyspace 119866 resulting in payoff The payoff of gamers comesmainly from the gain obtained by behaviors 119898

119896(119905)and their

own loss 119888119896(119905)

and therefore the payoff function is 119906119896(119905)

=

119898119896(119905)

minus 119888119896(119905)

119896(119905) isin 119866 The information recipient will obtain

Table 1 Strategy space of nodes

Symbol identification Behavior mode119862 Cooperative119880 Uncooperative1198601

Level 1 attack1198602

Level 2 attack

119860119899

Level 119899 attack

the maximum payoff from the correct information providedor forwarded by the sending node or forwarding node Onthe contrary rejection or attack will reduce the payoff At themoment of 119905 the payoff function of normal nodes can beexpressed as 119906

119862(119905) ge 119906

119880(119905) ge 0 ge 119906

1198601

(119905) ge sdot sdot sdot ge 119906119860119899

(119905)while the payoff function of attack nodes can be expressed as119906119860119899

(119905) ge sdot sdot sdot ge 1199061198601

(119905) ge 0 ge 119906119880(119905) ge 119906

119862(119905)

334 Trust Level In the attack models mentioned abovethe attacks are characterized by changing time referenceand tampering with the spatial reference Changes of timereference reflect on the increase of the number of hops fromthe beacon node to the receiving node Information of eachanchor node obtained by unknown nodes has time weightswhich can be used to determine attack payoff The biggerthe time weight is the greater the attack payoff will beand so the higher the influence of attacks on the accuracyof coordinates of unknown nodes will be In Figure 1 themalicious coordinate data of the beacon node 1198877 reachesthe unknown node 119873 through 3 hops of which the timeinformation is 3119879 (119879 is the time interval of each segment)Obviously the longer the time is the greater the influence ofattacks on positioning will be Tampering of spatial referencedata reflects on the fact that coordinate information ischanged by the malicious node In Figure 1 the maliciousnode 1198861 changes its coordinates to the coordinates of 1198877ndash11988710and the distance between these coordinates and the node tobe positioned is much larger than two hops of the unknownnode 119873 seriously affecting the positioning accuracy of theunknown node

Dempster Shafer (abbreviated D-S) evidence theory isadopted in this paper to calculate the trust values [15] basedon the data information of time and space Trust levels aredefined by trust values We use three variables 119886

119894 119887119894 119888119894 to

quantify the degree of a node behavior 119886119894represents the

measurement of a note that is not attacked 119887119894represents

the measurement of a note that has been attacked and 119888119894

represents the measurement of a note whose behavior isunknownThemeasurement of node behavior can be dividedinto the following situations

(1) Measurement analysis of behavior of time parameterAssuming that 120573

119905= (119905 minus Δ119905)Δ119905

1198861015840

119894= 1198861015840

119894+ 1

1198871015840

119894= 1198871015840

119894

4 International Journal of Distributed Sensor Networks

1198881015840

119894= 1198881015840

119894

minus 1 le 120573119905le 1

1198861015840

119894= 1198861015840

119894

1198871015840

119894= 1198871015840

119894+ 120573119905

1198881015840

119894= 1198881015840

119894

120573119905gt 1

(1)

(2) Measurement analysis of behavior of spatialparameter To represent the Euclidean distancebetween any two beacon nodes we use119889119894119895= radic(119909

119894minus 119909119895)2+ (119910119894minus 119910119895)2

119886119894119895= 119886119894119895+ 1

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895

0 le 119889119894119895le 2119903

119886119894119895= 119886119894119895

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895+ [

119889119894119895minus 2119903

119903

]

119889119894119895gt 2119903

(2)

(3) Quantitative classification of trust levels If there isinformation of 119899 anchor nodes around the unknownnode we can determine the quantized values of eachnode based on the measurement of time and spacewith the following formula

119898119894(119860) =

11988610158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119861) =

11988710158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119862) =

11988810158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

(3)

where 11988610158401015840119894= 1198861015840

119894+119886119894 11988710158401015840119894= 1198871015840

119894+119887119894 and 11988810158401015840

119894= 1198881015840

119894+119888119894 where

119860 119861 and 119862 represent three exclusive trust states ofnodes namely ldquotrustrdquo ldquodistrustrdquo and ldquouncertaintyrdquo

(4) In our scheme a distinguished frameworkΘ = [119860 119861119862] is set up firstly The power set of Θ is 2Θ =

0 119860 119861 119862 119860 119861 119860 119862 119861 119862 119860 119861 119862Thenthe basic probability assignment (BPA) function isconstructed that is 119898 2

Θrarr [0 1] For 0 is

Nminus 1

N + 2le M lt

N

N+ 2

N minus 2

N + 2le M lt

Nminus 1

N + 2

0 le M lt1

N + 2

N

N+ 2le M lt

N+ 1

N + 2

N + 2le M lt 1

A1

A2

An

U

C

N+ 1

N + 2

1

N minus 1

N

N+ 1

Figure 3 Action-trust based mapping rule

an empty set and 119860 119861 119860 119862 119861 119862 119860 119861 119862 areconsidered to be impossible events in this paper weget 119898(0) = 119898(119860 119861) = 119898(119860 119862) = 119898(119861 119862) = 119898(119860 119861119862) = 0

335 Level Mapping By the above methods the timeand space parameters of mobile positioning can be con-verted into trust levels and a parameter 119872 can be deter-mined in the trust levels of each node where 119872 =

MAX119898(119860)119898(119861)119898(119862) The game space of behaviors of anode is 119860

1 1198602 119860

119899 119880 119862 consisting of 119899 + 2 elements

We construct the following rules (Figure 3) to map the trustvalue to game behavior one by oneThe bigger the trust valueis the higher level the mapped behavior will be The trustlevels of nodes can be used to identify the elements of thebehavior space by establishing the mapping relationship

4 Game Calculation with Strategy Evolution

41 Strategic Game Every node has a trust vector 119879 =

(1198791198601

1198791198602

119879119880 119879119881)119879 so we define the behavior game space

of each node as 119895 isin 1198601 1198602 119860

119899 119880 119862 In the mapping

relationship every element of the trust vector 119872 is theprobability of the behavior space hence 0 le 119879

119895le 1 and

sum119873+2

119895=1119879119895= 1

We assume that in the process of positioning thebehavior of the information sender is identified as 119894

and the behavior of participating node is identifiedas 119895 where 119894 119895 isin 119860

1 1198602 119860

119899 119880 119862 We define

the trust assignment relationship matrix as 119879119894119895 then

the element of this matrix model is the trust levelof a node when it faces the sender with the behavior

International Journal of Distributed Sensor Networks 5

identification of 119895 and the mode selection identification of119894

[119879119894119895](119873+2)times(119873+2)

= 120579

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

119873 119873 minus 1 sdot sdot sdot

1 1 1

119873 + 2 119873 + 2 119873 + 1

1 119873 + 1 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

+ (1 minus 120579)

sdot

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 1 119873 + 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

1 1 1

119873 + 1 119873 + 1 119873 + 1

119873 + 2 119873 + 2 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

(4)

The matrix 119879119894119895

defines the trust level identifications of anode based on different behaviors of the information senderwhen the node is receiving the information (120579 = 0) andforwarding the information (120579 = 1) For example when thereceiving node or forwarding node receives the behavior ofthe information sender A1 the higher the level of the selectedattack is the lower its trust value will be

For a node the purpose of adopting strategic gameduring positioning is to choose a behavior with higher trust

degree through behavior identification thus achieving thebest positioning results According to this rule the expectedbehavior of each node which participates in the game is 119879lowast

119879lowast= 120579

[

[

[

[

[

[

[

119880 (119873 + 1)

119880 (119873 + 1)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

+ (1 minus 120579)

[

[

[

[

[

[

[

119862 (119873 + 2)

119862 (119873 + 2)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

(5)

42 Update Mechanism At the initial phase the node has ahigher willingness to collaborate and its initial trust vector isdefined as 119879(0) = (0 0 0 1)

119879 At the time point of 119905 thelevel identification of instantaneous trust119870

119894119895can be obtained

according to the trust matrix [119879119894119895](119873+2)times(119873+2)

the relay nodeidentity 120579 the behavior identity of the information transmis-sion node 119895 and the behavior identity of the participatingnode 119894

The update equation of the trust vector can be expressedas

119879 (119905 + 1) = A (120575119894119895119879 (119905) + (1 minus 120575

119894119895)119870119894119895) (6)

where 120575119894119895

is the time factor 120575119894119895

= (1205751198601

1205751198602

120575119880 120575119881)

describing the degree of coupling between the transient effectand the trust vector of the previous moment The greaterthe 120575 is the more dependent the trust vector will be on thevalue of the previous moment in the system whereas theinstantaneous trust has a relatively small impact on it andvice versa A is the trust transmission matrix whose roleis to overcome the misjudgment of the trust victor causedby monitoring errors or transmission mistakes The specificform is below

119860(119873+2)times(119873+2)

=

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

119901119873

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

1 minus 119901119873minus1

119873 + 2

119901119873minus1

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 1199011

119873 + 2

sdot sdot sdot

1 minus 1199011

119873 + 2

1199011

1 minus 1199011

119873 + 2

1 minus 1199011

119873 + 2

1 minus 119901119873+1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873+1

119873 + 2

119901119873+1

1 minus 119901119873+1

119873 + 2

1 minus 119901119873+2

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 119901119873+2

119873 + 2

119901119873+2

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

(7)

where 119901119873represents the probability of the trust level being

correctly identified

43 The Conditions of Game Equilibrium In the process ofmobile localization the steady-state convergence condition

of the above mentioned game model is solved by meansof evolutionary game ideas and principles for maximizingpayoffAccording to the evolutionary game theory when thesystem is in initial operation each member node 119899 thatparticipates in localization selects the appropriate actionparticipation way in accordance with the expectation action

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

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RotatingMachinery

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Journal ofEngineeringVolume 2014

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

from being affected by the attack through the establishmentof protection mechanisms (Verifiable Multilateration SeR-Loc etc) or removing malicious nodes from the networkusing the effective detection and filtering methods (DRBTSARMMSE and a voting-based algorithm etc) The secondmethod is based on security equipment It can improvethe defense capability of the network by adding securityequipment in the physical layer

Lazos et al [7] present a robust positioning system calledROPE which utilizes a location verification technique toidentify the location claims of the sensor nodes before datacollection

Yang et al [8] analyze the outlier data detection problemand design a stray monitoring algorithm based on generalcycle bilateration which reduced to data from the group toimprove localization accuracy

Yu et al [9] propose a BRS-based robust secure local-ization (BRSL) algorithm aiming at reducing the impact ofthe malicious attackers in the network The BRSL methodincludes two phases the setup trust evaluation frameworkand the localization stage

Wei and Guan [10] introduce a novel scheme calleda lightweight positioning verification algorithm (LPVA) itdoes not rely on dedicated hardware equipment under thecondition of network attack resistance and can be used in thelow-cost network

Xiao et al [11] propose a robust network localizationalgorithm call RobustLoc based on a robust patch mergingoperation that can reject outliers for both multilateration andpatch merging

The above studies mainly eliminate the fake beacon infor-mation (ROPE RobustLoc etc) or detect malicious nodes(LPVA BRSL etc) or increase equipment to improve local-ization accuracy but seldom deal with action information ofsensor nodes when nodes are mobile Our proposal utilizedan improved game theory and the sensor nodesrsquo pluralisticbehavior in the network to establish a trust-preferentialstrategy which make the beacons cooperate effectively

3 Network Model

31 Network Environment In an environment under attacka mobile wireless sensor network consists of anchor nodesunknown nodes and malicious nodes nodes with knowncoordinates are called anchor nodes nodes whose coordi-nates are unknown are called unknown nodes and nodeswhich are captured and possibly attack are called maliciousnodes All nodes are randomly distributed in the two-dimensional space of the network and on the move

As shown in Figure 1 the communication radius of eachnode in the network is represented by 119903 and the maximummoving speed is represented by119881max Each node has a uniqueID and the coordinates of unknown nodes are estimatedby obtaining the coordinate information of adjacent anchornodes

32 AttackModel In the sequentialMonte-Carlo localizationalgorithm coordinates of unknown nodes are calculated

b1

b2

b3b4

b5

b6

b7 b8

b9

b10

N

d1

d2

d3d4

d5

d6

d8

d7d10

d12

d9

d11

Attack channel

a1

a2

2r

2r

Figure 1 Attack model with long attack distance

N

a1

a2

2r2r

b1

b2

b3b4

b5

b6

b7 b8

b9

b10

d1

d7d2

d3d4

d5

d6

d9d8

d10

d11

d12

Attack channel

Figure 2 Attack model with short attack distance

through sample set [12] The unknown node will selectlocations of anchor nodes within single hop and two hopsas members of the sample set and therefore the accuracyof location information of anchor nodes within this scopedetermines the accuracy of positioning [13] The attackmodels used in this paper are shown in Figures 1 and2 The unknown node 119873 can monitor the informationof anchor nodes (1198871ndash1198876) Meanwhile it may be attackedby the malicious node 1198861 The malicious node 1198861 obtainsthe information of anchor nodes (1198877ndash11988710) provided by 1198862(from the region of 1198862) through the attack channel andtransmits this information to the unknown nodes Nodesto be positioned will mistakenly take such beacon nodesas reference information within its two-hop range causinglocalization errors of unknown nodes We assume that theattack channel between malicious nodes is independent ofdistance Potential cases of attacks are shown in Figure 1where the distance between malicious nodes is long andestimation of coordinates of unknown nodes based oncoordinates transmitted by malicious nodes will cause largeerrors In Figure 2 the distance between malicious nodesis relatively short and the two-node scopes of maliciousnodes have an area of intersection in which the node 1198876 islocated

In a multihop network we use 119879 to represent the timeof each hop For the unknown node119873 the distance betweenit and 1198891ndash1198896 is one hop and the communication time is 119879

International Journal of Distributed Sensor Networks 3

To obtain data 1198897 channel has to cover three hops so itscommunication time is 3119879

33 Game Model

331 Game Participants In the process of mobile position-ing every unknown node will obtain the information of bea-con nodes within one hop or two hops [14] For attacks whichmay exist in data transmission links all nodes involved in thetransmission of information are gameparticipantsThereforeparticipants in the game model include information sender119879 information recipient 119877 and 119899 information forwarders 119864Throughout information transmission the data sent by thesending nodemay travel through 119899 forwarding nodes to reachthe receiving node so the number of participants of the gameis 119899 + 2

332 Strategy Space In this paper we define the strategyspace according to the different behaviors of nodes Nodebehaviors include cooperative uncooperative and attackbehavior According to the different attack effect the attackbehavior is divided into 119899 level and the attack level isdetermined by the attack effect For example the influenceof the attack in Figure 1 is much greater than that in Figure 2so the attack level in Figure 1 is higher than in Figure 2 Wedivide node actions into multiple levels according to theireffects We call the behaviors taken by nodes which areshown in Table 1 strategy space

In the strategy space set of nodes 119866 = 119862119880 1198601

1198602 119860

119899 119862 119880 represent cooperative behaviors and

uncooperative behaviors respectively Cooperative behaviorsrefer to the cooperative response of nodes such as receiv-ing or forwarding after listening to signals Uncooperativebehaviors refer to the fact that the nodes do not deal with theinformation which needs receiving or forwarding that is noresponse will be carried out where the set 119860

1 1198602 119860

119899

represents a collection of different levels of attacks Attacklevel depends on the degree of influence of reference coordi-nates on the positioning accuracy In the positioning processfor example different attacks have different effects on theaccuracy of positioning The longer the distance betweenfalse coordinates and actual coordinates (Figure 1) is thestronger the attackrsquos destructive power will be the bigger thepositioning error will be and the higher the attack level willbe The false coordinate information (Figure 2) with shortdistance can help localization when anchor nodes are sparseso its attack level is low

333 Game Payoff In the game process of transmission ofpositioning information the payoff of a participant afterchoosing a strategy at the moment of 119905 can be 119906

119896(119905) where

119896(119905) isin 119866 For the attack nodes and each informationsender every gamer who participates in the informationtransmission will choose a behavior mode in the strategyspace 119866 resulting in payoff The payoff of gamers comesmainly from the gain obtained by behaviors 119898

119896(119905)and their

own loss 119888119896(119905)

and therefore the payoff function is 119906119896(119905)

=

119898119896(119905)

minus 119888119896(119905)

119896(119905) isin 119866 The information recipient will obtain

Table 1 Strategy space of nodes

Symbol identification Behavior mode119862 Cooperative119880 Uncooperative1198601

Level 1 attack1198602

Level 2 attack

119860119899

Level 119899 attack

the maximum payoff from the correct information providedor forwarded by the sending node or forwarding node Onthe contrary rejection or attack will reduce the payoff At themoment of 119905 the payoff function of normal nodes can beexpressed as 119906

119862(119905) ge 119906

119880(119905) ge 0 ge 119906

1198601

(119905) ge sdot sdot sdot ge 119906119860119899

(119905)while the payoff function of attack nodes can be expressed as119906119860119899

(119905) ge sdot sdot sdot ge 1199061198601

(119905) ge 0 ge 119906119880(119905) ge 119906

119862(119905)

334 Trust Level In the attack models mentioned abovethe attacks are characterized by changing time referenceand tampering with the spatial reference Changes of timereference reflect on the increase of the number of hops fromthe beacon node to the receiving node Information of eachanchor node obtained by unknown nodes has time weightswhich can be used to determine attack payoff The biggerthe time weight is the greater the attack payoff will beand so the higher the influence of attacks on the accuracyof coordinates of unknown nodes will be In Figure 1 themalicious coordinate data of the beacon node 1198877 reachesthe unknown node 119873 through 3 hops of which the timeinformation is 3119879 (119879 is the time interval of each segment)Obviously the longer the time is the greater the influence ofattacks on positioning will be Tampering of spatial referencedata reflects on the fact that coordinate information ischanged by the malicious node In Figure 1 the maliciousnode 1198861 changes its coordinates to the coordinates of 1198877ndash11988710and the distance between these coordinates and the node tobe positioned is much larger than two hops of the unknownnode 119873 seriously affecting the positioning accuracy of theunknown node

Dempster Shafer (abbreviated D-S) evidence theory isadopted in this paper to calculate the trust values [15] basedon the data information of time and space Trust levels aredefined by trust values We use three variables 119886

119894 119887119894 119888119894 to

quantify the degree of a node behavior 119886119894represents the

measurement of a note that is not attacked 119887119894represents

the measurement of a note that has been attacked and 119888119894

represents the measurement of a note whose behavior isunknownThemeasurement of node behavior can be dividedinto the following situations

(1) Measurement analysis of behavior of time parameterAssuming that 120573

119905= (119905 minus Δ119905)Δ119905

1198861015840

119894= 1198861015840

119894+ 1

1198871015840

119894= 1198871015840

119894

4 International Journal of Distributed Sensor Networks

1198881015840

119894= 1198881015840

119894

minus 1 le 120573119905le 1

1198861015840

119894= 1198861015840

119894

1198871015840

119894= 1198871015840

119894+ 120573119905

1198881015840

119894= 1198881015840

119894

120573119905gt 1

(1)

(2) Measurement analysis of behavior of spatialparameter To represent the Euclidean distancebetween any two beacon nodes we use119889119894119895= radic(119909

119894minus 119909119895)2+ (119910119894minus 119910119895)2

119886119894119895= 119886119894119895+ 1

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895

0 le 119889119894119895le 2119903

119886119894119895= 119886119894119895

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895+ [

119889119894119895minus 2119903

119903

]

119889119894119895gt 2119903

(2)

(3) Quantitative classification of trust levels If there isinformation of 119899 anchor nodes around the unknownnode we can determine the quantized values of eachnode based on the measurement of time and spacewith the following formula

119898119894(119860) =

11988610158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119861) =

11988710158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119862) =

11988810158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

(3)

where 11988610158401015840119894= 1198861015840

119894+119886119894 11988710158401015840119894= 1198871015840

119894+119887119894 and 11988810158401015840

119894= 1198881015840

119894+119888119894 where

119860 119861 and 119862 represent three exclusive trust states ofnodes namely ldquotrustrdquo ldquodistrustrdquo and ldquouncertaintyrdquo

(4) In our scheme a distinguished frameworkΘ = [119860 119861119862] is set up firstly The power set of Θ is 2Θ =

0 119860 119861 119862 119860 119861 119860 119862 119861 119862 119860 119861 119862Thenthe basic probability assignment (BPA) function isconstructed that is 119898 2

Θrarr [0 1] For 0 is

Nminus 1

N + 2le M lt

N

N+ 2

N minus 2

N + 2le M lt

Nminus 1

N + 2

0 le M lt1

N + 2

N

N+ 2le M lt

N+ 1

N + 2

N + 2le M lt 1

A1

A2

An

U

C

N+ 1

N + 2

1

N minus 1

N

N+ 1

Figure 3 Action-trust based mapping rule

an empty set and 119860 119861 119860 119862 119861 119862 119860 119861 119862 areconsidered to be impossible events in this paper weget 119898(0) = 119898(119860 119861) = 119898(119860 119862) = 119898(119861 119862) = 119898(119860 119861119862) = 0

335 Level Mapping By the above methods the timeand space parameters of mobile positioning can be con-verted into trust levels and a parameter 119872 can be deter-mined in the trust levels of each node where 119872 =

MAX119898(119860)119898(119861)119898(119862) The game space of behaviors of anode is 119860

1 1198602 119860

119899 119880 119862 consisting of 119899 + 2 elements

We construct the following rules (Figure 3) to map the trustvalue to game behavior one by oneThe bigger the trust valueis the higher level the mapped behavior will be The trustlevels of nodes can be used to identify the elements of thebehavior space by establishing the mapping relationship

4 Game Calculation with Strategy Evolution

41 Strategic Game Every node has a trust vector 119879 =

(1198791198601

1198791198602

119879119880 119879119881)119879 so we define the behavior game space

of each node as 119895 isin 1198601 1198602 119860

119899 119880 119862 In the mapping

relationship every element of the trust vector 119872 is theprobability of the behavior space hence 0 le 119879

119895le 1 and

sum119873+2

119895=1119879119895= 1

We assume that in the process of positioning thebehavior of the information sender is identified as 119894

and the behavior of participating node is identifiedas 119895 where 119894 119895 isin 119860

1 1198602 119860

119899 119880 119862 We define

the trust assignment relationship matrix as 119879119894119895 then

the element of this matrix model is the trust levelof a node when it faces the sender with the behavior

International Journal of Distributed Sensor Networks 5

identification of 119895 and the mode selection identification of119894

[119879119894119895](119873+2)times(119873+2)

= 120579

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

119873 119873 minus 1 sdot sdot sdot

1 1 1

119873 + 2 119873 + 2 119873 + 1

1 119873 + 1 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

+ (1 minus 120579)

sdot

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 1 119873 + 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

1 1 1

119873 + 1 119873 + 1 119873 + 1

119873 + 2 119873 + 2 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

(4)

The matrix 119879119894119895

defines the trust level identifications of anode based on different behaviors of the information senderwhen the node is receiving the information (120579 = 0) andforwarding the information (120579 = 1) For example when thereceiving node or forwarding node receives the behavior ofthe information sender A1 the higher the level of the selectedattack is the lower its trust value will be

For a node the purpose of adopting strategic gameduring positioning is to choose a behavior with higher trust

degree through behavior identification thus achieving thebest positioning results According to this rule the expectedbehavior of each node which participates in the game is 119879lowast

119879lowast= 120579

[

[

[

[

[

[

[

119880 (119873 + 1)

119880 (119873 + 1)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

+ (1 minus 120579)

[

[

[

[

[

[

[

119862 (119873 + 2)

119862 (119873 + 2)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

(5)

42 Update Mechanism At the initial phase the node has ahigher willingness to collaborate and its initial trust vector isdefined as 119879(0) = (0 0 0 1)

119879 At the time point of 119905 thelevel identification of instantaneous trust119870

119894119895can be obtained

according to the trust matrix [119879119894119895](119873+2)times(119873+2)

the relay nodeidentity 120579 the behavior identity of the information transmis-sion node 119895 and the behavior identity of the participatingnode 119894

The update equation of the trust vector can be expressedas

119879 (119905 + 1) = A (120575119894119895119879 (119905) + (1 minus 120575

119894119895)119870119894119895) (6)

where 120575119894119895

is the time factor 120575119894119895

= (1205751198601

1205751198602

120575119880 120575119881)

describing the degree of coupling between the transient effectand the trust vector of the previous moment The greaterthe 120575 is the more dependent the trust vector will be on thevalue of the previous moment in the system whereas theinstantaneous trust has a relatively small impact on it andvice versa A is the trust transmission matrix whose roleis to overcome the misjudgment of the trust victor causedby monitoring errors or transmission mistakes The specificform is below

119860(119873+2)times(119873+2)

=

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

119901119873

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

1 minus 119901119873minus1

119873 + 2

119901119873minus1

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 1199011

119873 + 2

sdot sdot sdot

1 minus 1199011

119873 + 2

1199011

1 minus 1199011

119873 + 2

1 minus 1199011

119873 + 2

1 minus 119901119873+1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873+1

119873 + 2

119901119873+1

1 minus 119901119873+1

119873 + 2

1 minus 119901119873+2

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 119901119873+2

119873 + 2

119901119873+2

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

(7)

where 119901119873represents the probability of the trust level being

correctly identified

43 The Conditions of Game Equilibrium In the process ofmobile localization the steady-state convergence condition

of the above mentioned game model is solved by meansof evolutionary game ideas and principles for maximizingpayoffAccording to the evolutionary game theory when thesystem is in initial operation each member node 119899 thatparticipates in localization selects the appropriate actionparticipation way in accordance with the expectation action

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

To obtain data 1198897 channel has to cover three hops so itscommunication time is 3119879

33 Game Model

331 Game Participants In the process of mobile position-ing every unknown node will obtain the information of bea-con nodes within one hop or two hops [14] For attacks whichmay exist in data transmission links all nodes involved in thetransmission of information are gameparticipantsThereforeparticipants in the game model include information sender119879 information recipient 119877 and 119899 information forwarders 119864Throughout information transmission the data sent by thesending nodemay travel through 119899 forwarding nodes to reachthe receiving node so the number of participants of the gameis 119899 + 2

332 Strategy Space In this paper we define the strategyspace according to the different behaviors of nodes Nodebehaviors include cooperative uncooperative and attackbehavior According to the different attack effect the attackbehavior is divided into 119899 level and the attack level isdetermined by the attack effect For example the influenceof the attack in Figure 1 is much greater than that in Figure 2so the attack level in Figure 1 is higher than in Figure 2 Wedivide node actions into multiple levels according to theireffects We call the behaviors taken by nodes which areshown in Table 1 strategy space

In the strategy space set of nodes 119866 = 119862119880 1198601

1198602 119860

119899 119862 119880 represent cooperative behaviors and

uncooperative behaviors respectively Cooperative behaviorsrefer to the cooperative response of nodes such as receiv-ing or forwarding after listening to signals Uncooperativebehaviors refer to the fact that the nodes do not deal with theinformation which needs receiving or forwarding that is noresponse will be carried out where the set 119860

1 1198602 119860

119899

represents a collection of different levels of attacks Attacklevel depends on the degree of influence of reference coordi-nates on the positioning accuracy In the positioning processfor example different attacks have different effects on theaccuracy of positioning The longer the distance betweenfalse coordinates and actual coordinates (Figure 1) is thestronger the attackrsquos destructive power will be the bigger thepositioning error will be and the higher the attack level willbe The false coordinate information (Figure 2) with shortdistance can help localization when anchor nodes are sparseso its attack level is low

333 Game Payoff In the game process of transmission ofpositioning information the payoff of a participant afterchoosing a strategy at the moment of 119905 can be 119906

119896(119905) where

119896(119905) isin 119866 For the attack nodes and each informationsender every gamer who participates in the informationtransmission will choose a behavior mode in the strategyspace 119866 resulting in payoff The payoff of gamers comesmainly from the gain obtained by behaviors 119898

119896(119905)and their

own loss 119888119896(119905)

and therefore the payoff function is 119906119896(119905)

=

119898119896(119905)

minus 119888119896(119905)

119896(119905) isin 119866 The information recipient will obtain

Table 1 Strategy space of nodes

Symbol identification Behavior mode119862 Cooperative119880 Uncooperative1198601

Level 1 attack1198602

Level 2 attack

119860119899

Level 119899 attack

the maximum payoff from the correct information providedor forwarded by the sending node or forwarding node Onthe contrary rejection or attack will reduce the payoff At themoment of 119905 the payoff function of normal nodes can beexpressed as 119906

119862(119905) ge 119906

119880(119905) ge 0 ge 119906

1198601

(119905) ge sdot sdot sdot ge 119906119860119899

(119905)while the payoff function of attack nodes can be expressed as119906119860119899

(119905) ge sdot sdot sdot ge 1199061198601

(119905) ge 0 ge 119906119880(119905) ge 119906

119862(119905)

334 Trust Level In the attack models mentioned abovethe attacks are characterized by changing time referenceand tampering with the spatial reference Changes of timereference reflect on the increase of the number of hops fromthe beacon node to the receiving node Information of eachanchor node obtained by unknown nodes has time weightswhich can be used to determine attack payoff The biggerthe time weight is the greater the attack payoff will beand so the higher the influence of attacks on the accuracyof coordinates of unknown nodes will be In Figure 1 themalicious coordinate data of the beacon node 1198877 reachesthe unknown node 119873 through 3 hops of which the timeinformation is 3119879 (119879 is the time interval of each segment)Obviously the longer the time is the greater the influence ofattacks on positioning will be Tampering of spatial referencedata reflects on the fact that coordinate information ischanged by the malicious node In Figure 1 the maliciousnode 1198861 changes its coordinates to the coordinates of 1198877ndash11988710and the distance between these coordinates and the node tobe positioned is much larger than two hops of the unknownnode 119873 seriously affecting the positioning accuracy of theunknown node

Dempster Shafer (abbreviated D-S) evidence theory isadopted in this paper to calculate the trust values [15] basedon the data information of time and space Trust levels aredefined by trust values We use three variables 119886

119894 119887119894 119888119894 to

quantify the degree of a node behavior 119886119894represents the

measurement of a note that is not attacked 119887119894represents

the measurement of a note that has been attacked and 119888119894

represents the measurement of a note whose behavior isunknownThemeasurement of node behavior can be dividedinto the following situations

(1) Measurement analysis of behavior of time parameterAssuming that 120573

119905= (119905 minus Δ119905)Δ119905

1198861015840

119894= 1198861015840

119894+ 1

1198871015840

119894= 1198871015840

119894

4 International Journal of Distributed Sensor Networks

1198881015840

119894= 1198881015840

119894

minus 1 le 120573119905le 1

1198861015840

119894= 1198861015840

119894

1198871015840

119894= 1198871015840

119894+ 120573119905

1198881015840

119894= 1198881015840

119894

120573119905gt 1

(1)

(2) Measurement analysis of behavior of spatialparameter To represent the Euclidean distancebetween any two beacon nodes we use119889119894119895= radic(119909

119894minus 119909119895)2+ (119910119894minus 119910119895)2

119886119894119895= 119886119894119895+ 1

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895

0 le 119889119894119895le 2119903

119886119894119895= 119886119894119895

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895+ [

119889119894119895minus 2119903

119903

]

119889119894119895gt 2119903

(2)

(3) Quantitative classification of trust levels If there isinformation of 119899 anchor nodes around the unknownnode we can determine the quantized values of eachnode based on the measurement of time and spacewith the following formula

119898119894(119860) =

11988610158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119861) =

11988710158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119862) =

11988810158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

(3)

where 11988610158401015840119894= 1198861015840

119894+119886119894 11988710158401015840119894= 1198871015840

119894+119887119894 and 11988810158401015840

119894= 1198881015840

119894+119888119894 where

119860 119861 and 119862 represent three exclusive trust states ofnodes namely ldquotrustrdquo ldquodistrustrdquo and ldquouncertaintyrdquo

(4) In our scheme a distinguished frameworkΘ = [119860 119861119862] is set up firstly The power set of Θ is 2Θ =

0 119860 119861 119862 119860 119861 119860 119862 119861 119862 119860 119861 119862Thenthe basic probability assignment (BPA) function isconstructed that is 119898 2

Θrarr [0 1] For 0 is

Nminus 1

N + 2le M lt

N

N+ 2

N minus 2

N + 2le M lt

Nminus 1

N + 2

0 le M lt1

N + 2

N

N+ 2le M lt

N+ 1

N + 2

N + 2le M lt 1

A1

A2

An

U

C

N+ 1

N + 2

1

N minus 1

N

N+ 1

Figure 3 Action-trust based mapping rule

an empty set and 119860 119861 119860 119862 119861 119862 119860 119861 119862 areconsidered to be impossible events in this paper weget 119898(0) = 119898(119860 119861) = 119898(119860 119862) = 119898(119861 119862) = 119898(119860 119861119862) = 0

335 Level Mapping By the above methods the timeand space parameters of mobile positioning can be con-verted into trust levels and a parameter 119872 can be deter-mined in the trust levels of each node where 119872 =

MAX119898(119860)119898(119861)119898(119862) The game space of behaviors of anode is 119860

1 1198602 119860

119899 119880 119862 consisting of 119899 + 2 elements

We construct the following rules (Figure 3) to map the trustvalue to game behavior one by oneThe bigger the trust valueis the higher level the mapped behavior will be The trustlevels of nodes can be used to identify the elements of thebehavior space by establishing the mapping relationship

4 Game Calculation with Strategy Evolution

41 Strategic Game Every node has a trust vector 119879 =

(1198791198601

1198791198602

119879119880 119879119881)119879 so we define the behavior game space

of each node as 119895 isin 1198601 1198602 119860

119899 119880 119862 In the mapping

relationship every element of the trust vector 119872 is theprobability of the behavior space hence 0 le 119879

119895le 1 and

sum119873+2

119895=1119879119895= 1

We assume that in the process of positioning thebehavior of the information sender is identified as 119894

and the behavior of participating node is identifiedas 119895 where 119894 119895 isin 119860

1 1198602 119860

119899 119880 119862 We define

the trust assignment relationship matrix as 119879119894119895 then

the element of this matrix model is the trust levelof a node when it faces the sender with the behavior

International Journal of Distributed Sensor Networks 5

identification of 119895 and the mode selection identification of119894

[119879119894119895](119873+2)times(119873+2)

= 120579

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

119873 119873 minus 1 sdot sdot sdot

1 1 1

119873 + 2 119873 + 2 119873 + 1

1 119873 + 1 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

+ (1 minus 120579)

sdot

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 1 119873 + 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

1 1 1

119873 + 1 119873 + 1 119873 + 1

119873 + 2 119873 + 2 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

(4)

The matrix 119879119894119895

defines the trust level identifications of anode based on different behaviors of the information senderwhen the node is receiving the information (120579 = 0) andforwarding the information (120579 = 1) For example when thereceiving node or forwarding node receives the behavior ofthe information sender A1 the higher the level of the selectedattack is the lower its trust value will be

For a node the purpose of adopting strategic gameduring positioning is to choose a behavior with higher trust

degree through behavior identification thus achieving thebest positioning results According to this rule the expectedbehavior of each node which participates in the game is 119879lowast

119879lowast= 120579

[

[

[

[

[

[

[

119880 (119873 + 1)

119880 (119873 + 1)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

+ (1 minus 120579)

[

[

[

[

[

[

[

119862 (119873 + 2)

119862 (119873 + 2)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

(5)

42 Update Mechanism At the initial phase the node has ahigher willingness to collaborate and its initial trust vector isdefined as 119879(0) = (0 0 0 1)

119879 At the time point of 119905 thelevel identification of instantaneous trust119870

119894119895can be obtained

according to the trust matrix [119879119894119895](119873+2)times(119873+2)

the relay nodeidentity 120579 the behavior identity of the information transmis-sion node 119895 and the behavior identity of the participatingnode 119894

The update equation of the trust vector can be expressedas

119879 (119905 + 1) = A (120575119894119895119879 (119905) + (1 minus 120575

119894119895)119870119894119895) (6)

where 120575119894119895

is the time factor 120575119894119895

= (1205751198601

1205751198602

120575119880 120575119881)

describing the degree of coupling between the transient effectand the trust vector of the previous moment The greaterthe 120575 is the more dependent the trust vector will be on thevalue of the previous moment in the system whereas theinstantaneous trust has a relatively small impact on it andvice versa A is the trust transmission matrix whose roleis to overcome the misjudgment of the trust victor causedby monitoring errors or transmission mistakes The specificform is below

119860(119873+2)times(119873+2)

=

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

119901119873

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

1 minus 119901119873minus1

119873 + 2

119901119873minus1

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 1199011

119873 + 2

sdot sdot sdot

1 minus 1199011

119873 + 2

1199011

1 minus 1199011

119873 + 2

1 minus 1199011

119873 + 2

1 minus 119901119873+1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873+1

119873 + 2

119901119873+1

1 minus 119901119873+1

119873 + 2

1 minus 119901119873+2

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 119901119873+2

119873 + 2

119901119873+2

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

(7)

where 119901119873represents the probability of the trust level being

correctly identified

43 The Conditions of Game Equilibrium In the process ofmobile localization the steady-state convergence condition

of the above mentioned game model is solved by meansof evolutionary game ideas and principles for maximizingpayoffAccording to the evolutionary game theory when thesystem is in initial operation each member node 119899 thatparticipates in localization selects the appropriate actionparticipation way in accordance with the expectation action

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

1198881015840

119894= 1198881015840

119894

minus 1 le 120573119905le 1

1198861015840

119894= 1198861015840

119894

1198871015840

119894= 1198871015840

119894+ 120573119905

1198881015840

119894= 1198881015840

119894

120573119905gt 1

(1)

(2) Measurement analysis of behavior of spatialparameter To represent the Euclidean distancebetween any two beacon nodes we use119889119894119895= radic(119909

119894minus 119909119895)2+ (119910119894minus 119910119895)2

119886119894119895= 119886119894119895+ 1

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895

0 le 119889119894119895le 2119903

119886119894119895= 119886119894119895

119887119894119895= 119887119894119895

119888119894119895= 119888119894119895+ [

119889119894119895minus 2119903

119903

]

119889119894119895gt 2119903

(2)

(3) Quantitative classification of trust levels If there isinformation of 119899 anchor nodes around the unknownnode we can determine the quantized values of eachnode based on the measurement of time and spacewith the following formula

119898119894(119860) =

11988610158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119861) =

11988710158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

119898119894(119862) =

11988810158401015840

119894

11988610158401015840

119894+ 11988710158401015840

119894+ 11988810158401015840

119894

(3)

where 11988610158401015840119894= 1198861015840

119894+119886119894 11988710158401015840119894= 1198871015840

119894+119887119894 and 11988810158401015840

119894= 1198881015840

119894+119888119894 where

119860 119861 and 119862 represent three exclusive trust states ofnodes namely ldquotrustrdquo ldquodistrustrdquo and ldquouncertaintyrdquo

(4) In our scheme a distinguished frameworkΘ = [119860 119861119862] is set up firstly The power set of Θ is 2Θ =

0 119860 119861 119862 119860 119861 119860 119862 119861 119862 119860 119861 119862Thenthe basic probability assignment (BPA) function isconstructed that is 119898 2

Θrarr [0 1] For 0 is

Nminus 1

N + 2le M lt

N

N+ 2

N minus 2

N + 2le M lt

Nminus 1

N + 2

0 le M lt1

N + 2

N

N+ 2le M lt

N+ 1

N + 2

N + 2le M lt 1

A1

A2

An

U

C

N+ 1

N + 2

1

N minus 1

N

N+ 1

Figure 3 Action-trust based mapping rule

an empty set and 119860 119861 119860 119862 119861 119862 119860 119861 119862 areconsidered to be impossible events in this paper weget 119898(0) = 119898(119860 119861) = 119898(119860 119862) = 119898(119861 119862) = 119898(119860 119861119862) = 0

335 Level Mapping By the above methods the timeand space parameters of mobile positioning can be con-verted into trust levels and a parameter 119872 can be deter-mined in the trust levels of each node where 119872 =

MAX119898(119860)119898(119861)119898(119862) The game space of behaviors of anode is 119860

1 1198602 119860

119899 119880 119862 consisting of 119899 + 2 elements

We construct the following rules (Figure 3) to map the trustvalue to game behavior one by oneThe bigger the trust valueis the higher level the mapped behavior will be The trustlevels of nodes can be used to identify the elements of thebehavior space by establishing the mapping relationship

4 Game Calculation with Strategy Evolution

41 Strategic Game Every node has a trust vector 119879 =

(1198791198601

1198791198602

119879119880 119879119881)119879 so we define the behavior game space

of each node as 119895 isin 1198601 1198602 119860

119899 119880 119862 In the mapping

relationship every element of the trust vector 119872 is theprobability of the behavior space hence 0 le 119879

119895le 1 and

sum119873+2

119895=1119879119895= 1

We assume that in the process of positioning thebehavior of the information sender is identified as 119894

and the behavior of participating node is identifiedas 119895 where 119894 119895 isin 119860

1 1198602 119860

119899 119880 119862 We define

the trust assignment relationship matrix as 119879119894119895 then

the element of this matrix model is the trust levelof a node when it faces the sender with the behavior

International Journal of Distributed Sensor Networks 5

identification of 119895 and the mode selection identification of119894

[119879119894119895](119873+2)times(119873+2)

= 120579

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

119873 119873 minus 1 sdot sdot sdot

1 1 1

119873 + 2 119873 + 2 119873 + 1

1 119873 + 1 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

+ (1 minus 120579)

sdot

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 1 119873 + 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

1 1 1

119873 + 1 119873 + 1 119873 + 1

119873 + 2 119873 + 2 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

(4)

The matrix 119879119894119895

defines the trust level identifications of anode based on different behaviors of the information senderwhen the node is receiving the information (120579 = 0) andforwarding the information (120579 = 1) For example when thereceiving node or forwarding node receives the behavior ofthe information sender A1 the higher the level of the selectedattack is the lower its trust value will be

For a node the purpose of adopting strategic gameduring positioning is to choose a behavior with higher trust

degree through behavior identification thus achieving thebest positioning results According to this rule the expectedbehavior of each node which participates in the game is 119879lowast

119879lowast= 120579

[

[

[

[

[

[

[

119880 (119873 + 1)

119880 (119873 + 1)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

+ (1 minus 120579)

[

[

[

[

[

[

[

119862 (119873 + 2)

119862 (119873 + 2)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

(5)

42 Update Mechanism At the initial phase the node has ahigher willingness to collaborate and its initial trust vector isdefined as 119879(0) = (0 0 0 1)

119879 At the time point of 119905 thelevel identification of instantaneous trust119870

119894119895can be obtained

according to the trust matrix [119879119894119895](119873+2)times(119873+2)

the relay nodeidentity 120579 the behavior identity of the information transmis-sion node 119895 and the behavior identity of the participatingnode 119894

The update equation of the trust vector can be expressedas

119879 (119905 + 1) = A (120575119894119895119879 (119905) + (1 minus 120575

119894119895)119870119894119895) (6)

where 120575119894119895

is the time factor 120575119894119895

= (1205751198601

1205751198602

120575119880 120575119881)

describing the degree of coupling between the transient effectand the trust vector of the previous moment The greaterthe 120575 is the more dependent the trust vector will be on thevalue of the previous moment in the system whereas theinstantaneous trust has a relatively small impact on it andvice versa A is the trust transmission matrix whose roleis to overcome the misjudgment of the trust victor causedby monitoring errors or transmission mistakes The specificform is below

119860(119873+2)times(119873+2)

=

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

119901119873

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

1 minus 119901119873minus1

119873 + 2

119901119873minus1

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 1199011

119873 + 2

sdot sdot sdot

1 minus 1199011

119873 + 2

1199011

1 minus 1199011

119873 + 2

1 minus 1199011

119873 + 2

1 minus 119901119873+1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873+1

119873 + 2

119901119873+1

1 minus 119901119873+1

119873 + 2

1 minus 119901119873+2

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 119901119873+2

119873 + 2

119901119873+2

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

(7)

where 119901119873represents the probability of the trust level being

correctly identified

43 The Conditions of Game Equilibrium In the process ofmobile localization the steady-state convergence condition

of the above mentioned game model is solved by meansof evolutionary game ideas and principles for maximizingpayoffAccording to the evolutionary game theory when thesystem is in initial operation each member node 119899 thatparticipates in localization selects the appropriate actionparticipation way in accordance with the expectation action

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

identification of 119895 and the mode selection identification of119894

[119879119894119895](119873+2)times(119873+2)

= 120579

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

119873 119873 minus 1 sdot sdot sdot

1 1 1

119873 + 2 119873 + 2 119873 + 1

1 119873 + 1 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

+ (1 minus 120579)

sdot

[

[

[

[

[

[

[

[

[

[

[

119873 119873 sdot sdot sdot

119873 minus 1 119873 minus 1 sdot sdot sdot

sdot sdot sdot sdot sdot sdot sdot sdot sdot

119873 119873 119873

119873 minus 1 119873 minus 1 119873 minus 1

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 1 sdot sdot sdot

119873 + 1 119873 + 1 sdot sdot sdot

119873 + 2 119873 + 2 sdot sdot sdot

1 1 1

119873 + 1 119873 + 1 119873 + 1

119873 + 2 119873 + 2 119873 + 2

]

]

]

]

]

]

]

]

]

]

]

(4)

The matrix 119879119894119895

defines the trust level identifications of anode based on different behaviors of the information senderwhen the node is receiving the information (120579 = 0) andforwarding the information (120579 = 1) For example when thereceiving node or forwarding node receives the behavior ofthe information sender A1 the higher the level of the selectedattack is the lower its trust value will be

For a node the purpose of adopting strategic gameduring positioning is to choose a behavior with higher trust

degree through behavior identification thus achieving thebest positioning results According to this rule the expectedbehavior of each node which participates in the game is 119879lowast

119879lowast= 120579

[

[

[

[

[

[

[

119880 (119873 + 1)

119880 (119873 + 1)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

+ (1 minus 120579)

[

[

[

[

[

[

[

119862 (119873 + 2)

119862 (119873 + 2)

119862 (119873 + 2)

]

]

]

]

]

]

]

119879

(5)

42 Update Mechanism At the initial phase the node has ahigher willingness to collaborate and its initial trust vector isdefined as 119879(0) = (0 0 0 1)

119879 At the time point of 119905 thelevel identification of instantaneous trust119870

119894119895can be obtained

according to the trust matrix [119879119894119895](119873+2)times(119873+2)

the relay nodeidentity 120579 the behavior identity of the information transmis-sion node 119895 and the behavior identity of the participatingnode 119894

The update equation of the trust vector can be expressedas

119879 (119905 + 1) = A (120575119894119895119879 (119905) + (1 minus 120575

119894119895)119870119894119895) (6)

where 120575119894119895

is the time factor 120575119894119895

= (1205751198601

1205751198602

120575119880 120575119881)

describing the degree of coupling between the transient effectand the trust vector of the previous moment The greaterthe 120575 is the more dependent the trust vector will be on thevalue of the previous moment in the system whereas theinstantaneous trust has a relatively small impact on it andvice versa A is the trust transmission matrix whose roleis to overcome the misjudgment of the trust victor causedby monitoring errors or transmission mistakes The specificform is below

119860(119873+2)times(119873+2)

=

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

119901119873

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

sdot sdot sdot

1 minus 119901119873

119873 + 2

1 minus 119901119873minus1

119873 + 2

119901119873minus1

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873minus1

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 1199011

119873 + 2

sdot sdot sdot

1 minus 1199011

119873 + 2

1199011

1 minus 1199011

119873 + 2

1 minus 1199011

119873 + 2

1 minus 119901119873+1

119873 + 2

sdot sdot sdot sdot sdot sdot

1 minus 119901119873+1

119873 + 2

119901119873+1

1 minus 119901119873+1

119873 + 2

1 minus 119901119873+2

119873 + 2

sdot sdot sdot sdot sdot sdot sdot sdot sdot

1 minus 119901119873+2

119873 + 2

119901119873+2

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

]

(7)

where 119901119873represents the probability of the trust level being

correctly identified

43 The Conditions of Game Equilibrium In the process ofmobile localization the steady-state convergence condition

of the above mentioned game model is solved by meansof evolutionary game ideas and principles for maximizingpayoffAccording to the evolutionary game theory when thesystem is in initial operation each member node 119899 thatparticipates in localization selects the appropriate actionparticipation way in accordance with the expectation action

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

Table 2 Default parameter settings

Model parameter Default settingThe number of node119873 5000The ratio of beacon node 120588 02Communication radium 119903 50mMaximum moving speed 119881max 10msProbability of identifying trust level 119901

119873075

Time factor 120575119894119895= (1205751198601 1205751198602 120575

119880 120575119881) (05 05 05 05)

space 119879lowast and the trust decision-making framework At thetime point of 119905 + 1 the probability of the node 119899 selecting theaction 119886

119899(119905 + 1) = 119894 isin 119860

1 1198602 119860

119899 119880 119862 is obtained by

the following formula

Pr [119886119899(119905 + 1) = 119894] =

Pr [119886119899(119905) = 119894] 119875

119899119894(119905)

sum119873+2

119895=1Pr [119886119899(119905) = 119895] 119875

119899119895(119905)

(8)

where 119875119899119894(119905) is the instantaneous payoff the participating

node 119899 obtains by selecting the action of which the actionspace is identified as 119894 at the time point of 119905

The sufficient condition for the evolutionary convergenceis proven in the literature and ultimately the acquired gameconvergence condition is

119875120579

1minus 119875120579

119873+2lt 0 120579 = 0 1

119901119894gt

1

119873 + 2

(9)

5 Performance Evaluation

51 Simulation Setting In this section we designed a mobilenetwork simulation experiment to verify the effects of thetrust game-basedmobile localizationmethod on cooperationand localization performance of the mobile sensor networknode and conducted the simulation in Matlab The defaultsetting is with 5000 nodes deployed and moving within the10000m times 10000m area at random The moving speed is inthe range of [0 119881max] (where 119881max is the maximum movingspeed) The default parameters are as in Table 2

52 Simulation Results

(1) The simulation has analyzed the effect of the gamealgorithm on node cooperation In the case of dif-ferent ratios of malicious nodes (20 40 and60 resp) the situations of nodes participating incooperation via game are shown in Figure 4 TheFigure shows that with the increase of the gamenumber the ratio of nodes which select cooperationalso increases Finally the ratio value of nodes whichselect cooperation tends to be stabilized In the initialstate the ratios of malicious nodes are 20 40 and60 after the game is stable the ratios of cooperativemembers have been raised from 458 36 and196 to 839 786 and 724 Simulation results

0 50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Game index

Coo

pera

tive p

opul

atio

n20 malicious ratio40 malicious ratio60 malicious ratio

Figure 4 The overall effect of cooperative performance undervarious original malicious ratios

show that the algorithm can effectively improve coop-eration of nodes ensure transmission of localizationdata and maintain the proper work of the networkeven under the situation of malicious attack

(2) In the case of different ratios of malicious nodes(20 40 and 60 resp) the mobile game-basedsecure localization (GSL) algorithm and the mobilelocalization algorithm without using the game arecompared as shown in the figure Figures 5 and 6show the situations of localization accuracy under the20 40 and malicious nodes coverage conditionsIt can be clearly seen from the figure that by usingthe game approach the localization accuracy has beenimproved significantly and the rate of improvementreaches about 20ndash50 Meanwhile for networkenvironment with a higher ratio of malicious nodes(60) (Figure 7) the localization results can convergeto achieve localization in harsh environments byapplying this algorithm Simulation results show thatthe game-based localization algorithm can effectivelyinhibit aggressive behaviors of malicious nodes andimprove the localization accuracy of mobile nodes

(3) We compare the following three methods in thesimulations the GSL algorithm (the game theory isused) the DBSL algorithm (the improved D-S fusionmethod is used [15]) the BRS-based robust securelocalization (BRSL) algorithm [9] Figure 8 showsthe comparison results of localization error underdifferent malicious ratio The proportion of attackersranges from 5 to 60 As the number of attackers

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

0 5 10 15 20 25 30 35 40 45 50

04

05

06

07

08

09

1

11

12

13

Time

20 MR location convergence

20 MR without GSL20 MR with GSL

Estim

ate e

rror

(r)

Figure 5 The effect of localization under original malicious ratio20

0 5 10 15 20 25 30 35 40 45 500

02

04

06

08

1

12

14

Time

40 MR location convergence

40 MR without GSL40 MR with GSL

Estim

ate e

rror

(r)

Figure 6 The effect of localization under original malicious ratio40

increases the localization error increases as wellGSL can obtain more accurate results compared withDBSL and BRSL In particular when malicious ratiois high GSL has better inhibition effect on attackerrsquosnumber

6 Conclusions

This paper presents a mobile network node localizationalgorithm based on game strategies Features are extractedunder the situation of the mobile sensor network beingattacked and the mapping relation between the attack leveland the trust level is established At the same time trust and

0 5 10 15 20 25 30 35 40 45 50070809

111121314151617

Time

60 MR location convergence

60 MR without GSL60 MR with GSL

Estim

ate e

rror

(r)

Figure 7 The effect of localization under original malicious ratio60

5 10 15 20 25 30 35 40 45 50 55 60

1

2

GSLDBSLBRSL

Estim

ate e

rror

(r)

The ratio of malicious nodes ()

The comparison results of localization error22

02040608

12141618

Figure 8 The comparison results of localization errors underdifferent malicious ratio

cooperation model and the payoff space of the strategy gameare built effectively suppressing the behavior of maliciousnodes in network Finally the game update mechanism andequilibrium conditions are provided to ensure the stabilityand convergence of the algorithm Simulation results showthat the proposed mobile node localization algorithm basedon game strategies takes full advantage of the dynamiccharacteristics of the algorithm and motivates cooperativebehavior of member nodes this algorithm can achieve nodesrsquolocalization and improve localization accuracy in harshenvironments especially in the situation with a higher ratioof initial malicious nodes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

Acknowledgments

The authors are grateful to the anonymous reviewers fortheir industrious work and insightful comments This workis supported by Natural Science Foundation of China underGrant no 61371135

References

[1] H Chenji and R Stoleru ldquoToward accurate mobile sensornetwork localization in noisy environmentsrdquo IEEE Transactionson Mobile Computing vol 12 no 6 pp 1094ndash1106 2013

[2] Z Wang Y Wang M Ma and J Wu ldquoEfficient localization formobile sensor networks based on constraint rules optimizedMonte Carlo methodrdquo Computer Networks vol 57 no 14 pp2788ndash2801 2013

[3] KW K LuiW-KMa H C So and F K Chan ldquoSemi-definiteprogramming algorithms for sensor network node localizationwith uncertainties in anchor positions andor propagationspeedrdquo IEEE Transactions on Signal Processing vol 57 no 2 pp752ndash763 2009

[4] G J Han H H Xu T Q Duong J Jiang and T HaraldquoLocalization algorithms of wireless sensor networks a surveyrdquoTelecommunication Systems vol 52 no 4 pp 2419ndash2436 2013

[5] Z Li and H Shen ldquoGame-theoretic analysis of cooperationincentive strategies in mobile ad hoc networksrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1287ndash1303 2012

[6] H-Y Shi W-L Wang N-M Kwok and S-Y Chen ldquoGametheory for wireless sensor networks a surveyrdquo Sensors vol 12no 7 pp 9055ndash9097 2012

[7] L Lazos R Poovendran and S Capkun ldquoROPE robustposition estimation in wireless sensor networksrdquo in Proceedingsof the 4th International Symposium on Information Processingin Sensor Networks (IPSN rsquo05) pp 324ndash331 University ofCalifornia Los Angeles Los Angeles Calif USA August 2005

[8] Z Yang L Jian C Wu and Y Liu ldquoBeyond triangle inequalitysifting noisy and outlier distance measurements for localiza-tionrdquoACMTransactions on Sensor Networks vol 9 no 2 article26 2013

[9] N Yu L R Zhang and Y J Ren ldquoBRS-based robust securelocalization algorithm for wireless sensor networksrdquo Interna-tional Journal of Distributed Sensor Networks vol 2013 ArticleID 107024 9 pages 2013

[10] Y Wei and Y Guan ldquoLightweight location verification algo-rithms for wireless sensor networksrdquo IEEE Transactions onParallel and Distributed Systems vol 24 no 5 pp 938ndash9502013

[11] L Xiao Y Chen W S Lin and K J R Liu ldquoIndirectreciprocity security game for large-scale wireless networksrdquoIEEE Transactions on Information Forensics and Security vol 7no 4 pp 1368ndash1380 2012

[12] R Feng X Xu X Zhou and J Wan ldquoA trust evaluationalgorithm forwireless sensor networks based on node behaviorsand D-S evidence theoryrdquo Sensors vol 11 no 2 pp 1345ndash13602011

[13] A Attar H Tang A V Vasilakos F R Yu and V C M LeungldquoA survey of security challenges in cognitive radio networkssolutions and future research directionsrdquo Proceedings of theIEEE vol 100 no 12 pp 3172ndash3186 2012

[14] Q Xiao K Bu Z Wang and B Xiao ldquoRobust localizationagainst outliers in wireless sensor networksrdquoACMTransactionson Sensor Networks vol 9 no 2 article 24 2013

[15] N Yu L Zhang and Y Ren ldquoA novel D-S based securelocalization algorithm for wireless sensor networksrdquo Securityand Communication Networks vol 7 no 11 pp 1945ndash1954 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of