A Walking Beacon-Assisted Localization in Wireless Sensor Networks

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1 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. A Walking Beacon-Assisted Localization in Wieless Senso Netwoks Bin Xiao 1 1 Depatment of Computing Hong Kong Polytechnic Univesity, HK csbxiao@comp.polyu.edu.hk Hekang Chen 1,, Shuigeng Zhou Dept. of Compute Science and Engineeing Fudan Univesity, Shanghai, China {hkchen, sgzhou}@fudan.edu.cn Abstact The localization of the senso node is a fundamental poblem in senso netwoks and can be implemented using poweful and expensive beacons. Beacons, the fewe the bette, can acquie thei position knowledge eithe fom a GPS device o by vitue of being manually placed. In this pape, we popose two distibuted methods to localization of senso nodes using a single moving beacon whee senso nodes compute thei position estimate based on the ange-fee technique. The fist method uses the aival and depatue infomation of a walking beacon and the second method exploits the vaiance of the Received Signal Stength (RSS) fom the beacon. We povide the uppe bound of the estimation eo fo these methods in an ideal envionment. Citical to the location accuacy of senso nodes ae two moe paametes, the adio tansmission ange of the beacon, and how often the beacon boadcasts its position. Simulation esults show the location estimate eo of senso nodes applying the poposed two methods. The esults ae consistent to the theoetical analysis and the aveage estimate eos could be within one mete. I. INTRDUCTIN Wieless senso netwoks (WSN) ae a cuent focus of eseach inteest because of thei boad applicability in aeas such as envionmental obsevation, militay monitoing, building monitoing and disaste elief. The pefomance of WSNs is cucially influenced by how accuately senso nodes within the netwok ae localized. Senso localization infomation is used in the self-oganization and configuation of netwoks, in deciding whee events take place, tacking moving tagets [1], [], assisting taffic outing [3], [4] and poviding the netwok geogaphic coveage [5]. Cental to such location awae opeations ae the techniques used to identify the position of each senso node. Constaints of cost and powe consumption make it infeasible to equip each node in a netwok with a Global Positioning System (GPS) [6]. It is possible, howeve, to equip a small numbe of sensos. Such sensos nodes, in this pape efeed to as beacons - may be static o mobile and may be used to identify the position of othe nodes in a senso netwok. This is done with eithe the ange-based o the ange-fee technique. The ange-based technique [7], [8], [9], [10] can detect the position of a node though the Received Signal Stength (RSS) measuement. RSS is a fundamental popety to eflect the distance between two senso nodes in the wieless communication envionment. The equipped RSSI (Received Signal Stength Indicato) in many senso platfoms, such as mica and micaz, makes the diect distance measuement possible. Howeve, the signal captue can be seveely affected by the envionmental intefeence, geatly degading detection accuacy. In the ange-fee technique [11], [1], [13], each senso node uses signals fom a few beacons to calculate its appoximate location. To diectly eceive signals, a node must fall inside the ovelapping tansmission aea of seveal beacons. Nonetheless, the infomation that a node is outside of the tansmission aea of a beacon can also be used to set a tighte bound on the location of a node. The moving beacon can be effectively utilized to locate the position of senso nodes in WSNs [14], [15], [16], [17]. If the beacon moves and peiodically boadcasts its position to nodes in its vicinity then a single beacon will suffice. Such a position-awae beacon can acquie its geogaphical position though GPS o the position can be known because it moves along a pedefined oute. Using a moving beacon that knows its position is boadly equivalent to using many stationay beacons each boadcasting once. A senso node can compute an aea to confine its location if it eceives the coodinate messages fom the beacon in a couple of times. nce a senso node has appoximately detemined its position it can help to localize its neighbo nodes o even distant nodes. Ultimately, the location estimate of each senso node is detemined by the moving beacon. Thus, the degee of accuacy with which a senso node is located is detemined by the knowledge of the oute that the beacon tavels and how often it emits a signal. In this pape, we popose two distibuted methods to localization of senso nodes using a moving beacon. The fist method uses the aival and depatue infomation of a walking beacon and the second method exploits the vaiance of the RSS fom the beacon. A senso node locally computes its position estimate based on the ange-fee technique. Note that the beacon can have a pio knowledge of the deployment aea of senso nodes and thus can move in staight lines to cove the whole aea. We povide the uppe bound of the estimation eo fo two methods in an ideal envionment. Citical to the location accuacy of senso nodes ae two paametes, the adio tansmission ange of the beacon, and how often the beacon boadcasts its position. These methods do not equie specially designed hadwae equipments (e.g., angle detection, time synchonization) in senso nodes in the localization context. They ae obust to be applied pactically in the eal life and ae scalable to /07/$ IEEE

2 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. locate each node given that the beacon can move to each cone of the senso netwok deployment aea, no matte that the senso netwok topology is isotopic o anisotopic [18]. Simulation esults show the location estimate eo of senso nodes applying the poposed two methods. The esults ae consistent to the theoetical analysis and the aveage estimate eos could be within one mete. This pape is oganized as follows. In Section II, we descibe the elated wok in the aea of senso node localization. Section III and IV pesent the distibuted localization techniques using the aival and depatue, RSS infomation of a moving beacon espectively. Section V demonstates the simulation esults of these methods in tems of RMSE (Root Mean Squae Eo) and Maximum estimate eos. Finally, we offe ou conclusion in Section VI. II. RELATED WRK Most localization methods ae static. That is to say, both the senso netwok and the beacons ae static. These static localization methods ae eithe ange-based o ange-fee. Range-based localization fist uses RSS, AA, TA o TDA to measue the distance o angle between an unknown node and a beacon, and then employs tilateation, tiangulation o maximum likelihood to estimate the position of the unknown node. These methods have two significant dawbacks: 1) they equie costly additional hadwae suppot, ) fading and noise can cause distance measuement eos [19]. Range-fee localization methods ae meant to ovecome these dawbacks as they do not equie the hadwae suppot fo measuing distances o angles. Instead, they exploit the communication and sensing anges. RSS oughly indicates the tansmission ange between two senso nodes and is an impotant paamete to be utilized in both the ange-based and ange-fee localization methods. How pecisely RSS can be used to indicate the eal tansmission ange is defined by the RSS model. The model [0] calculating RSS eflects the path loss using paametes, such as a efeenced distance, path loss exponent and a andom vaiation. Many ange-based localization methods [8], [9], [10] diectly use it to estimate the distance between two senso nodes. Howeve, the adio tansmission is always unstable caused by signal fading and backgound noise, which could ceate heavy vaiance of RSS. As a esult, the distance measuement by RSS will have significant eo, which ultimately leads to the position estimation unaccuacy. Rangefee methods [11], [1], [13] ae also using RSS to localize senso nodes in WSNs. RSSs in these methods ae not fo estimating absolute distances. Instead, these methods compae the value of RSS with each othe to captue the elative distance elationship among nodes. Tian He et al. [1], [13] popose an aea-based algoithm named APIT that, if nodes ae in the tiangula egions constucted by beacons, efines the aea whee nodes might be located. In ode to judge whethe a node falls in the a tiangula egion, it does RSS compaisons between itself and its neighbos. In [11], each unknown node sots the beacons in descending ode of RSS measuement. The position that fits the soted ode oughly epesents the location of the node. Satisfactoy pefomance of these methods, howeve, equies a high atio of beacons to nodes and a dense node connectivity. Mobile localization [14], [15], [16], [17], [1] using moving beacons avoids the poblems of static localization methods and is pactical. Galstyan et al. [1] popose a distibuted online algoithm using a moving beacon to localize static senso netwoks. This is extended to a geneal model using an unknown taget, in which adio communication and sensing constaints minimize the aea whee a node might be located. In [17], the authos pesent a localization scheme (REKF) with the assist of some mobile obots in a Delay-Toleant Senso Netwok (DTN). The simila wok to ous can be found in [16]. It pesents the eal usage of a moving beacon containing a GPS system to boadcast its positions. Each node computes its location estimate accoding to eithe the boadcasting positions of the moving beacon o the positions of its neighbos. Neithe of these methods, howeve, pesent the theoetical analysis about the maximum estimation eo o impovement of obustness in the eal envionment. u poposed methods diffe significantly fom pevious wok because they ae angefee methods employing a single poweful moving beacon, ae obust and scalable, and can be applied to a senso netwok of any connectivity. III. DISTRIBUTED LCALIZATIN USING ARRIVAL AND DEPARTURE F A MVING BEACN In this section, we pesent a ange-fee distibuted localization method AD that uses a mobile beacon to estimate the positions of senso nodes in the ideal envionment. Note that if a node can eceive a signal fom the beacon, thei distance is within adio tansmission ange of the beacon. We fist study how a node uses the boadcasting signal message fom the beacon to confine its estimation aea when the beacon is moving in a staight line. Then we will show the uppe bound of the estimation eo to the eal position of a node. A. Aival and Depatue of the Beacon Assume that a beacon moves in a staight line in the deployment aea of a senso netwok and at a cetain distance inteval called the boadcasting inteval s boadcasts a message containing its cuent position. The position of the beacon denotes the physical point at which it boadcasts a message. We also assume that a node can eceive messages fom the beacon only if it is inside the tansmission ange of the beacon. We define two states fo evey node: in and out. We also define two dynamic tansitions fom these two states: aival and depatue. out: The node is out of the boadcasting ange of the beacon. in: The node is within the boadcasting ange of the beacon. aival: A node eceives the cuent scheduled signal of beacon, but did not eceive the scheduled signal fom the beacon s pevious position. The status of the node is set

3 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. fom out to in. The beacon is now at the aival position. Its pevious position is called the peaival position. depatue: A node eceived the peceding scheduled signal fom the beacon, but does not eceive the scheduled signal fom the cuent position of the beacon. The status of the node is set fom in to out. The pevious position of the beacon is called the depatue position and the cuent position of the beacon is called the post-depatue position. Fig. 1. A B G Y Localization using aival and leaving infomation of the beacon. These two tansitions ae useful fo estimating the position of a senso node. The fact that tansitions always occu in a pai limit the possible position of the node into a small aea as shown in Figue 1. Suppose that the beacon is moving fom the left to ight along the x axis. Initially, the state of node G is set to out. When the beacon aives at position B, node G heas the beacon fo the fist time and its state is set to in. Node G can calculate the peaival position A accoding to the aival position B. Node G must fall inside the aea in the cicle centeed at B with adius and out of the cicle centeed at A, foming an aival constaint aea as in the left-hand cescent shape in Figue 1. When the beacon moves fowad, it will walk out of the ange of node G. LetC be the depatue position and D be the post-depatue position. The state of node G is set to out and it must fall inside the aea in the cicle centeed at C with adius and out of the cicle centeed at D, foming a depatue constaint aea as the ight-hand cescent shape in Figue 1. The aival constaint aea and depatue constaint aea will ceate an ovelap called the Aival and Depatue velap (AD). Thus, node G must fall in AD. The middle boadcasting positions between the aival and depatue positions do not povide valuable infomation because they cannot help to naow down the aea of AD. To estimate its position, a node should obtain these fou citical positions of the moving beacon: peaival position, aival position, depatue position and post-depatue position to compute its AD. We next povide the eo uppe bound of the position estimate of a node G when tansmission ange is and boadcasting inteval is s. Let the coodinates of node G be (x G,y G ). Without loss of geneality, we assume that the beacon stats moving along the x axis fom the coodinates (0, 0) and the node G eceives the fist signal fom the beacon when the beacon is at (s, 0) and the last signal when the beacon is at (ks, 0) whee k is the numbe of signals that C D the node heas between the aival position and the depatue position. The aival constaint aea of G can be pesented as: x + y > (1) (x s) + y () and the depatue constaint aea of G can be pesented as: (x k s) + y (3) (x (k +1) s) + y > (4) whee 1 k /s +1, guaanteeing that the aival constaint aea and the depatue constaint aea ovelap. It is obvious that the AD is symmetical along the x axis. The half AD (HAD) above x axis is called uppe HAD while the othe half AD is called lowe HAD. Assume that we can detemine whethe a detected node is above o below the line of movement of the beacon (we show the way in Section III-B). Without losing geneality, we analyze the uppe HAD to show the location estimate. Let the position estimate of node G be at the point (x,y ). As a esult, the maximum hoizontal eo MAX{ x x G } and maximum vetical eo MAX{ y y G } depict the uppe bounds of estimation eo in the x and y coodinates espectively. Accoding to Fomula (1) (4), we calculate that the maximum hoizontal eo using node as the position estimate of node G is { s/ if s ks (k 1)s (5) if <ks + s and the maximum vetical eo is { f(k 1) f(k +1) if s ks s (6) f(k 1) if s<ks + s ( k s) and k is the total numbe of whee f(k) = signals that the node heas fom the aival position until the depatue position. Fom Fomula 5, it is obvious that the uppe bound of the hoizontal coodinate estimation eo of node G is equal to s/. Fom Fomula 6 we know that f(k 1) f(k +1) is monotonously inceasing wheeas f(k 1) is monotonously deceasing. Theefoe, the uppe bound of the vetical coodinate estimation eo of node G equals to s s when k = s 1 (in the eal movement of a beacon, k should be an intege and this uppe bound still holds). The uppe bound of the position estimation eo of node G deceases when s deceases, which implies that to obtain an accuate localization of senso nodes, the moving beacon should shoten its message boadcasting inteval. B. Movement Patten of Beacon In this subsection, we descibe the movement patten of a beacon that can cove and localize each senso node accuately. The movement patten is shown in Figue in which the distance between two adjacent lines of movement is. In this patten, a node can detect its position once o twice. The scenaio in which a node can detect its position only once

4 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. Fig.. Line 7 Line 6 Line 5 Line 4 Line 3 Line Line 1 The tavese oute of the beacon fo the AD method. happens when the node stays in the uncoveed space that is not coveed by two consecutive boadcasting of the beacon as shown in Figue 3(a). The node does not eceive any signal fom the above o below the lines and obtains one AD fom the line acoss this uncoveed space. The position of the AD can help to identify the uncoveed space that the node esides in. Note that the uncoveed space is symmetical along the line of movement and we don t know whethe the node is above o below the line. Because the uncoveed space is elatively small, this space itself is a good position estimate of the node and it is not necessay to distinguish whethe it is above o below. The x coodinate of the cente point of the AD is k+1 s.wehave two situations of the intesection of possible uncoveed spaces with a veified AD. The fist situation is shown in Figue 3(b) whee the AD intesects with only one uncoveed space when k +1 is an odd numbe. We choose the cente node in the uncoveed space as the estimate position. The second situation is shown in Figue 3(c) whee the AD intesects with two uncoveed spaces when k +1 is an even numbe. To minimize the estimation eo, we choose the connection point of two uncoveed spaces as the estimate position. In both situations, the coodinates of node ae ( k+1 s, y line) whee y line is the y coodinate of the line of movement. Uncoveed Space AD aea that is the ovelap of two HADs. These two HADs povide a complementay estimate of a node to naow down the possible aea. In ode to simplify the position estimate fo nodes who obtain two HADs, we fist calculate the cental point of the each HAD sepaately and then set thei midpoint as the estimate position. IV. DISTRIBUTED LCALIZATIN USING RSS F A MVING BEACN In this section, we pesent the RSS localization method when the beacon moves in a staight line in the ideal situation. RSSI (Received Signal Stength Indicato) is always available in many senso platfoms such as mica and micaz. The most widely used assumption in the ideal situation is that the shote distance a senso node esides fom the beacon, the lage RSSI will be obtained. We do not use RSSI to estimate distance fom beacon, instead, we utilize the vaiance of RSSI to estimate the node position. Thus, ou RSS localization method also belongs to ange-fee technique. A B C D E F G Messages tansmission (a) The vaiance of RSS. x coodinate estimate D D E The maximum RSS The second lagest RSS (b) The x coodinate estimate of node. Fig. 4. Localization using RSS. Fig. 3. ks s (k+1)s (a) (b) (c) Uncoveed space when the beacon moves along a staight line. The scenaio in which a node detects its position twice happens fo most occasions if the node stays outside of the small uncoveed aea. Each detection ceates an estimate aea fo a node. This estimate aea can be easily distinguished as the uppe o lowe HAD. A node heaing a signal fom the ith line is below the line when it has aleady eceived a signal fom the (i 1)th line. thewise, the node is above the line. Thus, a node in this scenaio can be delimited into a moe accuate A. Location Estimate The location estimate of a senso node is deived fom the vaiance of eceived RSS fom the moving beacon. At fist, node does not eceive any signal fom a distant beacon. When the beacon moves close, the eceived RSS becomes stonge. Afte the beacon passes the point that is the neaest position to node, RSS will decease accodingly. Thus, node will get a RSS seies. This seies is shown in Figue 4(a) whee the height of columns indicates the size of RSS. Figue 4(b) shows how to compute the position estimate of node. Suppose that the beacon is moving along the x axis with boadcasting inteval to be s. The maximum signal stength eceived at node happens when the beacon is at point D and the second maximum signal stength is at point E. Thus, the x coodinate of node should be within D and E. Futhemoe,

5 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. given that D is the midpoint between D and E, node can conclude that its x axis coodinate is between point D and D. Fo simplicity, we set the midpoint between D and D as the x axis estimate of node. bviously, the maximum estimate eo of the x coodinate of node is s/4 as the x coodinate of node must eside in the inteval [D, D ]. B. Movement Patten Figue 5 shows the RSS movement patten fo the RSS localization method. When the beacon is moving along hoizontal lines, unknown nodes can only detemine thei x coodinates. Thus, the beacon needs to move along vetical lines fo nodes to estimate thei y coodinates. Given the RSS movement patten as shown in Figue 5, we know that the maximum y coodinate estimate eo is the same as the x coodinate, i.e., s/4. This estimate eo uppe bound is smalle than that of the AD method and only elevant to the boadcasting inteval (the value of s). Although the RSS movement patten is distinct fom that of the AD movement patten, the total taveling distance of the beacon in both movement pattens ae compaative. The disadvantage of the RSS method is that a small potion of nodes may not be localized if they eside in the uncoveed space as denoted in Figue 3. To ovecome this disadvantage, we can slightly shoten the distance between two moving staight lines of the beacon (smalle than ) to ensue that each senso node can eceive signals fom the beacon. Line 6 Line 5 Line 4 estimation eos. The thid one studies the pecentage of localized nodes out of all nodes in RSS. Pefomance unde vaious boadcasting intevals. In the fist set of simulations, we study the position estimate eos, i.e., RMSE and the maximum eo, of senso nodes when the boadcasting inteval of the beacon inceases fom 0.5m to 1.5m and its tansmission ange is = 6m. Figue 6 shows that both localization methods (AD and RSS) can yield accuate estimates whee the eal location of each senso node can be confined within a distance (smalle than 1.6m) to the calculated location. The aveage estimate eo is within 0.8m. The figue also illustates that the RSS localization method can achieve smalle RMSE and maximum eo than the AD localization method does. The estimate eos incease as the boadcasting intevals of the beacon incease. The maximum eos of both methods ae consistent to peviously theoetical analysis whee the coodinate uppe bounds of estimate eos fo a node is ( s, s s )inthe AD method wheeas ( s 4, s 4 ) in the RSS method. Estimate eos (m) RSS Localization.RMSE AD Localization.RMSE RSS Localization.Max. AD Localization.Max. Line Boadcasting inteval (m) Line Fig. 6. Location estimate eos unde vaious boadcasting intevals. Fig. 5. Line 1 The tavese oute of the beacon fo the RSS method. V. PERFRMANCE EVALUATIN In this section, we evaluate the pefomance of the poposed two localization methods: AD and RSS. The simulation is implemented as 50 nodes andomly distibuted in a 16m 16m aea and a moving beacon boadcasting its geogaphical position infomation with an adjustable tansmission ange. The boadcasting inteval of the beacon is s. The tavese outes of the beacon ae given in Figue and 5 fo AD and RSS espectively. We totally conduct thee sets of simulations. The fist and second sets investigate the pefomance with vaious boadcasting intevals and tansmission anges of the moving beacon in tems of the RMSE (Root Mean Squae Eo) and the maximum Pefomance unde vaious tansmission anges. In the second set of simulations, we show the impact of the beacon s tansmission ange on the position estimation accuacy. We set the boadcasting inteval s to be 0.5m and vay the tansmission ange fom 1m to 6m. Figue 7 shows that AD can achieve satisfactoy pefomance whee the RMSE and maximum eo ae smalle than 0.4m and 1m espectively. When the tansmission ange goes lage, both the RMSE and maximum eos of AD ise. The RSS method, howeve, outpefoms AD with smalle RMSE and maximum eos. Futhemoe, the cuves of RSS ae almost flat, which indicates that RSS is insensitive to the vaiance of the tansmission ange. Pecentage of localized nodes in RSS. In the last simulation, we study the pecentage of localized nodes in RSS unde vaious boadcasting intevals and tansmission anges. Although RSS cannot guaantee that all nodes will be localized due to the uncoveed space as descibed in Section IV-B, Figue 8 shows that the pecentage of localized nodes

6 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the ICC 007 poceedings. Fig. 7. Estimation eo (m) RSS Localization.RMSE AD Localization.RMSE RSS Localization.Max. AD Localization.Max Tansmission ange (m) Location estimate eos unde vaious tansmission anges. in RSS still eaches moe than 98%. When the boadcasting inteval inceases, the pecentage dops as shown in Figue 8(a). This is because the lage boadcasting inteval leads to bigge uncoveed space. n the othe hand, when we incease the tansmission ange, Figue 8(b) shows that the pecentage ises. The eason is that the incement of the tansmission ange educes the numbe of uncoveed spaces and thus educes the numbe of non-localized nodes. Pecentage of localized nodes (%) Boadcasting inteval (m) (a) Vaious boadcasting intevals Fig. 8. Pecentage of localized nodes (%) Tansmission ange (m) (b) Vaious tansmission anges Pecentage of localized nodes in RSS. VI. CNCLUSIN In this pape, we pesent two distibuted ange-fee localization methods (AD and RSS) that use only one moving beacon within a senso netwok. The basic idea of the AD method is to naow down the possible location of a node by using aival and depatue constaint aeas deived fom the moving beacon. The RSS method seeks the location of a senso fom a sequence of RSS boadcasted fom the moving beacon. Both methods employ the ange-fee techniques in the sense that they do not ely on the diect distance measuement fom RSS but on a sequence of constaints. We povide the uppe bound of the estimation eo fo two methods in an ideal envionment. Citical to the location accuacy of senso nodes ae two paametes, the adio tansmission ange of the beacon, and how often the beacon boadcasts its position. Anothe facto, tansmission ange, also affects the pefomance of the AD method. The RSS method, howeve, is not sensitive to its vaying. We conduct seveal simulations to evaluate these two methods. The simulations show that the esults of both methods ae consistent to theoetical analysis. Unde vaious simulation scenaios, both methods pefom well, with the aveage estimate eo smalle than one mete. The RSS method outpefoms the AD method which can educe the estimate eo by 50%. Howeve, the disadvantage is that the RSS method cannot guaantee all nodes to be localized when the tavese oute gap of the beacon is bigge o equal to. In such condition, the localized nodes is still satisfying, with a pecentage ove 98%. ACKNWLEDGMENT This wok is patially suppoted by HK RGC CERG B- Q87, 007 CB China National 973 Pogam Gant, NSFC unde gant no , and by the Shuguang Schola Pogam of Shanghai Education Development Foundation. REFERENCES [1] W. Zhang and G. Cao, Dctc: Dynamic convoy tee-based collaboation fo taget tacking in senso netwoks, IEEE Tansactions on Wieless Communications, 004. [] J. Liu, J. Reich, and F. 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