Research Article A Game-Based Secure Localization Algorithm for Mobile Wireless Sensor Networks

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1 Internatonal Dstrbuted Sensor Networks Volume 205, Artcle ID 64207, 8 pages Research Artcle A Game-Based Secure Localzaton Algorthm for Moble Wreless Sensor Networks Tanyue Bao,,2 Jangwen Wan, Kefu Y, and Qang Zhang School of Instrumentaton Scence and Optoelectroncs Engneerng, Bejng Unversty of Aeronautcs and Astronautcs (Behang Unversty), Bejng 009, Chna 2 Northeast Petroleum Unversty, Daqng 6338, Chna Correspondence should be addressed to Jangwen Wan; jwwan@buaaeducn Receved 25 March 205; Revsed 23 June 205; Accepted 3 August 205 Academc Edtor: Feng Hong Copyrght 205 Tanyue Bao et al Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted The ssue of node localzaton s a fundamental problem n wreless sensor networks Recently, the localzaton problem for moble sensor networks n hostle envronment has receved sgnfcant attenton Due to the moblty of the sensor nodes, t s more challengng to acheve node localzaton n attacked sensor networks than n statc ones To address these challenges, the paper presents a novel game-based secure localzaton algorthm The nodes strategy level can be ndcated through the results of trust evaluaton and then by means of constructng reasonable strategy space and payoff functon usng game theory; all knds of nodes wthn the network can acheve the optmal payoffs The performance of our algorthm s evaluated by extensve smulaton experments The smulaton results show that the localzaton error of our proposed algorthm s lower than those of the exstng ones n attacked envronment Introducton Wth the development of mcrocomputer technology, moble wreless sensor networks (MWSNs) are wdely used n many felds, such as underwater sensor, border detecton, and anmal trackng [, 2 Locaton awareness s very mportant because many applcatons of MWSNs depend on the nformaton of locatons of sensor nodes Localzaton s to obtan the nodes poston [3, 4 In most exstng sensor networks, nodes are statc However, n some modern applcatons, localzatons become a dffculty, when nodes are movng and beng attacked [5 A moble node s unable to receve locaton nformaton rapdly and accurately when t s attacked [6 The false coordnates or dstance estmaton wll cause a major localzaton error for normal sensor nodes In ths case, some methods should be explored to elmnate or reduce the adverse nfluence caused by malcous beacon nodes and ensure safe localzaton n moble WSNs In ths paper, we propose a game-based securty localzaton (GSL) algorthm for solvng the moble node selflocalzaton problem wth the exstence of malcous node Frstly, node n multple hop transmsson decdes the behavor grade accordng to the tme and space nformaton Secondly, accordng to the behavor grade, the complete multrsk level strategy space s constructed and s updated over tme Fnally, node selects a behavor grade to obtan optmal benefts Smulaton experment results show that the algorthm can effectvely restran node s malcous behavors and boost the cooperaton ablty of the network The localzaton error wth GSL s lower than those wthout GSL n moble and attacked envronment The remander of ths paper s organzed as follows Secton 2 ntroduces related works on secure localzaton algorthms Secton 3 presents the network model, attack model, and game model Secton 4 provdes the detal of GSL algorthm Secton 5 presents the smulaton results and Secton 6 concludes the paper 2 Related Works The research n securty localzaton algorthm for wreless sensor networks s manly dvded nto two methods The frst method s based on sensor nodes It can prevent nodes

2 2 Internatonal Dstrbuted Sensor Networks from beng affected by the attack through the establshment of protecton mechansms (Verfable Multlateraton, SeR- Loc, etc), or removng malcous nodes from the network usng the effectve detecton and flterng methods (DRBTS, ARMMSE, and a votng-based algorthm, etc) The second method s based on securty equpment It can mprove the defense capablty of the network by addng securty equpment n the physcal layer Lazosetal[7presentarobustpostonngsystemcalled ROPE whch utlzes a locaton verfcaton technque to dentfy the locaton clams of the sensor nodes before data collecton Yang et al [8 analyze the outler data detecton problem and desgn a stray montorng algorthm based on general cycle blateraton, whch reduced to data from the group to mprove localzaton accuracy Yuetal[9proposeaBRS-basedrobustsecurelocalzaton (BRSL) algorthm, amng at reducng the mpact of the malcous attackers n the network The BRSL method ncludes two phases: the setup trust evaluaton framework and the localzaton stage We and Guan [0 ntroduce a novel scheme called a lghtweght postonng verfcaton algorthm (LPVA); t does not rely on dedcated hardware equpment under the condton of network attack resstance and can be used n the low-cost network Xao et al [ propose a robust network localzaton algorthm call RobustLoc, based on a robust patch mergng operaton that can reject outlers for both multlateraton and patch mergng The above studes manly elmnate the fake beacon nformaton (ROPE, RobustLoc, etc) or detect malcous nodes (LPVA, BRSL, etc) or ncrease equpment to mprove localzaton accuracy but seldom deal wth acton nformaton of sensor nodes, when nodes are moble Our proposal utlzed an mproved game theory and the sensor nodes pluralstc behavor n the network to establsh a trust-preferental strategy, whch make the beacons cooperate effectvely 3 Network Model 3 Network Envronment In an envronment under attack, a moble wreless sensor network conssts of anchor nodes, unknown nodes, and malcous nodes; nodes wth known coordnates are called anchor nodes, nodes whose coordnates are unknown are called unknown nodes, and nodes whch are captured and possbly attack are called malcous nodes All nodes are randomly dstrbuted n the twodmensonal space of the network and on the move As shown n Fgure, the communcaton radus of each node n the network s represented by r and the maxmum movng speed s represented by V max Each node has a unque ID, and the coordnates of unknown nodes are estmated by obtanng the coordnate nformaton of adjacent anchor nodes 32 Attack Model In the sequental Monte-Carlo localzaton algorthm, coordnates of unknown nodes are calculated b3 b2 b2 b3 d3 b d2 d N d4 d5 b4 d7 a d6 2r b5 b6 d8 Attack channel b7 d9 a2 d2 b8 d0 d 2r b0 Fgure : Attack model wth long attack dstance d3 b d2 d4 d b4 N d7 d5 a d6 b5 2r b6 b7 Attack channel d8 d9 a2 d2 b0 d0 2r b8 d Fgure 2: Attack model wth short attack dstance through sample set [2 The unknown node wll select locatonsofanchornodeswthnsnglehopandtwohops as members of the sample set, and therefore the accuracy of locaton nformaton of anchor nodes wthn ths scope determnes the accuracy of postonng [3 The attack models used n ths paper are shown n Fgures and 2 The unknown node N can montor the nformaton of anchor nodes (b b6) Meanwhle, t may be attacked by the malcous node a The malcous node a obtans the nformaton of anchor nodes (b7 b0) provded by a2 (from the regon of a2) through the attack channel and transmts ths nformaton to the unknown nodes Nodes to be postoned wll mstakenly take such beacon nodes as reference nformaton wthn ts two-hop range, causng localzaton errors of unknown nodes We assume that the attack channel between malcous nodes s ndependent of dstance Potental cases of attacks are shown n Fgure where the dstance between malcous nodes s long, and estmaton of coordnates of unknown nodes based on coordnates transmtted by malcous nodes wll cause large errors In Fgure 2, the dstance between malcous nodes s relatvely short, and the two-node scopes of malcous nodes have an area of ntersecton n whch the node b6 s located In a multhop network, we use T to represent the tme of each hop For the unknown node N,thedstancebetween t and d d6 s one hop and the communcaton tme s T b9 b9

3 Internatonal Dstrbuted Sensor Networks 3 To obtan data, d7 channel has to cover three hops, so ts communcaton tme s 3T 33 Game Model 33 Game Partcpants In the process of moble postonng, every unknown node wll obtan the nformaton of beacon nodes wthn one hop or two hops [4 For attacks whch may exst n data transmsson lnks, all nodes nvolved n the transmsson of nformaton are game partcpants Therefore, partcpants n the game model nclude nformaton sender T, nformaton recpent R, andn nformaton forwarders E Throughout nformaton transmsson, the data sent by the sendng node may travel through n forwardng nodes to reach the recevng node, so the number of partcpants of the game s n Strategy Space In ths paper, we defne the strategy space accordng to the dfferent behavors of nodes Node behavors nclude cooperatve, uncooperatve, and attack behavor Accordng to the dfferent attack effect, the attack behavor s dvded nto n level, and the attack level s determned by the attack effect For example, the nfluence of the attack n Fgure s much greater than that n Fgure 2, so the attack level n Fgure s hgher than n Fgure 2 We dvde node actons nto multple levels accordng to ther effects We call the behavors taken by nodes, whch are shown n Table, strategy space In the strategy space set of nodes G = {C,U,A, A 2,,A n }, {C, U} represent cooperatve behavors and uncooperatve behavors, respectvely Cooperatve behavors refer to the cooperatve response of nodes, such as recevng or forwardng after lstenng to sgnals Uncooperatve behavors refer to the fact that the nodes do not deal wth the nformaton whch needs recevng or forwardng; that s, no response wll be carred out where the set {A,A 2,,A n } represents a collecton of dfferent levels of attacks Attack level depends on the degree of nfluence of reference coordnates on the postonng accuracy In the postonng process, for example, dfferent attacks have dfferent effects on the accuracy of postonng The longer the dstance between false coordnates and actual coordnates (Fgure ) s, the stronger the attack s destructve power wll be, the bgger the postonng error wll be, and the hgher the attack level wll be The false coordnate nformaton (Fgure 2) wth short dstance can help localzaton when anchor nodes are sparse, so ts attack level s low 333 Game Payoff In the game process of transmsson of postonng nformaton, the payoff of a partcpant after choosng a strategy at the moment of t can be u k(t),where k(t) G For the attack nodes and each nformaton sender, every gamer who partcpates n the nformaton transmsson wll choose a behavor mode n the strategy space G, resultng n payoff The payoff of gamers comes manly from the gan obtaned by behavors m k(t) and ther own loss c k(t), and therefore the payoff functon s u k(t) = m k(t) c k(t), k(t) G The nformaton recpent wll obtan Symbol dentfcaton C U A A 2 A n Table : Strategy space of nodes Behavor mode Cooperatve Uncooperatve Level attack Level 2 attack Level n attack themaxmumpayofffromthecorrectnformatonprovded orforwardedbythesendngnodeorforwardngnodeon thecontrary,rejectonorattackwllreducethepayoffatthe moment of t, the payoff functon of normal nodes can be expressed as u C (t) u U (t) 0 u A (t) u An (t), whle the payoff functon of attack nodes can be expressed as u An (t) u A (t) 0 u U (t) u C (t) 334 Trust Level In the attack models mentoned above, the attacks are characterzed by changng tme reference and tamperng wth the spatal reference Changes of tme reference reflect on the ncrease of the number of hops from thebeaconnodetotherecevngnodeinformatonofeach anchor node obtaned by unknown nodes has tme weghts whch can be used to determne attack payoff The bgger the tme weght s, the greater the attack payoff wll be, and so the hgher the nfluence of attacks on the accuracy of coordnates of unknown nodes wll be In Fgure, the malcous coordnate data of the beacon node b7 reaches the unknown node N through 3 hops, of whch the tme nformaton s 3T (T s the tme nterval of each segment) Obvously, the longer the tme s, the greater the nfluence of attacks on postonng wll be Tamperng of spatal reference data reflects on the fact that coordnate nformaton s changed by the malcous node In Fgure, the malcous node a changes ts coordnates to the coordnates of b7 b0, and the dstance between these coordnates and the node to be postoned s much larger than two hops of the unknown node N, serously affectng the postonng accuracy of the unknown node Dempster Shafer (abbrevated D-S) evdence theory s adopted n ths paper to calculate the trust values [5 based on the data nformaton of tme and space Trust levels are defned by trust values We use three varables, a, b, c,to quantfy the degree of a node behavor a represents the measurement of a note that s not attacked, b represents the measurement of a note that has been attacked, and c represents the measurement of a note whose behavor s unknown The measurement of node behavor can be dvded nto the followng stuatons: () Measurement analyss of behavor of tme parameter Assumng that β t = (t Δt)/Δt: a =a +, b =b,

4 4 Internatonal Dstrbuted Sensor Networks c =c ; βt N N +2 M< N N +2 A N a =a, b =b +β t, N 2 N M< N +2 N +2 A 2 N c =c ; βt > () 0 M< N +2 A n (2) Measurement analyss of behavor of spatal parameter To represent the Eucldean dstance between any two beacon nodes, we use d j = (x x j ) 2 +(y y j ) 2 a,j =a,j +, b,j =b,j, c,j =c,j ; N N+ M< N +2 N +2 N+ N +2 M< Fgure 3: Acton-trust based mappng rule U C N+ a,j =a,j, b,j =b,j, 0 d j 2r (2) an empty set and {A, B}, {A, C}, {B, C}, {A, B, C} are consdered to be mpossble events n ths paper, we get m(0) = m(a, B) = m(a, C) = m(b, C) = m(a, B, C) = 0 c,j =c,j +[ d j 2r ; r d j >2r (3) Quanttatve classfcaton of trust levels If there s nformaton of n anchor nodes around the unknown node, we can determne the quantzed values of each node based on the measurement of tme and space wth the followng formula: m (A) = m (B) = m (C) = a a a a +b b +b c +b +c +c +c, where a =a +a, b =b +b,andc =c +c,where A, B, andc represent three exclusve trust states of nodes, namely, trust, dstrust, and uncertanty (4) In our scheme, a dstngushed framework Θ=[A, B, C s set up frstly The power set of Θ s 2 Θ = {0, {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}}Then the basc probablty assgnment (BPA) functon s constructed, that s, m : 2 Θ [0, For0 s (3) 335 Level Mappng By the above methods, the tme and space parameters of moble postonng can be converted nto trust levels, and a parameter M can be determned n the trust levels of each node, where M = MAX{m(A), m(b), m(c)} Thegamespaceofbehavorsofa node s {A,A 2,,A n,u,c},consstngofn+2elements We construct the followng rules (Fgure 3) to map the trust valuetogamebehavoronebyonethebggerthetrustvalue s, the hgher level the mapped behavor wll be The trust levels of nodes can be used to dentfy the elements of the behavor space by establshng the mappng relatonshp 4 Game Calculaton wth Strategy Evoluton 4 Strategc Game Every node has a trust vector T = (T A,T A2,,T U,T V ) T,sowedefnethebehavorgamespace of each node as j {A,A 2,,A n,u,c}inthemappng relatonshp, every element of the trust vector M s the probablty of the behavor space; hence 0 T j,and j= T j = We assume that n the process of postonng the behavor of the nformaton sender s dentfed as and the behavor of partcpatng node s dentfed as j, where, j {A,A 2,,A n,u,c} We defne the trust assgnment relatonshp matrx as T,j ; then the element of ths matrx model s the trust level of a node when t faces the sender wth the behavor

5 Internatonal Dstrbuted Sensor Networks 5 dentfcaton of j and the mode selecton dentfcaton of : [T,j () () N N N N =θ [ [ N N + ( θ) N N N N [ N+ N+ [ N N N N N N N+ N+ N N N N N N N+ N+ N+ The matrx T,j defnes the trust level dentfcatons of a node based on dfferent behavors of the nformaton sender whenthenodesrecevngthenformaton(θ = 0)and forwardng the nformaton (θ =) For example, when the recevng node or forwardng node receves the behavor of the nformaton sender A, the hgher the level of the selected attack s, the lower ts trust value wll be For a node, the purpose of adoptng strategc game durng postonng s to choose a behavor wth hgher trust (4) degree through behavor dentfcaton, thus achevng the best postonng results Accordng to ths rule, the expected behavor of each node whch partcpates n the game s T : U (N+) T U (N+) =θ [ [ C () T C () C () + ( θ) [ [ C () T (5) 42 Update Mechansm At the ntal phase, the node has a hgher wllngness to collaborate, and ts ntal trust vector s defned as T(0) = (0,0,,0,) T Atthetmepontoft, the level dentfcaton of nstantaneous trust K,j can be obtaned accordng to the trust matrx [T,j () (),therelaynode dentty θ, the behavor dentty of the nformaton transmsson node j, and the behavor dentty of the partcpatng node The update equaton of the trust vector can be expressed as T (t+) = A (δ,j T (t) +( δ,j )K,j ), (6) where δ,j s the tme factor δ,j = (δ A,δ A2,,δ U,δ V ), descrbng the degree of couplng between the transent effect andthetrustvectoroftheprevousmomentthegreater the δ s, the more dependent the trust vector wll be on the value of the prevous moment n the system, whereas the nstantaneous trust has a relatvely small mpact on t, and vce versa A s the trust transmsson matrx, whose role s to overcome the msjudgment of the trust vctor caused by montorng errors or transmsson mstakes The specfc form s below: p N p N p N p N p N p p N p N N A () () = p p p p p, (7) p N+ p N+ p p N+ N+ [ p p p [ where p N represents the probablty of the trust level beng correctly dentfed 43 The Condtons of Game Equlbrum In the process of moble localzaton, the steady-state convergence condton of the above mentoned game model s solved by means of evolutonary game deas and prncples for maxmzng payoffaccordng to the evolutonary game theory, when the system s n ntal operaton, each member node n that partcpates n localzaton selects the approprate acton partcpaton way n accordance wth the expectaton acton

6 6 Internatonal Dstrbuted Sensor Networks Table 2: Default parameter settngs Model parameter Default settng The number of node N 5000 The rato of beacon node ρ 02 Communcaton radum r 50 m Maxmum movng speed V max 0 m/s Probablty of dentfyng trust level p N 075 Tme factor δ,j =(δ A,δ A2,,δ U,δ V ) (05, 05,, 05, 05) space T and the trust decson-makng framework At the tme pont of t+, the probablty of the node n selectng the acton a n (t + ) = {A,A 2,,A n,u,c}s obtaned by the followng formula: Pr [a n (t) =P n, (t) Pr [a n (t+) = = j= Pr [a n (t) =jp n,j (t), (8) where P n, (t) s the nstantaneous payoff the partcpatng node n obtans by selectng the acton of whch the acton space s dentfed as,at the tmepont oft The suffcent condton for the evolutonary convergence s proven n the lterature, and ultmately the acqured game convergence condton s P θ Pθ <0, p > 5 Performance Evaluaton θ=0, (9) 5 Smulaton Settng In ths secton, we desgned a moble network smulaton experment to verfy the effects of the trust game-based moble localzaton method on cooperaton andlocalzatonperformanceofthemoblesensornetwork node and conducted the smulaton n Matlab The default settng s wth 5,000 nodes deployed and movng wthn the 0000 m 0000 m area at random The movng speed s n the range of [0, V max (where V max s the maxmum movng speed) The default parameters are as n Table 2 52 Smulaton Results ()Thesmulatonhasanalyzedtheeffectofthegame algorthm on node cooperaton In the case of dfferent ratos of malcous nodes (20%, 40%, and 60%, resp), the stuatons of nodes partcpatng n cooperaton va game are shown n Fgure 4 The Fgure shows that, wth the ncrease of the game number, the rato of nodes whch select cooperaton also ncreases Fnally, the rato value of nodes whch select cooperaton tends to be stablzed In the ntal state, the ratos of malcous nodes are 20%, 40%, and 60%; after the game s stable, the ratos of cooperatve membershavebeenrasedfrom458%,36%,and 96% to 839%, 786%, and 724% Smulaton results Cooperatve populaton % malcous rato 40% malcous rato 60% malcous rato Game ndex Fgure 4: The overall effect of cooperatve performance under varous orgnal malcous ratos show that the algorthm can effectvely mprove cooperaton of nodes, ensure transmsson of localzaton data, and mantan the proper work of the network even under the stuaton of malcous attack (2) In the case of dfferent ratos of malcous nodes (20%, 40%, and 60%, resp), the moble game-based secure localzaton (GSL) algorthm and the moble localzaton algorthm wthout usng the game are compared, as shown n the fgure Fgures 5 and 6 show the stuatons of localzaton accuracy under the 20%, 40%, and malcous nodes coverage condtons It can be clearly seen from the fgure that by usng the game approach the localzaton accuracy has been mproved sgnfcantly, and the rate of mprovement reaches about 20% 50% Meanwhle, for network envronment wth a hgher rato of malcous nodes (60%) (Fgure 7), the localzaton results can converge to acheve localzaton n harsh envronments by applyng ths algorthm Smulaton results show that the game-based localzaton algorthm can effectvely nhbt aggressve behavors of malcous nodes and mprove the localzaton accuracy of moble nodes (3) We compare the followng three methods n the smulatons: the GSL algorthm (the game theory s used); the DBSL algorthm (the mproved D-S fuson method s used [5); the BRS-based robust secure localzaton (BRSL) algorthm [9 Fgure 8 shows the comparson results of localzaton error under dfferent malcous rato The proporton of attackers ranges from 5% to 60% As the number of attackers

7 Internatonal Dstrbuted Sensor Networks 7 Estmate error (r) % MR locaton convergence Estmate error (r) % MR locaton convergence % MR wthout GSL 60% MR wth GSL Tme Fgure 7: The effect of localzaton under orgnal malcous rato 60% % MR wthout GSL 20% MR wth GSL Tme Fgure 5: The effect of localzaton under orgnal malcous rato 20% Estmate error (r) 4 40% MR locaton convergence % MR wthout GSL 40% MR wth GSL Tme Fgure 6: The effect of localzaton under orgnal malcous rato 40% ncreases, the localzaton error ncreases as well GSL can obtan more accurate results compared wth DBSL and BRSL In partcular when malcous rato s hgh, GSL has better nhbton effect on attacker s number 6 Conclusons Ths paper presents a moble network node localzaton algorthm based on game strateges Features are extracted under the stuaton of the moble sensor network beng attacked and the mappng relaton between the attack level andthetrustlevelsestablshedatthesametme,trustand Estmate error (r) The comparson results of localzaton error GSL DBSL BRSL The rato of malcous nodes (%) Fgure 8: The comparson results of localzaton errors under dfferent malcous rato cooperaton model and the payoff space of the strategy game are bult, effectvely suppressng the behavor of malcous nodes n network Fnally, the game update mechansm and equlbrum condtons are provded to ensure the stablty and convergence of the algorthm Smulaton results show that the proposed moble node localzaton algorthm based on game strateges takes full advantage of the dynamc characterstcs of the algorthm and motvates cooperatve behavor of member nodes; ths algorthm can acheve nodes localzaton and mprove localzaton accuracy n harsh envronments, especally n the stuaton wth a hgher rato of ntal malcous nodes Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper

8 8 Internatonal Dstrbuted Sensor Networks Acknowledgments The authors are grateful to the anonymous revewers for ther ndustrous work and nsghtful comments Ths work s supported by Natural Scence Foundaton of Chna under Grant no [5 N Yu, L Zhang, and Y Ren, A novel D-S based secure localzaton algorthm for wreless sensor networks, Securty and Communcaton Networks,vol7,no,pp ,204 References [ H Chenj and R Stoleru, Toward accurate moble sensor network localzaton n nosy envronments, IEEE Transactons on Moble Computng,vol2,no6,pp094 06,203 [2 Z Wang, Y Wang, M Ma, and J Wu, Effcent localzaton for moble sensor networks based on constrant rules optmzed Monte Carlo method, Computer Networks, vol 57, no 4, pp , 203 [3 KWKLu,W-KMa,HCSo,andFKChan, Sem-defnte programmng algorthms for sensor network node localzaton wth uncertantes n anchor postons and/or propagaton speed, IEEE Transactons on Sgnal Processng,vol57,no2,pp , 2009 [4GJHan,HHXu,TQDuong,JJang,andTHara, Localzaton algorthms of wreless sensor networks: a survey, Telecommuncaton Systems,vol52,no4,pp ,203 [5 Z L and H Shen, Game-theoretc analyss of cooperaton ncentve strateges n moble ad hoc networks, IEEE Transactons on Moble Computng,vol,no8,pp ,202 [6 H-Y Sh, W-L Wang, N-M Kwok, and S-Y Chen, Game theoryforwrelesssensornetworks:asurvey, Sensors, vol2, no7,pp ,202 [7 L Lazos, R Poovendran, and S Capkun, ROPE: robust poston estmaton n wreless sensor networks, n Proceedngs of the 4th Internatonal Symposum on Informaton Processng n Sensor Networks (IPSN 05), pp , Unversty of Calforna, Los Angeles, Los Angeles, Calf, USA, August 2005 [8 ZYang,LJan,CWu,andYLu, Beyondtranglenequalty: sftng nosy and outler dstance measurements for localzaton, ACM Transactons on Sensor Networks,vol9,no2,artcle 26, 203 [9NYu,LRZhang,andYJRen, BRS-basedrobustsecure localzaton algorthm for wreless sensor networks, Internatonal Dstrbuted Sensor Networks, vol203,artcle ID07024,9pages,203 [0 Y We and Y Guan, Lghtweght locaton verfcaton algorthms for wreless sensor networks, IEEE Transactons on Parallel and Dstrbuted Systems, vol 24, no 5, pp , 203 [ L Xao, Y Chen, W S Ln, and K J R Lu, Indrect recprocty securty game for large-scale wreless networks, IEEE Transactons on Informaton Forenscs and Securty,vol7, no 4, pp , 202 [2 R Feng, X Xu, X Zhou, and J Wan, A trust evaluaton algorthm for wreless sensor networks based on node behavors and D-S evdence theory, Sensors, vol, no 2, pp , 20 [3 AAttar,HTang,AVVaslakos,FRYu,andVCMLeung, A survey of securty challenges n cogntve rado networks: solutons and future research drectons, Proceedngs of the IEEE,vol00,no2,pp ,202 [4 Q Xao, K Bu, Z Wang, and B Xao, Robust localzaton aganst outlers n wreless sensor networks, ACM Transactons on Sensor Networks,vol9,no2,artcle24,203

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