Novel Virtul nhor Noe-se Loliztion lgorithm for Wireless Sensor Networks Pengxi Liu Xinming Zhng Shung Tin Zhiwei Zho Peng Sun Deprtment of Computer Siene n Tehnology University of Siene n Tehnology of Chin nhui Provine-MOST Co-Key Lortory of High Performne Computing n Its pplition Hefei 3007 P.R. Chin xinming@ust.eu.n strt The ury of loliztion is signifint riterion to evlute the prtil utility of loliztion lgorithm in wireless sensor networks. In mostly loliztion lgorithms one of the min methos to improve loliztion ury is to inrese the numer of nhor noes. ut the numer of nhor noes is lwys limite euse of the hrwre restrit suh s ost energy onsumption n so on. In this pper we propose novel lgorithm with smll extr logil overhe whih uses the shortest-hop pth sheme to upgre virtul nhor noes while the rel numer of physil nhors is the sme s efore. This lgorithm firstly hooses out some speil noes from ll the unknown ones to figure out more urte positions of them n then mkes these ones s new virtul nhor noes ssist other unknowns in lolizing together with the rel nhors. The simultion results illustrte our lgorithm hs improve the ury of loliztion gretly. Keywors-ury; nhor noe; loliztion; sensor networks I. INTRODUCTION Wireless Sensor Network (WSN) [] refers to group of inexpensive sensors linke y wireless meium the sensors re provie with sense omputtion n wireless ommunition pility. WSNs usully re rrnge t speil sout region n sense speil physis informtion in the region. Sensor noes re often eploye y rnom estrewing (irplne estrewing for exmple) n only few of noes ssemle with Glol Positioning System (GPS) whih n pture their position fter estrewing ut most of the noes nnot quire suh informtion. The pplition of WSNs is often relte to the positions of noes for instne in ttlefiel whih nees to etet the enemies positions for orret ttking. So the loliztion of sensor noes hs eome hot topi in WSNs. t present mny loliztion lgorithms for sensor networks hve een propose. n most of them suppose tht the network inlues smll numer of nhor noes whih know their own positions eforehn y either using GPS or eing mnully onfigure. The other mjority of noes re unknown position noes lle unknowns. The nhors n ssist the unknowns to e lote. ut for the existene of vrious errors the lotion preision will e restrite n some noes even nnot e lote. So the improvement of This pper is prtilly supporte y the Ntionl Nturl Siene Fountion of Chin uner Grnt No. 606737 n 605737; the Ntionl Grn Funmentl Reserh 973 Progrm of Chin uner Grnt No.006C303006; the Open Fountion of nhui Provine Key Lortory Proeeings of Softwre of the in Sixth Computing Interntionl n Communition Conferene 005-006. on Networking (ICN'07) loliztion preision with lower ost less energy onsumption n less hrwre support hs eome more n more importnt. This pper proposes n lgorithm nme Virtul nhor Noe-se Loliztion lgorithm (VNL). The new lgorithm figures out highly preise positions for some speil unknowns n then these noes re upgre s virtul nhors to ssist in loting the rest unknowns long with primry rel nhors. The ulk of the loliztion systems hve propose y now n pply this lgorithm to improve their loliztion preision in the se of ense WSN with few n sttere nhors. The rest of the pper is orgnize s follows: Setion II isusses previous work in loliztion for sensor networks n nlyzes the error of some typil lgorithms. Setion III esries our Virtul nhor Noe-se Loliztion lgorithm. Setion IV evlutes the lgorithmi performne y simultions. Setion V rws onlusion. II. ERROR NLYSIS OF TYPICL LOCLIZTION LGORITHMS. Relte Works Loliztion in sensor network is wiely stuie prolem whih n e roly lssifie into two tegories: rnge-se n rnge-free. Rnge-se tehnique relies on point-to-point istne estimtes or ngle estimtes to infer lotion. For exmple Time Of rrivl (TO) [] Time Differene On rrivl (TDO) ngle Of rrivl (O) n Reeive Signl Strength Initor (RSSI) [4] ll use the istne informtion n the typil lgorithm is Eulien. The ltter oes not require the mesurement of physil istne-relte properties. The Centroi pproximte Point in Tringle Test (PIT) Knowlege-se Positioning DVhop morphous [5] n so on re ll rnge-free lgorithms. In Centroi lgorithm [6] the nhors sen out eons to neighor noes t perioi intervls the eons inlue nhor s position informtion. reeiver noe infers proximity to olletion of nhor noes. The lotion of the noe is then estimte to e the entroi of the nhor noes from whih it n reeive eon pkets. In [7] uthors propose PIT in whih given three nhor noes ny sensor noe n etermine if it lies insie the tringle. In this loliztion sheme eh sensor noe performs numerous PT
tests with ifferent omintion of uile nhor noes n infers its lotion s the enter of grvity of the intersetion re of ll the tringles in whih the noe lies in. In Knowlege-se Positioning [8] sensors from the sme group n ln in ifferent lotions n those lotions usully follow proility istriution tht n e known priori. In this sheme eh sensor first fins out the numer of its neighors from eh group. With this oservtion sensor estimtes lotion se on the priniple of the mximum likelihoo estimtion (MLE).. Error nlysis We hoose two onrete lgorithms whih elong to the ove two tegories respetively to rry out error nlysis. Eulien [9] is Rnge-se lgorithm propose y Niulesu et l. Minly onsiering the lol topology surrouning the nhor noes they present metho whih n figure out the lotions of unknown noes severl hops wy from the nhor noes. s shown in the Figure ([9].Figure) unknown noes n C re in the neighorhoo of nhor noe L n these two noes re lso in the neighorhoo of eh other. Unknown noe is in the neighorhoo of n C respetively ut it is not in the neighorhoo of nhor noe L. s for the qurngle CL ll of its eges n the igonl C re known to us. Then the length of L n e figure out oring to the theory of geometry. ut there re two possile results for the lotion of noe : n. If s nother neighor noe D is in the neighorhoo of nhor noe L n either noe of n C then we n use D to reple or C. fter this we n ompute the length of L gin in orer to quire the orret lotion of noe. y using this metho repetely when unknown noes quire three or more istnes to the nhor noes they n e lolize. preision of loliztion they will quire. Some noes my even e not ple of eing lolize. DV-hop [9] is Rnge-free lgorithm whih is lso propose y Niulesu et l. In the lgorithm nhor noes generte pkets inluing their lotion informtion n flg whih is initilize s to represent the numer of hops wy from them. These pkets re spre in the flooing moe n when they re trnsmitte y the rely noes the flg of hops is inrese y. Then noe etermines how mny hops wy it is from n nhor noe. The nhor noes ompute their hops to other nhors s well n use simple formul to etermine the verge hop length. This vlue will e rost n when ny unknown noe reeives it the reeiver n estimte the istnes to the nhor noes. fter it quires three or more estimte vlue from nhor noes the lotion of itself n lso e figure out. DV-hop lgorithm ssumes tht it is pplie to the network of high ensity of noes. The pth with shortest hops is similr to stright line. It hs the flw tht in prtil pplition influene y the surrounings the ommunition rnge of eh noe is not stnr irle ielly. s shown in Figure ([7].Figure 3) it is quite nomlisti polygon. This se ssoite with the influene of network topology mkes the istne of every hop is muh ifferent with eh other. So if we use the verge istne of eh hop to ompute the istne from unknown noes to nhor noes in the network whih lks nhor noes the error of loliztion will e lrge. Figure. Irregulr rio pttern of sensor Figure. Eulien propgtion metho The rnging error is the min flw of Rnge-se lgorithm. t present there re severl min rnging tehniques suh s TO TDO O RSSI. Let us tke RSSI for exmple. It minly uses the RF signl to trnslte signl strength into istne estimtes. euse of the oviously ifferent rosting ttenution for the sme istne use y the refletion multi-pth rost n ntenn gin et the preision of rnging is not stisftory [3]. The experiments in pper [] show tht the rnging error of RSSI n e s lrge s 50%. The existene of rnging error will influene the estimtion of the istne etween the neighor noes in the Eulien lgorithm. This error n e umulte hop y hop n t lst it will e foun tht the frther the noes re wy from nhor noes the poorer Figure 3. n exmple to show the error use y DV-hop In orer to further illuminte this prolem we onsier n extreme se (Figure 3): ssume tht there is shortest-hop pth. rely noe C is n-hops wy from n n-hops wy from too. The ommuniting rius of eh noe is r. If the verge istne of hops is r from to C n r/ from
to C. The rel istne from to is D r 3 = nr + n nr = n the rel istne from to C is D C = nr. lthough se on DV-hop we will get ' D 3 DC = = nr s the istne of n C. The error is 4 ' DC DC = nr. 4 The error will inrese with the inrese of the hops. In other wors if nhor noe is nerer to whih mens n (hops wy from ) n e smller the istne from C s rel position to its position estimtes will e shorter too. se on the ove nlysis we n rw the onlusion: in wireless sensor networks the preision of lolizing loliztion lgorithm is relte to the ensity of nhor noes. When the ensity of nhor noes inreses the istne (hops) from unknown noes to the nhor noes will e reue n so oes the umulte error. t lst the preision of the loliztion will e enhne. III. VIRTUL NCHOR NODE-SED LOCLIZTION LGORITHM There n e only few nhor noes eploye in the network ue to high ost n energy issue. Tke the GPS for exmple GPS n e use to onfigure sensor noe for lolizing other noes thus this noe with GPS n work s n nhor. ut the GPS system is highly energy onsumptive n expensive so it n only e eploye in smll numer of sensor noes. Oviously there is ontrition etween the loliztion preision enhne y inresing the numer of nhor noes n the physil resoure onsumption reution y eresing hrwre equippe. Therefore we propose Virtul nhor Noe-se Loliztion lgorithm in whih we figure out some speil unknowns positions highly urte firstly n then these noes s virtul nhors re together with the rel ones to help the reminers to e lolize. The preision of loliztion is improve with no more hrwre neee.. The Seletion of Virtul nhor Noe We tke the sme ssumption s use in DV-hop [9] whih is tht in ense network the shpe of the pth with the smllest hop ount is symptoti to eeline. We hoose the noes whih n e upgre s virtul nhors from ll the unknowns y the following steps. Eh unknown shll eie whether or not it lies on the shortest-hop pth etween two nhor noes. If yes then it shll reor the relte informtion of the two nhors. t the eginning of our loliztion lgorithm eh nhor noes will rost the flooing pkets. In this kin of pket setor H is sve in pket heer to ount the times for whih the pket hve een forwre. Initilly H is set to. Eh noe will mintin vrile h to ompute the smllest hops to eh nhor noe. Every time flooing pket rrives the following work shll e one on the reeiving noe (Figure 4): if we never reeive the flooing pket from the nhor noe (sy ) then set h s H; else { ompre the lol vrile h with H; if h<= H then isr this pket; else { h=h; forwr this pket (tht is why h for C is 4); } } Figure 4. Exmple of noe otining the shortest-hop pth from n nhor When n nhor noe (sy ) gets to know the hops wy from the other en nhor (sy ) it () will rost pkets to inform the hop istne etween them ( n ). This hop vlue is store in setor nme Shortest-hop (Shortest-hop =7) (Figure 5). On reeiving suh kin of pket the intermeite noe (sy C) will o the following juge: If the sum or solute ifferene etween the hop istnes from itself to the two en nhors equls Shortest-hop ( h + h = Shortest-hop or Mx( h h ) Min( h h ) = Shortest-hop ). Then the intermeite noe (C) is on the shortest-hop pth etween the two nhors ( n ) n it (C) will reor the relte position informtion out them ( n ). Figure 5. noe juges whether or not it is on the shortest-hop pth etween two nhors To reue the ommunition overhe prt of the nhor noes shll e selete to rost flooing pkets first. While the rest will wit until they reeive flooing pkets from other nhor noes.
. The Upgre of Virtul nhor Noe If ertin noe E lies on the shortest-hop pth from nhor noe ( X ) to ( X ) n the shortest-hop pth from nhor noe C( X ) to D( X ) then the oorintes of the rossing point of eeline n CD n e use to enote E s position. Now we shll ompute E oorintes in following wy: Xe K Y = e K K Y Y Y Y Let K = K = X X X X X Y = X i () X Y X K =. K K X Y = X X Y X To mke our omputtion preise when noe lies on n shortest-hop pths etween nhors we will figure out m= C n oorintes for the noe: ( X ) ( X ) ( X m m ). The finl result omes out s the verge of ll these oorintes: ( X ) = X + X + + X m m Y+ Y + + Ym m () When noe gets its oorintes it is upgre s virtul nhor noe utomtilly. Then it will rost pkets to inform its position. C. Theoretil nlysis of the lgorithm In our lgorithm we ssume tht in ense WSN pths with shortest hops re symptoti to eeline. When noe lies on two shortest-hop pths etween two ifferent nhor pirs it lies on the ross point of the two pths. In the implementtion of our lgorithm eh noe will reor the shortest-hop pths whih it lies on n it shll ompute oorinte pir oring to eh two. fter tht Centroi [6] is use to ompute the verge vlue of ll the oorinte pirs n the finl result is this noe s position. This noe shll e upte s n nhor noe to help to lolize other noes. The ifferene of relte positions of the nhor noes shll result in ifferent numer of results. Figure 6() shows tht when nhors form onvex qurngle n nhors men tht t most C 4 n noes n e upte. While in sitution in Figure 6() the numer of noes tht n e upte jumps to 4 3C n thus even smll numer of nhors n upte quite few noes into virtul nhor noes. Topologilly the Eulien lgorithm works well on those noes jent to nhors. If suh noes re upgre into nhor noes the nhor noes will group together enser n enser whih mkes little ontriution to the loliztion of the whole network. Comprtively our lgorithm will upgre the noes right in the mile of the pth etween nhor noes. n the newly upgre noes shll get the nhors to istriute more uniformly when the numer of nhor noes is firly few t the eginning. IV. PERFORMNCE EVLUTION In this setion we will rry out simultions to evlute the effet of Eulien n DV-hop [9] rme with our lgorithm on the preision of the loliztion. We lso use the lnguge of ml n the tool of ocml omplier n Cygwin[0]. s the error of loliztion minly omes from the umulte error use y hops we esign to eploy 500 noes rnomly in n re of whih the x-xis n y-xis oth rnge from 000m to 3000m n the ommuniting rius of eh noe is 00m (Figure 7). Figure 7. Noe istriution () () Figure 6. The reltionship of numer n istriution etween virtul nhors n rel ones The nhor noes re selete from ll of the noes proportionlly. We efine the riterion for error s the rtio of the Eulien istne etween the rel n figure oorintes to the ommuniting rius of noes. The experimentl t of four groups of whose the rnging errors
re 0~50% 0~40% 0~30% 0~0% respetively s shown in Figure 8-. loliztion mking it more urte. fter using our lgorithm the loliztion eomes muh more preise even if the perentge of rel nhor noes inreses. The urve of error is smooth n so is the flutution of the whole urve not like tht of Eulien lgorithm. When the rnging error is 0~50% n the perentge of nhor noes is % Eulien rme with VNL n hieve the lolizing level whih Eulien lgorithm n only hieve when the rnging error is 0~0% n the perentge of nhor noes is 0%. The low prie n ovious improvement to the Eulien lgorithm mkes it more suitle for loliztion. Figure 8. Loliztion error omprison when the rnging error is 0-50% Figure. Loliztion error omprison when the rnging error is 0-0% Figure 9. Loliztion error omprison when the rnging error is 0-40% The error of DV-hop lgorithm minly origintes from the influene of environment. The irregulr polygonl ommunition rnge n the topology of network use the gret ifferene of rel istne of eh hop. So we simplify the onition to esign the experimentl senrio s follows: In the re of whih the x-xis n y-xis oth rnge from 0m to 0000m we eploy 00 noes rnomly. The nhor noes re selete proportionlly n rnomly n the ommuniting rius of eh noe is rnom numer less thn 00m. Menwhile we gurntee tht the istne etween hops is lrge enough. This is lso lssil senrio in nother iel onition (Figure ). Figure 0. Loliztion error omprison when the rnging error is 0-30% From the results of simultion we n see tht the error of Eulien loliztion ereses oviously with the inrese of the perentge of nhor noes. In the lrge sle wireless sensor networks with ense noes n sprse nhor noes when using the Eulien optimize y our VNL the newly upgre noes inrese the perentge of nhors (inlue virtul ones) gretly. Then the hops from unknown noes to the nhor noes will erese. So it lessens the effet of the rnging error n umulte error on the Figure. Noe istriution From the experimentl results (Figure 3) we n see tht in this senrio the VNL lgorithm lso performs well in ssisting loliztion.
Figure 3. Loliztion error omprison V. CONCLUSION oth the preision n the ost of loliztion re importnt riterions to evlute the loliztion lgorithms. se on the summry of previous loliztion lgorithms in this pper we propose istriute lgorithm for virtul nhor noes upgring. It n inrese the ensity of virtul nhor noes t low physil ost n ssist some lgorithms whih lrey exist to enhne the preision of loliztion in the network with ense noes. The experimentl results hve proven tht our metho is effetive. In the future we will try to further enhne the preision of lolizing of new virtul nhor noes to improve the whole network loliztion ury. REFERENCES [] I. F. kyiliz W. Su. Snkrsurrmnim n E. Cyiri Wireless sensor networks: survey Computer Networks Journl 38(4) pp. 393-400. [] J. eutel Geolotion in PioRio Enviroment M.S. Thesis ETH Zurih Eletronis Lortory UC-erkley Deemer 999. [3] E. Elnhrwy X. Li R.P. Mrtin The limits of loliztion using signl strength: omprtive stuy Pro. of st IEEE Interntionl Conferene on Sensor n ho Communitions n Networks (SECON 004) 004. [4] P. hl n V. N. Pmnhn RDR: n in-uiling RF se user lotion n trking system Pro. of the IEEE INFOCOM pp. 775-784 Mrh 000. [5] R. Ngpl H. Shroe n J. hrh. Orgnizing glol oorinte system from lol informtion on n ho sensor network Pro. of the n Interntionl Workshop on Informtion Proessing in Sensor Networks (IPSN 03)volume 634 of Leture Notes in Computer Siene. Springer Verlg erlin pr.003. [6] N. ulusu J. Heiemnn n D. Estrin GPS-less low ost outoor loliztion for very smll evies IEEE Personl Communitions 7 (5) pp. 8-34 Otoer 000. [7] T. He C. Hung. M. lum J.. Stnkoivi n T. elzher Rnge-Free loliztion shemes for lrge sle sensor networks Pro. of CM MoiCom 003. [8] Lei Fng Wenling Du Peng Ning eon-less lotion isovery sheme for wireless sensor networks Pro. of IEEE INFOCOM Mrh 005. [9] D. Niulesu n. Nth DV se positioning in -ho networks Journl of Teleommunition Systems 003. [0] http://ml.inri.fr