Multi-hop-based Monte Carlo Localization for Mobile Sensor Networks

Transcription

1 Mult-hop-based Monte Carlo Localzaton for Moble Sensor Networks Jyoung Y, Sungwon Yang and Hojung Cha Department of Computer Scence, Yonse Unversty Seodaemun-gu, Shnchon-dong 34, Seoul , Korea {jyy, swyang, Abstract Many low-cost localzaton technques have been proposed for wreless sensor networks. However, few consder the moblty of networked sensors. In ths paper, we propose an effectve and practcal localzaton technque especally desgned for moble sensor networks. Our system s based on the sequental Monte Carlo method, but dssmlar to other conventonal localzaton schemes, our algorthm covers a large sensor feld wth very few anchor nodes by nformaton floodng. The algorthm works wthout knowledge of the maxmum transmsson range, and covers some of the problems caused by the floodng beacons. We dscuss factors to mplement the algorthm n the real world and present several solutons. Our mechansm s mplemented n a real envronment, and ts feasblty s valdated by experments. The smulaton results show that our algorthm outperforms conventonal Monte Carlo localzaton schemes by decreasng estmaton errors by up to 50%, and the overhead of the algorthm could be mnmzed by approprately adjustng the system parameters. Index Terms locaton estmaton, moblty, probablty, wreless sensor network I. INTRODUCTION In wreless sensor networks, many applcatons such as vehcle trackng or envronment montorng systems assume that the system knows the locaton of each sensor node. Snce manual deployment of each node s not effectve, an automatc localzaton technque s requred. Usng GPS (Global Postonng System) [] s a smple soluton, but the method s mpractcal due to deployment constrants and cost. Hence, developng an effectve localzaton scheme s a fundamental and mportant ssue n wreless sensor networks. Numerous localzaton technques for wreless sensor networks have recently been proposed. Many technques calculate the poston of nodes based on the nformaton of a set of anchor nodes that know the locatons. The methods typcally assume statc network topologes; however, many sensor network applcatons demand the consderaton of moble sensor nodes. The Prnceton ZebraNet project [2] s a good example of a moble sensor network applcaton that explores wreless protocols and poston-aware computaton from a power-effcent perspectve. One of the project s fundamental requrements s to fnd the nodes locaton on moble objects. If the project adopts a localzaton technque for the moble sensors, they could reduce much of the cost for the system. Some recent work also dscusses localzaton when dealng wth moble nodes [3], [4]. However, most of the studes suggest that supportng moblty can be acheved by repeatng the statc localzaton algorthm. They perodcally repeat the algorthms and calculate new postons for the nodes. These methods are feasble n certan crcumstances; however, we beleve that a new localzaton algorthm should specfcally consder the moblty of sensor nodes. There are several challenges to desgnng a localzaton algorthm for moble sensor networks. Frst, the algorthm should work relably n the deployment condton, where the locaton of the node changes contnuously. Many prevous localzaton schemes for statc networks restrct envronment condtons such as unformly dstrbuted anchor nodes or a fxed rado transmsson range. In a moble sensor network, localzaton schemes should overcome these assumptons. Second, the localzaton should have mnmum overhead. Snce the localzaton s a part of the whole applcaton, the method cannot consume most of the resources such as CPU, battery, and network

2 resource. In ths paper, we are nterested n a localzaton system n whch both anchor nodes and sensor nodes have moblty. The moble sensor networks consst of poston-aware anchor nodes and poston-unaware general nodes. We propose a practcal localzaton algorthm that works n a large moble sensor network feld wth very few anchor nodes usng the sequental Monte Carlo method [5]. The localzaton technque s based on global nformaton gathered through mult-hop propagaton. Wth the mult-hop anchors nformaton, every general node constructs locaton boundares where the nodes could possbly exst and estmate the locaton. Our system s free from addtonal hardware and knowledge of the maxmum rado transmsson range. The rest of ths paper s organzed as follows. In Secton Ⅱ, we descrbe prevous localzaton schemes. The motvaton for our work s explaned n Secton Ⅲ. In Secton Ⅳ, we propose a new localzaton technque. Secton Ⅴdescrbes mplementaton ssues of the system. In Secton Ⅵ, we analyze the performance of our system through both experments and smulatons. Secton Ⅶ concludes the paper. II. RELATED WORK Varous technques to estmate the locaton of wreless sensor nodes are found n the lterature. The well-known range-based methods typcally use receved rado sgnal strength [6], [7], tme dfference of arrval of dfferent sgnals [8], [9] or angle of arrval [0] as a rangng measure. However, the rangng measure usually provdes unrelable data [] or requres addtonal devces to mplement. Several localzaton schemes have been desgned to localze sensor nodes wthout range nformaton. Many such technques assume that some nodes already know ther global postons, and nformaton from these nodes s used to estmate the unknown node s locaton. Many schemes focus on mprovng the accuracy. Centrod [2] by Nrupama et al. s a smple localzaton scheme wthout rangng. Each node n the system calculates the center of the locatons of all anchor nodes the node hears and regards the center as ts poston. Locaton error can be reduced by deployng the anchor nodes n good postons [3], but ths assumpton s not approprate for a moble ad-hoc network. Nculescu et al. [4] proposed an ad-hoc postonng system (APS). APS ncludes three dfferent propagaton methods: DV-hop, DV-dstance, and Eucldean. These methods obtan relatvely accurate results n mult-hop networks. Among the methods, DV-hop converts hop count to the dstance between an unknown node and an anchor node. The system calculates a corrected factor, whch means the average dstance of a hop, and uses the factor for converson. The method s mplemented n other work and compared wth other mechansms [5]. Lm et al. [6] proposed the Proxmty Dstance Map (PDM), whch calculates the partcular transformaton matrx to convert hop count to dstance. The matrx characterzes ansotropc network topologes and proxmtes to the anchor nodes n all drectons. Shang et al. [7], [8] proposed mult-dmensonal-scalng-based localzaton methods MDS-map and MDS-map(P). MDS-map, the frst model of ther scheme, gathers the connectvty nformaton of the sensor nodes and bulds a relatve map of the sensor feld by usng mult-dmensonal scalng. Ths method s accurate compared to other methods. However, the tme complexty of constructng a relatve map s O(n 3 ), where n s the number of nodes. Shang et al. also proposed the dstrbuted verson of MDS-map, MDS-map(P), but the methods are not approprate for a moble network due to the computatonal complexty. MCL [9] s desgned for moble sensor networks based on the sequental Monte Carlo method. Sensor nodes randomly predct ther postons based on ther prevous postons, and flter the predcton by usng the transmsson range of the seed nodes. When the nodes obtan a suffcent number of poston samples, the locatons are estmated by calculatng the center of the sample postons. Dssmlar to the other localzaton method, the movement of sensor nodes mproves the method s estmaton accuracy. A range-based verson of MCL has also been proposed [20]. Ths verson provdes a samplng and flterng method based on range measurements, and weghs each vald sample to obtan accurate estmaton results. Baggo et al. [2], [22] proposed an enhanced Monte Carlo localzaton scheme, MCB. By reducng the samplng area, MCB draws good samples, and thereby the number of teratons to construct the sample set s reduced. Computaton overhead s reduced by the mechansm; however, the algorthm stll depends on specfc parameters such as fxed rado transmsson range. In our work, we propose a new localzaton mechansm based on the sequental Monte Carlo method wth mult-hop

3 propagaton. Our method keeps the strengths of prevous Monte Carlo localzaton algorthms and removes some of ther weaknesses. III. MOTIVATION Prevous range-free localzaton algorthms desgned for moble sensor networks [9], [2], [22] have two major constrants. Frst, a suffcent number of anchors are requred for the algorthms. The poston estmaton of MCL depends on local anchor nformaton; hence, the locaton error could be large when the densty of anchor nodes s low. Although MCL s an extenson approach that ncludes nformaton about the neghbors, the problem s not solved completely. Accordng to the smulaton results of MCL [9], MCL needs more than one anchor n a one-hop transmsson range to obtan reasonable accuracy. Ths number of anchors s relatvely small but not suffcent to apply the algorthm n a real envronment. We suggest that floodng anchor nformaton allows the system to work wth a few anchors n the sensor network feld. Second, the prevous algorthms assume that the fxed rado transmsson range s known. In a real envronment, however, the rado range vares by resdual battery, geometrc characterstcs, and many other factors. Especally, the maxmum transmsson range s affected by how far away a node s from the ground. Often, n moble sensor deployment, the heght of a node usually vares due to the feature of the moble object. Snce fgurng out the rado transmsson range s dffcult n real envronments, we should remove the assumpton. These constrants are possbly lfted by DV-hop [4]. It floods anchor nformaton to entre sensor feld. Every anchor receves nformaton about the other anchors and calculates the average one-hop dstance by usng the nformaton. The average dstance s used to convert the nodes hop count to actual dstance. However, the dstance converson shows negatve results such as unstable transmsson range n real deployment [23]. Fg.. Dstance error occurrence wth DV-hop (experment) We mplemented the DV-hop propagaton method and observed the dfference between the actual dstance and the estmated dstance. We deployed 25 sensor motes n varous topologes. Several fundamental problems should be consdered when deployng sensor network applcatons n the real world. We dscuss the mplementaton ssues n SectonⅤ. Fg. llustrates the error dstrbuton for the dstance estmaton experment. The results show that DV-hop causes both overestmaton and underestmaton problems. We also smulated the DV-hop to analyze the dstance estmaton error n large moble sensor networks. Detals of the smulaton are descrbed n Secton Ⅵ. Fg. 2 llustrates the smulaton results obtaned wth 400 nodes n a 500mx500m of network feld wth a 50m transmsson range. Fg. 2. Dstance error occurrence wth DV-hop (smulaton) The smulaton results show that overestmaton occurs more frequently than underestmaton. The results also show that DV-hop overestmates the dstance badly when the hop count s large. Some of the reasons whch occur the error explan these results.

4 Fg. 3. Cases causng dstance estmaton error Fg. 3 shows the specfc cases n whch dstance estmaton error s occurred. In Fg. 3 (a), overestmaton occurs when general node G computes the dstance from the anchors, A and A2. In DV-hop, the hop dstance s calculated from the rato of total absolute dstances to the total hop counts between anchors. The calculated hop dstance would be smlar to the actual rado transmsson range; however, G s not on the boundary of the rado range. Although G s closer to the anchor A than G2, DV-hop regards G as beng apart from A as far as G2. Fg. 3 (b) llustrates the stuaton n whch the propagaton path does not form a straght lne. Although G3 s relatvely close to A, the path from A to G3 generates three hop communcatons; hence, G3 assumes t s on the dashed arc. Ths stuaton occurs often when the number of hop counts from an anchor s large. Under a condton such as Fg. 3 (c), both overestmaton and underestmaton arse. When G5 calculates the dstance from the anchors A and A2, G5 overestmates the dstance from A and underestmates the dstance from A2. Even n the stuaton of ansotropc deployment of nodes, DV-hop calculates only the average hop dstance between anchors and apples the value to the whole network. The dstance error of DV-hop ncreases when appled to a moble sensor network snce the network topology changes durng the propagaton progress. Dstance overestmaton and underestmaton of the DV-hop propagaton algorthm occurs for dfferent reasons and wth dfferent frequency; hence, proper solutons for each case are requred to apply the DV-hop n a real envronment. In our work, we adopt the DV-hop propagaton method as a part of our localzaton system to calculate the average hop dstance. We modfy the estmated dstance to apply DV-hop to our system. IV. MULTI-HOP-BASED MONTE CARLO LOCALIZATION In ths secton, we descrbe the proposed localzaton algorthm for moble sensor networks. Frst, we state the problem and descrbe an overvew of prevous work on whch we conceptually base our algorthm. Our localzaton algorthm s descrbed subsequently. A. Background We consder the localzaton problem for a moble sensor network. Sensor nodes are deployed n the sensor feld, and all have ther own moblty. The network topology can be dynamcally changed by moble nodes. We are partcularly nterested n the stuaton when the densty of anchor nodes s low. We assume that full network connectvty s guaranteed n spte of node moblty. A sensor feld conssts of two types of sensor nodes: general nodes and anchor nodes. General nodes are not aware of ther locatons, whereas anchor nodes always know ther exact postons and send beacon messages contanng locaton nformaton. We assume that at least three anchor nodes exst n the network and that all nodes are equally lkely to move n any drecton wth any speed between 0 and v. The problem s to estmate the locaton max of general nodes wth knowledge about the poston of anchor nodes and the hop count between the anchor nodes and general nodes. The sequental Monte Carlo (SMC) [5] method s a group of smulaton-based methods from a sequence of probablty dstrbutons. The method s extensvely used to solve sequental Bayesan nference problems n econometrcs, sgnal processng, and robotcs. SMC methods approxmate the sequence of probablty dstrbutons of nterest usng a large set of random samples. As the number of partcles goes to nfnty, the convergence of these partcle approxmatons toward the sequence of probablty dstrbutons can be ensured under weak assumptons. Localzaton technques based on SMC were developed early n robotcs [24]. Robotcs localzaton assumes a pre-learned map, and tres to estmate the robot s poston based on ts moton and perceptons. However, n sensor networks, nodes have lmted knowledge of local nformaton and computatonal power. The sensor network verson of the SMC-based localzaton was ntroduced by MCL [9]. MCL uses the local anchors locatons and the maxmum rado transmsson range. The MCL algorthm s as follows: At the frst step, a set of

5 Propagaton Intal propagaton: Intally the anchors have no knowledge of other anchors. flood beacon message wthout corrected factor for each anchor node do calculate corrected factor flood beacon message end do Locaton Estmaton for each general node j do L t = {} whle(sze( L ) < N) do t //Construct predcton area wth mult-hop constrants P t = { xmn, xmax, ymn, ymax} //Predcton R { l l s selected wtn P wth p( l l ) > 0} = t t t t t //Flterng R { l l R p( o l ) > 0} fltered = t t t t Lt = choose( Lt R end do end do fltered, N) Fgure 4. Mult-hop-based Monte Carlo Localzaton 2 N postons, L = { l, l,..., l } s randomly selected for the ntal locatons of the nodes. A predcton phase follows n whch every node predcts ts poston based on the prevous locaton and maxmum speed. The flterng phase, after predcton, decdes f the predcted poston s vald. The nodes use one- and two-hop anchors nformaton to flter the poston. One-hop anchors are assumed to be wthn the rado transmsson range r of the sensor node. Two-hop anchor postons, gathered from neghbor nodes, are used for negatve nformaton. In other words, the anchors are assumed to be n the range 2r but not n a radus r. The nodes repeat the predcton and flterng untl they obtan a suffcent number of vald postons. A node consders the center of the vald postons to be ts new locaton. These processes, except for ntalzaton, operate at every tme unt. B. Mult-hop-based Monte Carlo Localzaton In ths secton, we descrbe our localzaton scheme, Mult-hop-based Monte Carlo Localzaton (MMCL). In MMCL, anchors flood locaton nformaton perodcally. Each node uses the mult-hop nformaton and constructs locaton boundares shaped as rngs. The MMCL localzaton procedure conssts of two parts. The frst part provdes an average hop dstance among anchor nodes as DV-hop does. Every sensor node obtans the average hop dstance from the anchor nodes and calculates ts poston. The second part s to run the sequental Monte Carlo process n each sensor node. The MMCL localzaton system repeats these processes n every tme perod. Fg. 4 provdes the overvew of the MMCL localzaton algorthm. The hop dstance calculaton s smlar to DV-hop. In the begnnng of each localzaton perod, every anchor node floods the sensor feld wth a beacon message that contans the anchor s exact locaton, ID, sequences, and hop counts ntally set to zero. Each unknown sensor node mantans an anchor table { ID, x, y, h, s } where x and y represent the poston of the anchor, h the hop counts, and s the sequence number. The node updates the table when the node receves a beacon message from a new anchor, a new sequence number, or smallest hop counts from a anchor. When an anchor node receves a suffcent number of locaton messages from other anchor nodes, the corrected factor s calculated as shown n Equaton () [4]. In tradtonal DV-hop, the anchor node floods the corrected factor c to unknown nodes after the beaconng, whch generates large network communcaton overhead. In our algorthm, we attached the corrected factor to the next beacon message,.e., the beacon messages have another data feld for the corrected factor. Hence, we use only half of the packet transmssons, compared to DV-hop. We stochastcally analyzed the characterstcs of the moble network and obtaned parameters to modfy the dstance calculaton for consderng dstance estmaton error. 2 2 ( X X j ) + ( Y Y j ) c = h () j, for all anchor nodes j The second part of MMCL, the poston calculaton, s operated on each unknown node at fxed perods. Durng the perod, nodes gathers anchor nformaton and relay the data to other nodes and calculate the poston at the end of the perod. Instead of decdng the dstance from an anchor node, each node assumes that t s located n a certan range from the anchor node. Equaton (2) represents the dstance range that each node assumes. The sze of the dstance range depends on the value ofα and β. The parameters should be decded carefully snce the unknown node must exst n

6 every dstance range to calculate the poston correctly. The defnte values of α and β are descrbed n Secton Ⅳ-C. c α d c β (2) Fg. 5. Mult-hop constrants, predcton area, and vald regon Before predctng the poston of an unknown node, the node draws a predcton area, as shown n Fg. 5. The dark rectangle n the mddle of Fg. 5 llustrates the predcton area. The maxmum speed of the node s also used for predcton area estmaton. The coordnates of the rectangle area are represented as follows: n x max( max( x c β ), x v ) (3) mn = t = x y max mn n = mn( mn( x + c β ), xt + vmax ) (4) = n = max( max( y c β ), yt vmax ) (5) = n ymax = mn( mn( y + c β ), yt + vmax ) (6) = If the anchor dstances and speed constrant are dsjonted, the node assumes that the prevous locaton has a large error, and excludes the speed constrant for predcton area estmaton. The predcton area helps to draw good samples durng the predcton phase [2]. In the predcton phase, each node generates unformly dstrbuted random values nsde the predcton area. After the predcton, the node goes through the flterng phase. If the predcton s located n a vald range from every anchor, the node saves the poston as a sample. Otherwse, the node dscards the predcton and fnds another poston. The entre predcton and flterng phases n a node are represented as follows: Predcton f x x x y y y mn t max mn t max p( lt lt ) = 0 otherwse max Flterng flter ( l ) a A, c α d( l, a) c t = a t a β Here, A s the set of anchors that an unknown node has recognzed, and d( l t, a) represents the Eucldean dstance from anchor a to predcted locaton l t. After obtanng a suffcent number of vald samples, the nodes regard ther locatons as the average of the vald samples. All of these steps are processed at every estmaton perod. C. Parameter Decson Ths secton descrbes the decson process of the parameters, α and β, n Equaton (2). These parameters present approprate dstance ranges from anchor nodes to general nodes. To decde the specfc parameter value of MMCL, we smulated the DV-hop propagaton method and analyzed the dstance estmaton errors. Smulaton results were obtaned wth an average of 30 executons wth dfferent random number generator seeds. We assumed 75 to 400 sensor nodes were deployed n a 500mx500m area of the sensor feld. Each sensor node has a 50m rado transmsson range and the same length of maxmum speed. Three anchors among the sensor nodes calculate the corrected factor and flood the nformaton about the locaton and the calculated corrected factor. α = h 0.4 (7) β = h + 2 (8) As we noted n Secton Ⅲ, t s necessary to consder underestmaton and overestmaton errors separately to compensate for the dstance error. Fg. 2 n Secton Ⅲ showed that the dstance error s n proporton to the hop count n the case of overestmaton. We constructed varous boundares accordng to the hop counts. Fg. 6 shows the rato of nodes that exst n the boundares. When we construct the boundary as 40% of the estmated dstance by DV-hop, only a few percentages of nodes are postoned nsde the boundary. In other words, most of the dstances between an anchor and nodes are greater than c h 0. 4, where c and h represent the corrected factor and hop count from anchor, respectvely. We choose the boundary as a negatve constrant of MMCL; hence,α s set as Equaton (7), where h s the hop count from the anchor, and every node regards t as located out of the boundary.

7 Fg. 6. Doman of overestmaton Fg. 7. Doman of underestmaton In the case of underestmaton, the dstance estmaton error of DV-hop occurs n two cases: non-unform nodes densty and the movement of nodes durng beacon propagaton. Snce underestmaton s not affected by other elements, we added ncreasng values to hop counts and constructed the boundary as a multple of the corrected factor and the ncreased hop counts. Fg. 7 llustrates the rato of nodes that are located out of the tested boundary. Accordng to the results, more than 95% of the nodes are covered by the boundary of two addtonal hop counts. The boundary s chosen as a postve constrant of MMCL, whch means that a node exsts nsde the boundary. Hence, β s represented as Equaton (8). Wth the decson about α and β, Equaton (2) covers the expermental result n Fg.. V. EVALUATION In ths secton, we evaluated MMCL usng experments and smulatons. The real expermental results valdate the feasblty of MMCL, and the smulaton results show the performance characterstcs of our method n moble sensor networks. Fg. 8. System deployment A. Experment Results To valdate the feasblty of our work, we mplemented the algorthm n a real envronment and observed the performance of the algorthm. We used Tmote Sky [25] and TnyOS [26] for mplementaton. The radaton pattern of the nternal antenna n Tmote Sky s uneven so that the dfference n the measured RSS s up to 20dBm [27]. We modfed the mote hardware and attached an external antenna. For the evaluaton, we controlled the rado transmsson power and deployed the system n a small regon. Also we used external antenna for horzontally omndrectonal rado pattern. Although the system was not deployed n large outdoor feld, we adjusted the system to work smlar to the large feld n relatvely small area. Twenty-one general nodes and four anchor nodes were deployed n grd topology. The unt length of the grd was 90cm. We set the RSSI constrant to -75dbm, whch allows relable communcaton wthn 90cm but rarely transmts to 80cm far. Fg. 8 shows a snapshot of the deployment of the system. Evaluatng the accuracy of localzaton s dffcult whle the nodes are movng; hence, we estmated the nodes locatons n a statc stuaton for the evaluaton. Fg. 9 shows the locaton estmaton error of each node. The average locaton error was about 95cm. In the real-world mplementaton, t s dffcult to fnd out the exact maxmum transmsson range; hence, we cannot compare the results drectly wth those of the smulaton. However, we know the transmsson range s longer than 90cm and less than 80cm. If we apply 90cm as the maxmum rado range, the average locaton error rato to rado transmsson range s.06r, where r represents the rado range.

8 MMCL For the smulatons, 400 nodes were deployed n rectangular 500m x 500m regon. We assumed the transmsson range was 50m for all nodes. We vared the parameters such as the number of anchors, speed of nodes, TTL (maxmum hop count) of a beacon message, and transmsson range node IDs Fg. 9. Estmaton error for dfferent nodes n real system mplementaton Fg.. Estmaton error vs. anchors number (speed of nodes: r, TTL: 5 ) (a) Object tracng wth trangular topology (b) Object tracng wth grd topology Fg. 0. Trackng moble node wth MMCL Instead of measurng the exact accuracy of nodes n a moble envronment, we obtaned a trace of a moble node n network felds. Fg. 0 shows the results of tracng a moble node n dfferent topologes. Statc nodes guarantee the connectvty of the nodes. The estmated lne follows the real trajectory of a node. The expermental results valdate that MMCL works reasonably well n a real envronment. B. Smulaton Results The general performance of MMCL was analyzed through smulaton. We observed the characterstcs of MMCL n varous condtons and large networks. In our smulaton, we vared the parameters of the sensor networks. The accuracy of localzaton s drectly related to the number of anchors. As mentoned earler, prevous Monte Carlo method-based localzaton algorthms requre relatvely large number of anchors. Fg. shows the mpact of the number of anchors on the localzaton error. Although [9] barely mentoned nformaton floodng, we assumed a floodng verson of MCB (MCB_flood) for comparson. Estmaton errors nclude un-localzed nodes that chose random postons as ther locaton, and the results are represented as the rato of transmsson range. MCL has an average 4r of locaton error rato wth four anchors snce most of the nodes faled to obtan anchor nformaton. MCB reduces the computaton overhead, but the accuracy s smlar to MCL. Both mechansms work well wth 40 anchor nodes. MMCL outperforms other algorthms wth 50% less error wth few anchors. The accuracy of MMCL s smlar to the other mechansm when the number of anchor nodes s large. MCB_flood s as accurate as MMCL; however, the mechansm has a crtcal assumpton, about the knowledge of the fxed rado range, n ts mechansm. As we descrbed n Secton Ⅴ, fndng maxmum rado transmsson ranges s dffcult n the real world snce the transmsson range vares due to many other factors such as the remanng power, heght of a node, obstacles and so on. To nvestgate the effects of wrong nformaton about the transmsson range, we smulated MCB_flood wth the wrong transmsson range. We nputted 40 anchors for the

9 smulaton. Fg. 2 shows the mpact of transmsson range predcton error. If the expected rado range s smaller than the actual rado range, MCB_flood generates poor result. Wth a short transmsson range, MCB_flood fals to construct a samplng box and pcks random values for localzaton. When the knowledge of the rado range s longer than the actual range, the estmaton error also reduced snce the large transmsson range constructs too large a samplng box. On the other hand, MMCL does not requre pre-knowledge about the transmsson range; hence, the result s not nfluenced by ncorrect knowledge about rado range. Ths result also shows that MMCL s adaptable n real envronments. 5 global floodng, we could set up the maxmum hop count (TTL) of a beacon message. To observe the mpact of TTL, we vared the TTL for the system and smulated the accuracy of MMCL. Fg. 3 shows the smulaton result how TTL nfluences accuracy. MMCL requres suffcent TTL, but TTL does not affect estmaton error after some pont. The pont could change due to the network sze or number of anchors snce MMCL requres mult-hop communcaton between anchors. However, the results reveal that the system could reduce the communcaton overhead wthout loss of accuracy MCB_flood MMCL Transmsson range predcton error (%) Fg. 2. Estmaton error vs. knowledge of transmsson range Fg. 3. Estmaton error vs. TTL (number of anchors: 30, speed of nodes: r) Although MMCL s approprate for a moble sensor network, the mechansm has weaknesses. One problem s that floodng requres large communcaton overhead. Snce many applcatons n moble sensor networks are not only for trackng objects, communcaton overhead should be adaptvely reduced. One easy way to decrease the network overhead n MMCL s controllng floodng. Instead of Fg. 4. Estmaton error vs. speed of nodes (TTL: 5 ) Increasng the speed of the movng nodes s smlar to ncreasng the unt tme between locaton estmatons. If the locaton estmatons are less frequent, the relatve communcaton overhead would decrease. We vared the maxmum speed of nodes v max. In the smulaton, every node moves to a randomly chosen poston wthn v max from the prevous locaton. Fg. 4 shows the result of estmaton error nfluenced by speed of nodes. The result reveals two facts. Frst, the left half of the graph shows that the moblty of nodes makes the localzaton accurate. The second half of the graph shows the accuracy of localzaton s not nfluenced by the node s speed after some threshold. The system coverng fast moble nodes means the system supportng a long perod for localzaton. Ths does not mean a reducton of the absolute communcaton overhead. However, the applcaton has more tme to do other work nstead of localzaton; hence, the relatve communcaton overhead would be dmnshed. VI. CONCLUSION In ths paper, we proposed a mult-hop-based Monte

10 Carlo localzaton algorthm. By floodng anchor nformaton to the sensor feld, the number of sensors that cannot receve anchor nformaton decreases. The smulaton results show that, compared to other Monte Carlo-based algorthms, up to 50% of errors are reduced where anchor nodes are sparsely deployed. The results also show the network overhead could be reduced by controllng some of the system parameters. One of our key contrbutons s to have mplemented the proposed algorthm and checked the feasblty of the algorthm wth real experments. We presented mplementaton ssues and showed that our system operates reasonably well n a real envronment. Future work ncludes the valdaton of our algorthm n a densely deployed envronment. ACKNOWLEDGMENTS Ths work was supported by the Korea Scence and Engneerng Foundaton (KOSEF) through the Natonal Research Lab. The program was funded by the Mnstry of Scence and Technology (No. M J ), and the ITRC (Informaton Technology Research Center) programs of the IITA (Insttute of Informaton Technology Advancement) (IITA-2006-C ). REFERENCES [] B. Hoffman-Wellenhof, H. Lchteneeger, and J. Collns, Global Postonng System: Theory and Practce (4th ed.). New York: Sprnger-Verlag, 997. [2] P. Juang, H. Ok, Y. Wang, M. Martonos, L. S. Peh, and D. Rubensten, Energy-effcent computng for wldlfe trackng: Desgn tradeoffs and early experences wth ZebraNet, n Proc. ASPLOS-X, San Jose, 2002, pp [3] L. Lazos, S. Capkun, and R. Poovendran, ROPE: Robust poston estmaton n wreless sensor networks, n Proc. IPSN, Los Angeles, 2005, artcle No.43. [4] D. Moore, J. Leonard, D. Rus, and S. Teller, Robust dstrbuted network localzaton wth nosy range measurements, n Proc. Sensys, San Dego, 2004, pp [5] Fshman, G. S. (ed.), Monte Carlo Concepts, Algorthms, and Applcatons. New York: Sprnger-Verlag, 996. [6] P. Bahl and V. N. Padmanabhan, RADAR: An n-buldng RF-based user locaton and trackng system, n Proc. INFOCOM, Tel Avv, Israel, 2000, pp [7] K. Yedavall, B. Krshnamachar, S. Ravula, and B. Srnvasan, Ecolocaton: A technque for RF-based localzaton n wreless sensor networks, n Proc. IPSN, Los Angeles, 2005, artcle No. 38. [8] N. Pryantha, A. Chakaborty, and H. Balakrshnan, The Crcket locaton-support system, n Proc. MobCom, Boston, 2000, pp [9] A. Savvdes, C. C. Han, and M. B. Srvastava, Dynamc fne-graned localzaton n ad-hoc sensor networks, n Proc. Mobcom, Rome, Italy, 200, pp [0] D. Nculescu and B. Nath, Ad-hoc postonng system (APS) usng AOA, n Proc. INFOCOM, San Francsco, 2003, pp [] E. Elnahrawy, X. L, and R. Martn, The lmts of localzaton usng sgnal strength: A comparatve study, n Proc. SECON, Santa Clara, 2004, pp [2] N. Bulusu, J. Hedemann, and D. Estrn, GPS-less low cost outdoor localzaton for very small devces, IEEE Personal Communcatons Magazne, Vol. 7, No. 5, pp October, [3] N. Bulusu, J. Hedemann, and D. Estrn, Adaptve Beacon Placement, n Proc. ICDCS, Phoenx, 200, pp [4] D. Nculescu and B. Nath, Ad hoc postonng system (APS), n Proc. Globecom, San Antono, 200, pp [5] R. Stoleru and J. Stankovc, Probablty grd: A locaton estmaton scheme for wreless sensor networks, n Proc. SECON, Santa Clara, 2004, pp [6] H. Lm and J. C. Hou, Localzaton for ansotropc sensor networks, n Proc. INFOCOM, Mam, 2005, pp [7] Y. Shang, W. Ruml, and Y. Zhang, Localzaton from mere connectvty, n Proc. MobHoc, Annapols, 2003, pp [8] Y. Shang and W. Ruml, Improved MDS-based localzaton, n Proc. INFOCOM, Hong Kong, 2004, pp [9] L. Hu and D. Evans, Localzaton for moble sensor networks, n Proc. Mobcom, Phladelpha, 2004, pp [20] B. Dl, S. Dulman, and P. Havnga, Range-based localzaton n moble sensor networks, n Proc. EWSN, Zurch, 2006, Volume [2] A. Baggo and K. Langendoen, Monte-Carlo Localzaton for moble wreless sensor networks, MSN, to be publshed. [22] A. Baggo. Monte-Carlo localzaton for moble wreless sensor networks, Delft Unversty of Technology, Delft, Tech. Rep. PDS , June [23] S. W. Wong, J. G. Lm, S. Rao, and W. K. Seah, Densty-aware hop-count localzaton (DHL) n wreless sensor networks wth varable densty, n Proc. WCNC, New Orleans, 2005, pp [24] F. Dellaert, D. Fox, W. Burgard, and S. Thrun, Monte Carlo localzaton for moble robots, n Proc. ICRA, Detrot,999, pp [25] Tmote Sky. Avalable: [26] J. Hll, R. Szewczyk, A. Woo, S. Hollar, D. Culler, and K. Pster, System archtecture drectons for network sensors, n Proc. ASPLOS, Cambrdge, 2000, pp [27] S. Yang and H. Cha, An emprcal study of antenna characterstcs toward RF-based localzaton for IEE sensor nodes, EWSN, to be publshed.