Cooperative Node Localization for Mobile Sensor Networks

Transcription

1 8 IEEE/IFIP Iteratioal Coferece o Embedded ad Ubiquitous Computig Cooperative Node Localizatio for Mobile Sesor Networks Hogyag Che Uiversity of Tokyo, Japa hogyag@mcl.iis.u-tokyo.ac.jp Pei Huag Michiga State Uiversity, USA dolkoff@yahoo.com.c Hig Cheug So City Uiversity of Hog Kog hcso@ee.cityu.edu.hk Marcelo H. T. Martis Uiversity of Tokyo, Japa martis@mcl.iis.u-tokyo.ac.jp Kaoru Sezaki Uiversity of Tokyo, Japa sezaki@iis.u-tokyo.ac.jp Abstract I this paper, we propose a rage-free cooperative localizatio algorithm for mobile sesor etworks by combiig hop distace measuremets ad particle filterig. I the hop distace measuremet step, a differetial error correctio scheme is devised to reduce the positioig error accumulated over multiple hops. A backoff-based broadcast mechaism is also itroduced i our localizatio algorithm. It efficietly suppresses redudat broadcasts ad reduces message overhead. The proposed localizatio method has fast coverges with small locatio estimatio error. We verify our algorithm i various scearios ad compare it with covetioal localizatio methods. Simulatio results show that our proposal is superior to the state-of-the-art localizatio algorithms for mobile sesor etworks.. Itroductio Locatio awareess has become a importat feature for may wireless sesor etwork (WSN) applicatios. Examples of such applicatios iclude positio trackig, mappig, locatio-aided routig, ad others. Due to cost ad eergy costraits, ot all odes may have a reliable source of locatio iformatio (e.g., GPS receivers). Therefore, localizatio systems for WSNs usually employ a small set of odes who are aware of their ow coordiates (hereafter called achors) which will distribute this iformatio to regular odes i the etwork, helpig them estimate their ow positios. May localizatio algorithms have bee proposed over the past few years. Localizatio approaches for WSNs ca be divided ito two mai categories. Rage-based techiques require special hardware for estimatig the distace betwee achors ad regular odes, which may become prohibitively expesive. Rage-free techiques, o the other had, do ot impose such demad as a achor iforms other odes about its ow positio through message passig. After fiishig the distace-from-achor estimatio process, a regular ode ca determie its ow positio through a variety of methods, such as multilateratio, ad triagulatio. If ecessary, a optioal step is performed, i which regular odes exchage messages amog themselves to refie their locatios. We preset a algorithm based o hop distace measuremet ad particle filterig [6] which ca effectively achieve high locatio performace with relatively low commuicatio overhead ad computig complexity. Our algorithm is a distributed localizatio method devised to eable active cooperatio betwee regular odes ad their eighbors i mobile sesor etworks. Simulatio results show that the performace of the ew desig is superior to other covetioal localizatio algorithms. Whe compared to other algorithms, the proposed algorithm is more suitable for mobile WSNs i terms of commuicatio costs ad locatio accuracy. This paper makes two major cotributios to the localizatio problem i mobile WSNs. First, we preset a attractive localizatio scheme with higher accuracy ad lower commuicatio cost tha other state-of-the-art localizatio algorithms for mobile WSNs. Secod, we propose a backoff-based broadcast algorithm which suppresses redudat broadcasts ad reduces message overhead related to ode positioig. The rest of the paper is orgaized as follows. Sectio provides a overview of the related works o localizatio techiques for mobile WSNs. Sectio 3 describes the details of the proposed algorithm. I Sectio 4, simulatio results are reported ad a comparative study of the localizatio performace is coducted. Fially, Sectio 5 presets our cocludig remarks. Prior Work Localizatio has bee a field of itesive research sice the uprise of wireless ad hoc etworks. There are may techiques i the literature proposed for static ad mobile sesor etworks. I this sectio, we discuss some of the related works i mobile WSNs ad how they relate to ad differ from our proposal /8 $5. 8 IEEE DOI.9/EUC Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

2 Localizatio algorithms for mobile WSNs: Several works have bee proposed for mobile WSNs. [] is desiged for mobile sesor etworks based o the sequetial Mote Carlo method. A rage-based versio of has also bee proposed [5], which combies rage-based ad rage-free locatio iformatio to reduce the estimatio error. Baggio et al. [] improve the Mote Carlo localizatio scheme by reducig the sample predictio area. Their work, called, draws valid samples faster ad reduces the umber of iteratios ecessary to fill the sample set. Computatio overhead is reduced by this mechaism, but it still depeds o specific parameters such as the fixed radio trasmissio rage. Hsieh et al. [9] have proposed a localizatio algorithm which dyamically updates ad makes use of referece iformatio for cost-efficiecy, ad has a feasible solutio for odes receivig isufficiet achor iformatio. Differet from the former work o localizatio algorithms for mobile WSNs, we study the cooperatio betwee eighbor odes that achieve high localizatio performace. Our scheme belogs to the rage-free category of localizatio algorithms. Our approach differs from the above metioed works i three sigificat ways: first, differet from DV-Hop [] ad [], which are based o simple floodig mechaism, we propose a backoff-based floodig to efficietly suppress redudat broadcasts ad reduce commuicatio overhead. For the hop distace measuremet, a differetial error correctio scheme is devised to reduce the measuremet error accumulated over multiple hops for the average hop distace. Secod, our approach draws a more effective particle predictio area, borrowig some ideas from, based o the positios of virtual achor odes, created with the active cooperatio betwee regular odes ad its eighbors. Third, the sesor iformatio is used to reduce eve more the predictio area, thus reducig the estimatio error of the o-achor odes. Furthermore, our approach does ot require previous kowledge of the radio trasmissio rage for filterig. 3 Algorithm Developmet I this sectio, we provide the details of our proposed hop distace measuremet ad particle filter-based cooperative localizatio algorithm for mobile WSNs. For simplificatio purposes, we preset our algorithm for the twodimesioal sceario. Ituitively, our work ca be easily exteded to the three-dimesioal case. Our proposal ca be divided ito two mai steps: 3. Hop Distace Estimatio ad Backoff-based Message Broadcast I the first step, each achor ode broadcasts a beaco message throughout the etwork. The beaco message cotais the achor s locatio ad a hop cout with a iitial value of zero. Each receivig ode maitais the miimum hop cout value per achor ode from all beaco messages it receives. Beaco messages with a higher hop cout value from a give achor ode are igored ad discarded. O the other had, valid beaco messages are forwarded with a icremeted hop cout after each hop. I this way, all odes i the etwork ca fid their miimum hop couts to each achor ode. Noetheless, this simple floodig method may result i excessive message overhead. To deal with this issue, we propose a backoff-based broadcastig mechaism described at the ed of this sectio. Covetioal hop cout localizatio methods require two separate floodig stages: (a) hop cout accumulatio ad (b) average hop distace (correctio). I compariso, our method combies the correctio process with the hop cout accumulatio stage to reduce message trasmissios. Whe the effective hop distace is calculated i the floodig process, the hop cout is broadcasted simultaeously to all the odes i the etwork. This approach effectively helps to reduce the umber of trasmitted messages, cosequetly reducig the etwork eergy cosumptio ad the time spet o computig a ode s positio. Oce a achor ode receives the hop cout value from aother achor ode, it estimates the average distace of oe hop, amely hop distace, which will be used as a correctio factor to be trasmitted to the etire etwork. After receivig the hop distace, regular odes multiply it by the hop cout umber to derive their estimated physical distaces to the achor odes. For istace, the average hop distace betwee achor odes i ad j is calculated as: (x i x j ) +(y i y j ) ) HopDistace i,j = i j () h i,j where (x i,y i )ad(x j,y j ) are the coordiates of achors i ad j, respectively, ad h i,j is the umber of hops betwee them. After hop distace estimatio, it is straightforward to estimate the distace betwee two achor odes i ad j as follows. d i,j est = HopDistace i,j h i,j. () O the other had, the actual distace, d i,j true, betwee achor odes i ad j is give by d i,j true = i j (x i x j ) +(y i y j ) (3) Followig () ad (3), the differece betwee the estimated ad actual distaces, deoted by e i,j, ca be expressed as e i,j = d i,j est di,j true, (4) which correspods to the estimatio error. Here, we propose the usage of the differetial error i (4) as a correctio term to the origial hop distace estimatio preseted i (). The effective average hop distace, EffHopDistace i,j, betwee achor odes i ad j is de- 33 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

3 fied as [4]: EffHopDistace i,j = HopDistace i,j ei,j + e i,m, h i,j + h i,m (5) where h i,m is the umber of hops i-betwee, ad m is the secod-closest achor ode to the ukow-positio ode k. Whe achor odes i ad m broadcast their average hop distaces from j to regular ode k, the related hop cout value will also be broadcasted simultaeously to reduce the total umber of trasmitted messages. After obtaiig both messages from i ad m, k calculates e i,j ad e i,m usig eq. (4). Subsequetly, the effective average hop distace ca be calculated usig the received beaco iformatio via eq. (5). Based o eq. (5), k ca compute its distace d k,j eff to achor ode j: d k,j eff = EffHopDistace k,j h k,j (6) If i is the closest achor ode to k, it is more accurate to estimate the distace betwee k ad j by usig EffHopDistace i,j. From this priciple, a geeralizatio to ay regular ode is possible. That is, a give regular ode ca use the effective average hop distace obtaied from its closest achor ode to calculate the distaces to its eighbor odes. As show i Fig., simple floodig method suffers from high message overhead whe used to provide locatio iformatio to eighbor odes, thus we propose a backoff-based broadcast mechaism to suppress redudat messages. A ode may receive sequetial beaco messages about the same achor ad each oe of them leads to a smaller hop cout. As a result, this ode may eed to forward it several times. Fig. illustrates a achor message propagatio iitiated by achor ode A. Due to the radom expoetial backoff of the MAC layer, ode C may broadcast A s message before ode B. Suppose that ode D wis the ext chael cotetio, ad both odes E ad F set their miimum hop cout to 3. It is possible that ode B further fails the chael cotetio dispute with ode E, ad thus ode E broadcasts a achor message cotaiig the wrog miimum hop cout iformatio before it otices the right value. Oce the order is altered, the error is accumulated from each broadcast. Node E oly eeds to broadcast aother achor message after hearig the lower hop cout iformatio from ode B, but odes that are farther away from the achor ode may eed to forward it several times to correct the accumulated error. We observe that odes at the border of the trasmissio rage of a seder have the widest coverage of its two-hop eighbors. Therefore, we should give these odes the highest priority to broadcast. This has bee extesively studied to reduce redudat broadcasts ad collisios [, 8, 3]. However, previous methods oly alleviate the redudacy problem rather tha completely suppressig it. Givig receivers farther away from a seder higher pri- A C B D G Figure : A example of achor message propagatio ority to broadcast could solve the redudacy metioed above. However, ode G still suffers from redudat broadcast. Previous methods would allow ode B to broadcast before ode C. Accordig to these methods, ode E should broadcast before ode D ad it is likely that ode E would also broadcastbeforeodec. IfodeF wis the followig chael cotetio, ode G would get a wrog hop cout of 3. Based o these observatios, we propose a backoffbased floodig which works as follows. Nodes that are far away from the seder are expected to have a weaker received sigal stregth. Therefore, we set ISS = Pr RXT hresh for each ode, where ISS is the icrease i sigal stregth, Pr deotes the received sigal power, ad RXT hresh deotes the miimum sigal power for successfully decodig a packet. Each ode defers its broadcast of the achor message for ISS uit delay time uits, where uit delay should be large eough to cope with the radom backoff of the MAC layer. Otherwise, ode C may still broadcast before ode B due to its wiig of cotetio i chael access. Supposig that ode B is o the border of the trasmissio rage of ode A, it will broadcast immediately after hearig a achor message from ode A. Node E should calculate its sedig defermet accordig to the same rule. I order to cope with the loop problem, ode E should wait for a additioal delay before iitiatig its trasmissio. I geeral, if a ode is ot a oe-hop eighbor of a achor ode, it should wait for a additioal period before forwardig the achor s message. Suppose all odes that eed to broadcast are located withi a rig characteristiced by two circles with radius α R ad R, whereα is determied by the ode desity obtaied by overhearig. As a example, i Figure, C may ot eed to broadcast if there are may odes located withi the rig determied by two circles with radius.5r ad R. The additioal delay is the calculated with a Pr value that is expected at the.5r distace. Simulatio results show that i our proposed backoffbased floodig, all odes broadcast oly oce. E F 34 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

4 3. Positioig via Particle Filterig For the positioig step, due to locatio ucertaity iserted by mobility, a ode iserts virtual achors to aid o costraiig the localizatio error. Let (X i,y i ) be the coordiates of a virtual achor ode, where i = {,, 3,,M}. Here, we select the midpoit of two oeor two-hop eighbor odes as the positio of virtual achor ode as show i Fig.. Note that a ode ca estimate its distace to a achor ode ad other regular odes usig the effective average hop distace ad the umber of hops i-betwee. These distaces are used to costrai a small predictio area, from which particles are draw ad filtered.as show i Fig., the gray rectagle idicates the predictio area from where particles represetig possible locatios are extracted. The ode s curret velocity is also used to miimize the predictio area. The speed iformatio ca be collected from sesor data. For istace, sesor odes are able to estimate their velocities usig a threedimesioal accelerometer. As show i Fig., a regular Figure 3: System model betwee A ad regular ode E be d ad the distace betwee regular ode E ad achor ode B be d 3. The distace betwee the virtual achor ode D ad regular ode E is defied as d. Fially, θ is the agle betwee lie segmets AB ad AE, which ca be calculated from the cosie rule. After obtaiig the values of d, d ad d 3 from triagle ABE, we have: cos θ = d + d d 3. (7) d d Similarly, i triagle ADE,wehave: cos θ = (d /4) + d d d d. (8) Figure : Buildig the predictio box. ode k located at the ceter of the itersectio area is able to directly commuicate with three oe-hop eighbors. For each pair of oe-hop eighbors, a virtual achor ode i is created ad k builds a square of size d k,i eff cetered at i, d k,i eff beig the estimated distace betwee k ad i. Based o the curret velocity of sesor ode, the coordiates of the reduced samplig rectagle area are calculated as follows: x mi =max( max (X i d k,i i= eff ),x t v t ) x max =max( mi (X i + d k,i i= eff ),x t v t ) y mi =max( max (Y i d k,i i= eff ),y t v t ) y max =max( mi (Y i + d k,i j= eff ),y t v t ), where (X t,y t ) are the coordiates of particle l t. Whe we cosider two-hop eighbors, we replace d k,j eff with the estimated distace betwee regular ode k ad its twohop eighbor virtual achor odes. Based o Fig. 3, let the distace betwee achor odes A ad B be d, the distace Thus, we ca calculate the value of d based o eqs. (7) ad (8) as follows: d d = +d 3 d. (9) Predictio Phase If the achor s distace ad speed costrait are disjoited, for example at iitializatio time, the ode excludes the speed costrait whe calculatig the predictio area. The predictio area helps to draw valid particles i the predictio phase. The probability of a give curret locatio based o a previous estimate is give by the uiform distributio: p(l t L t ) { if xmi x = t x max y mi y u y max otherwise, () where (x t,y t ) are the coordiates of particle l t. Filterig Phase I the predictio phase, each ode geerates a set of uiformly distributed radom values iside the predictio area. If the draw particles are located iside the commuicatio rage of every eighbor, the ode saves this positio for the fial estimatio. Otherwise, the ode discards it ad repeats the predictio phase. The etire filterig phase i a ode 35 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

5 ca be represeted as follows: filter(l t )= a M,d(l t,a) r + v t b M,r v t d(l t,b) r + v t, where l t is the cocered particle, M ad N are the sets of oe-hop ad two-hop eighbors, respectively, r is the ode s radio rage, d(l t,a) is the distace betwee particle l t ad eighbor a, adv t is the curret velocity of a eighbor ode. After obtaiig a sufficiet umber of valid particles, the fial locatio estimate is calculated as the average of the particle set. 4 Performace Evaluatio The geeral performace of our algorithm was obtaied through simulatio, usig a adapted versio of the simulator provided by the authors of []. We evaluated the effectiveess of the backoff-based broadcast mechaism ad the locatio accuracy of our proposal i terms of ode speed, ode desity, achor desity, ad commuicatio irregularities, ad compared it to four other algorithms:,,, ad. For the followig results, we cosider a topology of 3 odes, placed i a radom uiform maer over a area of 5 5 square uits. Uless specified otherwise, we cosider a achor desity of, ode desity of, ad radio propagatio usig the uit disk model. These parameters were also varied ad their evaluatio ca be see i the ext subsectios. The radio rage was set to 5 uits ad the maximum speed to 5 uits per time iterval. Achor ad regular odes move usig a modified versio of the radom waypoit model, with o pauses betwee itervals i order to prevet the average speed decay problem [3]. I the case of -based algorithms (,, ad our approach), we used a fixed samplig set of 5 uits. Just like [], we have verified that this is the best cost-beefit solutio. While maitaiig more samples improves accuracy, it also icreases computatioal overhead ad memory requiremets. For each parameter, a set of 3 simulatio rus was performed ad results were averaged. 4. Evaluatio of the Broadcast Mechaism We ivestigate the effectiveess of the backoff-based broadcast mechaism which is adopted i step of our proposal. Fig. 4 shows the umber of beaco messages a achor ode eeds to broadcast usig simple floodig ad our proposed backoff-based floodig to guaratee ode localizatio. Nodes are ordered i icreasig distace to the achor ode located at the left bottom corer. The miimum hop cout of the farthest ode to the achor is 9. We ca observe that some odes have to broadcast the same related message up to five times i simple floodig. Geerally, the farther away a ode is from the achor ode, the more messages it eeds to broadcast to correct the accumulated error. I cotrast, i our proposed backoff-based floodig all odes obtai their correct miimum hop couts with a overhead of oe message per ode. Therefore, our desig effectively reduces the umber of redudat messages. I aother experimet, we distribute odes i a Number of achor messages distace (meters) 5 simple floodig backoff-based floodig distace (meters) Figure 4: Number of achor messages trasmitted per ode 5m 5m field ad vary the trasmissio rage from to 5 meters. The average total umber of achor messages used by all odes is preseted i Fig. 5. I geeral, as the trasmissio rage decreases, the accumulated error icreases. Distat odes eed to rebroadcast more times. A trasmissio rage less tha 6 meters caot esure coectivity ad thus the overhead decreases suddely. Fig. 5 shows that our algorithm scales well to etwork size ad substatially suppresses redudat broadcasts. Total umber of achor messages simple floodig backoff-based floodig Maximum trasmissio rage (meters) Figure 5: Average umber of achor messages used by all odes 4. Covergece Time The secod simulatio aalysis cocers the locatio accuracy covergece. As it ca be see from Fig. 6, the iitial sharp declie o the estimatio error curves of the -based algorithms is due to ew locatio aoucemets from achors beig icorporated ito the sequetial Mote Carlo process. This is followed by a stable phase declarig the balace betwee updates to the posterior locatio distributio ad ucertaity itroduced by mobility. ad our proposal give similar performace, though the latter achieves slightly better accuracy. This is due to a 3 4 Number of achor messages 36 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

6 smaller samplig area, which effectively speeds up the collectio of valid samples, ad also due to the optimized filterig phase, which uses actual sesor data for costraiig the filterig area, opposed to a theoretical maximum velocity boudary. ad do ot exploit positio history iformatio, so their accuracy does ot chage over time Time Uits Figure 6: Accuracy compariso Node desity Node desity Figure 7: Impact of ode desity Fig. 7 shows the impact of ode desity variatio o the accuracy of each algorithm while the achor desity is kept costat. ad the -based algorithms are slightly affected by ode desity. I the case of the based algorithms, eve whe there are oly two-hop achor eighbors, eough samples ca be filtered to obtai a decet locatio estimate. For, a higher desity of odes reduces the estimatio error of the hop size leadig to a higher accuracy as well. I our simulatio experimets, performs best whe the ode desity is over Achor desity Icreasig achor desity facilitates the retrieval of locatio iformatio by regular odes. Fig. 8 shows the average estimate error of differet localizatio algorithms whe the achor desity varies. We ca see that all -based algorithms take advatage of a higher achor desity, as more positio aoucemets will be available for filterig. The same happes to. I the case of, the impact over accuracy is egligible as iformatio from the whole etwork is used idepedet of the umber of achors available. Our proposal performs better tha the other algorithms for reasos explaied above (smaller samplig area ad better filterig techique) Achor desity Figure 8: Impact of achor desity 4.5 Node speed As we ca see from Fig. 9, for all the -based algorithms the maximum speed variatio does ot affect much the locatio accuracy. At higher speeds, odes hear ew achors more ofte which add ew iformatio to the filterig phase, keepig the sample set updated. O the other had, as larger distaces are traversed at each time uit, the samplig area becomes larger, decreasig the algorithm s accuracy. I the case of, it is assumed that all etwork iformatio is provided to every ode at each time uit, a coditio that is too optimistic for a real etwork. Therefore, ode speed also does ot affect its performace. Still, it ca be see that its estimatio error is higher tha the -based algorithms. Node speed also does ot affect. 4.6 Commuicatio Irregularities Although the uit disk model is a simple ad easy-to-use commuicatio framework, it does ot reflect the reality of wireless commuicatio. The measured sigal stregth of radios ca vary substatially with evirometal coditios ad atea irregularities. This also affects the localizatio accuracy. Although may complex studies o radio propagatio models have bee proposed, we decided to use the Degree of Irregularity (DoI) [7] to model trasmissio ad 37 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.

7 Velocity (r per time uit) Figure 9: Impact of ode speed receptio adversities for compariso purposes. The DoI parameter defies the radio sigal stregth variatio o each directio of radio propagatio. As its value icreases, multihop commuicatio is affected ad the localizatio error of every algorithm icreases, except for, as show i Fig.. We ca see from the results that our proposed algorithm degrades more gracefully. Despite the message exchage hardships, our proposal is still able to filter a larger umber of valid samples tha the other -based algorithms Degree of Irregularity Figure : Impact of commuicatio irregularities 5 Coclusio We preset a distributed hop distace measuremet ad particle filter-based cooperative localizatio algorithm for mobile WSNs. Our proposal is scalable, robust, ad selfadaptive to the dyamics of a mobile sesor etwork. Our proposed algorithm ca reduce the hop distace estimatio error accumulated over multiple hops by usig a differetial error correctio scheme. I order to efficietly suppress redudat broadcasts ad to reduce commuicatio overhead, a backoff-based broadcast mechaism is proposed. It also improves localizatio performaceby icludig particle filterig techology. Simulatio results show that the proposed algorithm achieves better performace tha other state-of-the-art algorithms. Ifluece of physical obstacles over the commuicatio model remais to be explored as future work. Ackowldegmet This work is supported by CREST Advaced Itegrated Sesig Techology project of Japa Sciece ad Techology Agecy. Refereces [] A. Baggio ad K. Lagedoe. Mote Carlo localizatio for mobile wireless sesor etworks. Ad Hoc Netw., 6(5):78 733, 8. [] S. Biswas ad R. Morris. ExOR: opportuistic multi-hop routig for wireless etworks. SIGCOMM Comput. Commu. Rev., 35(4):33 44, 5. [3] T. Camp, J. Boleg, ad V. Davies. A survey of mobility models for ad hoc etwork research. Wireless Commuicatios & Mobile Computig (WCMC): Special Issue o Mobile Ad Hoc Networkig: Research, Treds ad Applicatios, :483 5,. [4] H. Che, K. Sezaki, P. Deg, ad H. C. So. A improved dv-hop localizatio algorithm with reduced locatio error for wss. IEICE Trasactios o Fudametals, E9-A:3 36, Aug. 8. [5] B. Dil, S. Dulma, ad P. Haviga. Rage-based localizatio i mobile sesor etworks. Lecture Notes i Computer Sciece, 3868:64 79, 6. [6] A. Doucet, N. Defreitas, ad N. Gordo. Sequetial Mote Carlo Methods i Practice. Spriger,. [7] T. He, C. Huag, B. M. Blum, J. A. Stakovic, ad T. Abdelzaher. Rage-free localizatio schemes for large scale sesor etworks. I Proc. of ACM MobiCom, pages 8 95, New York, NY, USA, 3. [8] M. Heissebüttel, T. Brau, T. Beroulli, ad M. Wälchli. BLR: beaco-less routig algorithm for mobile ad-hoc etworks. Elsevier s Computer Commuicatios Joural (Special Issue), 7:76 86, 4. [9] Y.-L. Hsieh ad K. Wag. Efficiet localizatio i mobile wireless sesor etworks. I SUTC 6: Proc. of IEEE Iteratioal Coferece o Sesor Networks, Ubiquitous, ad Trustworthy Computig, pages 9 97, Washigto, DC, USA, 6. [] L. Hu ad D. Evas. Localizatio for mobile sesor etworks. I Proc. of ACM MobiCom, pages 45 57, New York, NY, USA, 4. [] R. Nagpal, H. Shrobe, ad J. Bachrach. Orgaizig a global coordiate system from local iformatio o a ad hoc sesor etwork. Lecture Notes i Computer Sciece, 634: , 3. [] D. Niculescu ad B. Nath. Ad hoc positioig system (APS). I Proc. of IEEE GLOBECOM, volume 5, pages 96 93, Nov.. [3] F. Ye, A. Che, S. Lu, ad L. Zhag. A scalable solutio to miimum cost forwardig i large sesor etworks. I IC- CNC: Proc. of the th Iteratioal Coferece o Computer Commuicatios ad Networks, pages 34 39,. 38 Authorized licesed use limited to: IEEE Xplore. Dowloaded o Jauary, 9 at 3:3 from IEEE Xplore. Restrictios apply.