Wreless Sensor Network, 010,, 807-814 do:10.436/wsn.010.11097 Publshed Onlne November 010 (http://www.scrp.org/journal/wsn) Range-Based Localzaton n Wreless Networks Usng Densty-Based Outler Detecton Abstract Khald K. Almuzan, Aaron Gullver Department of Electrcal and Computer Engneerng, Unversty of Vctora, Vctora, BC, Canada E-mal: kmuzan@ece.uvc.ca, agullve@ece.uvc.ca Receved August 13, 010; revsed September 15, 010; accepted October 18, 010 Node localzaton s commonly employed n wreless networks. For example, t s used to mprove routng and enhance securty. Localzaton algorthms can be classfed as range-free or range-based. Range-based algorthms use locaton metrcs such as ToA, TDoA, RSS, and AoA to estmate the dstance between two nodes. Proxmty sensng between nodes s typcally the bass for range-free algorthms. A tradeoff exsts snce range-based algorthms are more accurate but also more complex. However, n applcatons such as target trackng, localzaton accuracy s very mportant. In ths paper, we propose a new range-based algorthm whch s based on the densty-based outler detecton algorthm (DBOD) from data mnng. It requres selecton of the K-nearest neghbours (KNN). DBOD assgns densty values to each pont used n the locaton estmaton. The mean of these denstes s calculated and those ponts havng a densty larger than the mean are kept as canddate ponts. Dfferent performance measures are used to compare our approach wth the lnear least squares (LLS) and weghted lnear least squares based on sngular value decomposton (WLS-SVD) algorthms. It s shown that the proposed algorthm performs better than these algorthms even when the anchor geometry about an unlocalzed node s poor. Keywords: Localzaton, Postonng, Ad Hoc Networks, Range-Based, Wreless Sensor Network, Outler Detecton, Clusterng 1. Introducton The process of fndng the spatal locaton of nodes n a wreless network has been called localzaton, postonng, geolocaton, and self-organzng n the lterature. The term localzaton s the most popular and so s used here. In a wreless network, we can classfy the nodes nto three categores, anchor, unlocalzed, and localzed. The frst group of nodes know ther poston or coordnates and are called anchors. Nodes n the second group do not know ther poston and are called unlocalzed. The thrd group contans those nodes whch were n the second group but subsequently had ther postons estmated, and thus are called localzed. The locaton nformaton of nodes n a wreless network can be used for many useful purposes such as trackng moble nodes, determnng the coverage area, load and traffc management, node lfetme control, cluster formaton, and routng enhancement. There are many dfferent aspects to the localzaton problem, such as when localzaton should be performed and how frequently. Upon network start up, all nodes should be ntally localzed. However, ths may have to be repeated perodcally, for example f there are moble nodes n the network. The qualty or resoluton of the localzaton s an mportant consderaton. Sometmes, node locatons are requred wthn meters of ther actual postons, and other tmes wthn a few centmetres. Some applcatons only requre relatve localzaton, such as node A s n regon 1 and node B s n regon, or node A s close to node B. For example, montorng people n a buldng when we need to know how many have entered a gven room durng the day. The computatons assocated wth localzaton can bedstrbuted (done at each node), centralzed (done at a central unt), or both (done at cluster heads n the network). When the number of anchor nodes s low, they typcally cannot cover the entre wreless network. Ths means that some unlocalzed nodes may not be wthn range of a suffcent number of anchor nodes. In ths case, Copyrght 010 ScRes.
808 K. K. ALMUZAINI ET AL. localzed nodes can partcpate n the localzaton process by actng as anchors. Ths s called cooperatve localzaton. Localzaton algorthms can be dvded nto two categores: range-based and range-free. Range-free algorthms depend on proxmty sensng or connectvty nformaton to estmate the node locatons. These nclude CPE [1], centrod [], APIT [3], and the dstrbuted algorthm n [4]. Range-based algorthms estmate the dstance between nodes usng measurements such as tme of arrval (ToA) [5], tme dfference of arrval (TDoA) [6], receved sgnal strength (RSS) [7], or angle of arrval (AoA) [8]. Poston accuracy s not constant across the area of coverage, and poor geometry of the unlocalzed nodes relatve to the anchor nodes can lead to hgh geometrc dluton of precson (GDOP). GDOP s commonly used to descrbe localzaton accuracy. Generalzed GDOP (GGDOP) s a smlar measure used to compare the performance of localzaton algorthms. The proposed approach dffers from conventonal solutons to the localzaton problem n wreless networks. Typcally the locatons of the anchors wthn range and the estmated dstances between the unlocalzed node and these anchors are used to drectly estmate ts locaton. Instead, we use a mult-step process. An approach from data mnng called densty-based outler detecton (DB OD) [9] s employed whch uses the dstance to the K- nearest neghbours (KNN) to select the best (canddate) ponts, and these are averaged to get the estmated locaton of the unlocalzed node. The lnear least squares (LLS) [10] and the weghted lnear least squares sngular value decomposton (WLS-SVD) [11] algorthms as a benchmark. In [11], the WLS-SVD algorthm s compared wth a maxmum lkelhood (ML) algorthm [1], multdmensonal scalng (MDS) [13], and the best lnear unbased estmator approach based on least square calbraton (BLUE-LSC) [14]. Accordng to [11], WLS-SVD performs better than any of these three algorthms. The remander of the paper s organzed as follows. Dluton of precson s explaned n Secton, and the densty-based outler detecton technque s explaned n Secton 3. The proposed algorthm s presented n Secton 4. Some performance results are gven n Secton 5, and fnally some conclusons are gven n Secton 6. errors result n errors n the computed node coordnates. The magntude of the fnal error depends on both the measurement errors and the geometry of the structure nduced by the nodes. The contrbuton due to geometry s called the geometrc dluton of precson (GDOP). GDOP s used extensvely n the GPS communty as a measure of localzaton performance [15]. The dstrbuton of the anchors around an unlocalzed node can have a good or poor GDOP, as shown n Fgure 1. Another verson of GDOP s the generalzed geometry of dluton precson GGDOP. GGDOP depends on the geometry of the anchors around an unlocalzed node and the accuracy of the range measurements. GGDOP s defned as [16] m m (1) m where m 1 m 1 () and m m sn ( j) m (3) 1 j1, j> j The dstance error for node has a Gaussan dstrbuton wth varance. The angle s the orentaton of the th anchor or localzed node relatve to the node (a). Dluton of Precson Dluton of precson s a metrc whch descrbes how good an anchor node geometry s for localzaton. The dstance measurements used to compute the node coordnates always contan some error. These measurement (b) Fgure 1. Node locatons wth poor and good GDOP. (a) Nodes wth poor GDOP; (b) Nodes wth good GDOP. Copyrght 010 ScRes.
K. K. ALMUZAINI ET AL. 809 whose locaton s beng estmated, as shown n Fgure, and m s the number of anchors and localzed nodes nvolved n the estmaton. As the GGDOP ncreases, the localzaton error decreases. In [16], t was shown that for all { },{ },0 1/4 m 3. Densty-Based Outler Detecton The densty-based outler detecton algorthm s commonly used n anomaly detecton. The outler score s just the nverse of the densty score of a pont. The densty s the nverse of the mean dstance to the K-nearest neghbours of pont p [9] and s gven by (, ) (, ) (, ) d p y yn p K densty p K (4) N( p, K) where N( p, K ) s the set contanng the K-nearest neghbours of pont p, N( p, K) s the sze of ths set, and y s a nearest neghbour. The densty-based outler detecton algorthm s gven n Algorthm 1 [9]. Algorthm 1 Densty-based Outler Detecton 1: K s the number of nearest neghbours : for all ponts p do 3: determne N (p, K) for p 4: determne the densty of p 5: the outler score s the nverse of the densty 6: end for 4. The Proposed Algorthm The frst step n localzaton s to obtan dstance estmates for the unlocalzed nodes from the anchor and localzed nodes that are wthn range. These estmates provde the rad for crcles around the nodes. The ntersecton of these crcles for an unlocalzed node forms a set 1 j of ponts to be used n the remander of the algorthm. The key s to choose canddate ntersecton ponts whch are closest to each other. In the deal case the crcles n tersect on the unlocalzed node. For example, when we have three anchors, three ntersecton ponts le on the node, whle the other three do not. However, n practcal stuatons where nose and other sources of error exst, ths event s unlkely and the crcles ntersect as n Fg- -ure 1. In Fgure 3, the ntersecton ponts of the crcles around anchor nodes p 1 = (x 1,y 1 ) and p = (x,y ) are denoted as p 1 and p 1, and ther coordnates are gven by [17] and x x1 ( x x1)( r1 r ) x d y y1 (( r 1r) d )( d ( r r1) ) d y y1 ( y y1)( r1 r ) y d x x1 (( r 1r) d )( d ( r r1) ) d where the p 1 x-coordnate corresponds to the plus sgn n (5), and the correspondng y-coordnate corresponds to the mnus sgn n (6). The dstance between the anchor nodes s 1 1 1 (5) (6) d( p, p ) ( x x ) ( y y ) (7) Each unlocalzed node estmates ts dstance from each anchor or localzed node that t can receve a sgnal from. Ths node can estmate ts poston only f t s n range of three or more of these nodes. The ntersecton of the crcles formed from all estmates of the unlocalzed node provde a set of ponts. If we have m anchor and/or localzed nodes, then they form g groups where m m! g!( m )! (8) j j Fgure. An unlocalzed node wth multple anchors wthn ts range. Fgure 3. Intersecton of the dstance estmates for two anchors. Copyrght 010 ScRes.
810 K. K. ALMUZAINI ET AL. Each group conssts of two ponts as a result of the ntersecton between two anchor and/or localzed node estmates, as shown n Fgure 3. The total number of ponts f all estmates ntersect s g. The goal s to average a subset of these ponts to obtan the locaton estmate. The thrd step s to calculate the densty of each ntersecton pont. To do ths, the K-nearest neghbours, K g 1, of each ntersecton pont are used to calculate the densty accordng to (4). The ponts wth a densty hgher than the mean densty are selected as canddates. In some cases, the estmates are too small, resultng n crcles that do not ntersect. However, these ntersecton ponts can stll be calcuated, but they wll be complex numbers. If ths occurs, we consder the real part as the ntersecton pont n subsequent calculatons. Fgure 4 llustrates the steps of the proposed algo- (a) (b) (c) Fgure 4. The proposed algorthm wth four anchor nodes. (a) Step 1: Dstance estmates for an unlocalzed node from four anchors; (b) Step : The ntersecton ponts; (c) Step 3: The canddate ntersecton ponts. rthm for four anchor nodes. After the four dstance estmates are determned, the g = 1 ntersecton ponts are found. Note that because two pars of crcles do not ntersect, there are only w = 10 ponts n Fgure 4(a) (snce the real parts of the complex numbers are the same). Then the average densty for all ntersecton ponts s calculated as D w 1 densty( v, K) where v s an ntersecton pont and w s the number of ntersecton ponts. Fnally, the ponts wth densty gven by (4) greater than the average D are selected as canddate ponts. If the canddate ponts are v = { v1, v,... v q }, then the estmated locaton of the unlocalzed node s the average of these ponts w q v 1 û= (10) q We next consder the effect of employng localzed nodes to help n the localzaton of nodes whch do not have a suffcent number of anchors around them. If nodes wth transmsson range r are randomly deployed n an area A, then the probablty of an unlocalzed node beng wthn transmsson range of a gven node s r pr A The probablty of a node havng degree,.., e anchor or localzed nodes wthn ts range, s gven by (9) Copyrght 010 ScRes.
K. K. ALMUZAINI ET AL. 811 P( ) e! where N p r and N s the number of anchor and localzed nodes. Then the probablty of a node havng n or more anchor and localzed nodes wthn ts range s n1 p( n) 1 p( ) 5. Performance Results o In ths secton, the proposed algorthm LDBOT s compared wth the WLS-SVD [11] and LLS [10] algorthms va smulaton. We frst consder dstance to measure the accuracy of both technques. 100 nodes are deployed, 50% of whch are anchors whch are chosen randomly. The deployment area s A = 100 100 m, and the range s r = 10 m. The dstance error has a Gaussan dstrbuton wth varance d whch s a percentage of the actual dstance. As a performance measure, we use the mean error, whch s defned as u ( xˆ ) ( ˆ x y y) t 1 mean error (11) tu where u s the number of unlocalzed nodes, t s the number of trals, ( xˆ, y ˆ) s the estmated unlocalzed node poston, and (x, y) s the actual poston. The results were averaged over 10 4 trals. Localzed nodes were used wth the anchors to localze those unlocalzed nodes whch were not wthn range of a suffcent number of anchor and localzed nodes n the prevous teratons. The localzaton process ends when all nodes are localzed or all remanng unlocalzed nodes are solated,.e., not wthn range of three or more anchor or localzed nodes. Fgure 5 shows that the mean error wth the proposed algorthm outperforms that wth the LLS and WLS-SVD algorthms. Note that the rate of change of the error s also lower wth LDBOD. Next all algorthms are compared consderng the transmsson range of the wreless nodes. The deployment area, the number of nodes, and the number of anchors are the same as before but the transmsson range vares from 10 m to 50 m. The dstance error varance s fxed at 10% of the actual dstance between nodes. The results were agan averaged over 10 4 trals. Fgure 6 shows that the proposed algorthm performs better than the LLS and WLS-SVD algorthms at low transmsson ranges, n whch case the unlocalzed nodes are typcally wthn range of a small number of nodes. However, at hgh transmsson ranges all algorthms have smlar performance. The probablty that an unlocalzed node has 3 or more anchor or localzed nodes around t based on a gven transmsson range s llustrated n Fgure 7. Ths clearly Fgure 6. Mean error versus transmsson range. Fgure 5. Mean error versus dstance varance. Fgure 7. Probablty of node localzaton based on transmsson range. Copyrght 010 ScRes.
81 K. K. ALMUZAINI ET AL. shows that usng localzed nodes n the localzaton process mproves the probablty of localzng nodes. When the range exceeds 5 m, all unlocalzed nodes can be localzed. The anchor rato s one of the most mportant factors affectng localzaton accuracy. Thus we next comparethe algorthms wth a varyng percentage of anchor nodes. In ths case we are more nterested n the performance when the anchor rato s small because n a practcal system the number of anchor nodes wll be much lower than the number of unlocalzed nodes. The deployment area and the number of nodes are the same as before but the anchor rato vares from 0% to 80%. The transmsson range s fxed at 10 m and the dstance error varance s fxed at 10% of the actual dstance. The results are agan averaged over 10 4 trals. Fgure 8 shows that the proposed algorthm agan outperforms both the LLS and WLS-SVD algorthms, partcularly at low anchor ratos. The probablty that an unlocalzed node has 3 or more anchor or localzed nodes around t based on a gven anchor rato s shown n Fgure 9. Clearly the use of localzed nodes n the localzaton process mprove the probablty of node localzaton. Ths probablty reaches a maxmum of only 0.6 due to the small range of 10 m. Next we consder the effect of the node geometry on performance, wth GGDOP used as the geometry meas- -ure. Three anchor nodes are deployed on a crcle wth a fourth unlocalzed node n the center. The transmsson range s set to 30 m to ensure that the unlocalzed node s wthn range of the three anchors, and the dstance error varance s set to 10%. The anchors a 1, a, and a 3 are dstrbuted around the unlocalzed node u at angles aua 1 and aua 3 rangng from 1 to 101 (wth both angles the same). The results are averaged over 10 4 trals, and are shown n Fgure 10 for GGDOP and n Fgure 11 for angle between anchors. Both fgures show that the proposed algorthm performs better, partcularly when the geometry s poor,.e., low GGDOP or small angles. The LLS and WLS-SVD algorthms perform smlarly at all angles and GGDOP values because only Fgure 8. Mean error versus anchor rato. Fgure 10. Mean error versus GGDOP. Fgure 9. Probablty of node localzaton based on the anchor rato. Fgure 11. Mean error versus angle between anchors. Copyrght 010 ScRes.
K. K. ALMUZAINI ET AL. 813 (a) four nodes are deployed. At small angles, the geometry s poor, and as the angles ncrease the geometry approaches the deal case where the anchors are dstrbuted unformly on the crcle. Thus at angles of 101 the performance s very good, and all three algorthms perform smlarly. Fnally, we evaluated the algorthms wth dfferent anchor ratos and dstance error varances. Fgure 1 shows the resultng mean error surfaces. Clearly LDBOD outperforms the other algorthms at hgh dstance error varances (90%) and low anchor ratos (10%), whch s the most typcal, but also the most challengng envronment. The performance s smlar at hgh anchor ratos (90%) and low dstance error varances (10%), whch s close to the deal case, and therefore not lkely to occur n practce. 6. Conclusons A new range-based localzaton algorthm (LDBOD) has been presented whch s based on the densty-based outler detecton (DBOD) algorthm, a concept from data mnng. The proposed algorthm s used to select the best ponts (canddates) from a set of dstance estmate ntersecton ponts. The proposed algorthm was shown to outperform the LLS and recently proposed WLS-SVD algorthms. 7. References (b) (c) Fgure 1.Mean error surfaces. (a) Mean error surface for the LLS algorthm; (b) Mean error surface for the WLS-SVD algorthm; (c) Mean error surface for the LDBOD algorthm. [1] L. Doherty, K. S. J. Pster and L. El Ghaou, Convex Poston Estmaton n Wreless Sensor Networks, Proceedngs of IEEE INFOCOM, Anchorage, AK, Aprl 001, pp. 1655-1663. [] N. Bulusu, J. Hedemann and D. Estrn, GPS-Less Low-Cost Outdoor Localzaton for Very Small Devces, IEEE Personal Communcatons, Vol. 7, No. 5, October 000, pp. 8-34. [3] T. He, C. Huang, B. M. Blum, J. A. Stankovc and T. Abdelzaher, Range-Free Localzaton Schemes For Large Scale Sensor Networks, Proceedngs of ACM MobCom, San Dego, CA, September 003, pp. 81-95. [4] K. Almuzan and T. A. Gullver, A New Dstrbuted Range-Free Localzaton Algorthm for Wreless Networks, Proceedngs of IEEE Vehcular Technology Conference, Anchorage, AK, September 009, pp. 0-3. [5] I. Guvenc and Z. Sahnoglu, Threshold-Based TOA Estmaton for Impulse Rado UWB Systems, Proceedngs of IEEE Internatonal Conference on Ultra-Wdeband, Zurch, Swtzerland, September 005, pp. 40-45. [6] X. We, L. Wang and J. Wan, A New Localzaton Technque Based on Network TDOA Informaton, Proceedngs of IEEE Internatonal Conference on ITS Telecommuncatons, Chengdu, Chna, June 006, pp. 17-130. [7] A. Hatam, K. Pahlavan, M. Hedar and F. Akgul, On RSS and TOA Based Indoor Geolocaton A Compara- Copyrght 010 ScRes.
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