Mobility-Pattern Based Localization Update Algorithms for Mobile Wireless Sensor Networks

Transcription

1 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks Mohammad Y. Al-laho, Min Song, Jun Wang Deparmen of Elecrical and Compuer Engineering Old Dominion Universiy 231 Kaufman Hall Norfolk, VA 23529, USA {malla3, msong, Absrac. In mobile wireless sensor neworks, sensors move in he moniored area a any direcion and a any speed. Unlike many oher neworking hoss, sensor nodes do no have global addresses. Very ofen hey are idenified by using a locaion-based addressing scheme. Therefore, i is imporan o have he knowledge of he sensor locaion indicaing where he daa came from. In his paper, we design hree mobiliy-paern based localizaion updae algorihms. Specifically, we divide sensor movemens ino hree saes, Pause, Linear, and Random. Each sae adops differen localizaion updae algorihms. Analyical and simulaion resuls are provided o sudy he localizaion cos and locaion accuracy of he proposed localizaion-updae algorihm in differen mobiliy paerns. The analysis o hese resuls indicaes ha he localizaion cos is minimized and he locaion accuracy is improved. 1 Inroducion In mobile wireless sensor neworks, sensors move in he moniored area a any direcion and a any speed. Unlike many oher neworking hoss, sensor nodes do no have global addresses. Very ofen hey are idenified by using a locaion-based addressing scheme [5]. The rouing process also requires locaion-based naming where he users are more ineresed in querying a locaion of a phenomenon, raher han querying an individual node [5]. Therefore, i is imporan o have he knowledge of he sensor locaion indicaing where he dae came from. Many researches have been conduced o solve he localizaion problem of moving objecs. The mos famous one is he GPS sysem. Unforunaely, GPS is no a good choice for mobile wireless sensor neworks because of is significan power consumpion of he GPS receivers [7]. Inuiively, he localizaion of mobile wireless sensors can be performed by using predicion echniques o anicipae he possible nex sep of a sensor node based on he movemen paern model and he hisory of he movemen paern [4]. Unforunaely, i has been found ha predicion echniques are no always accurae [1]. Especially, when he movemen paern is no predicive (no linear he accuracy decreases significanly. A more reliable mehod is o inegrae he predicion echniques and localizaion updae algorihms. In his case, he localizaion updae algorihms can correc any inaccurae anicipaion. This mehod, however, is raher

2 2 Mohammad Y. Al-laho, Min Song, Jun Wang oo complex and needs many calculaions and filering echniques o refine he possible sampling daa colleced from previous movemens. The energy consumpion and he memory size resricions of a sensor node limi he use of hese predicion mehods. Anoher problem for mobile localizaion schemes in lieraure is ha hey impracically simplify he mobiliy paern and hus hey do no work well when nodes move randomly. The more he mobiliy paern deviaes from he linear paern, he more he locaion accuracy ges inaccurae and he updae cos ges higher. I is necessary o differeniae differen mobiliy paerns in he sysem. For each paern, a differen localizaion-updae scheme is used o ge he mos accurae resuls. I is worh o noe ha one of he criical design issues in mobile sensor localizaion is simpliciy, since wireless sensor nodes have limied power consumpion and compuaional capabiliy due o he small size of a node. In his paper, we design hree mobiliy-paern based localizaion updae algorihms. More specifically, we divide sensor movemens ino hree saes, Pause, Linear, and Random. Each sae adops differen localizaion updae algorihms. The objecives of his design are o 1 manage he localizaion updae period in opimal raes so ha he updae cos is minimized, and 2 keep he locaion error low. The res of he paper is organized as follows. Secion 2 presens he relaed work in localizaion updae algorihm for mobile wireless sensor neworks. In Secion 3, we inroduce he sysem models and our mobiliy-paern based localizaion updae algorihms. The numerical resuls are provided in Secion 4 o sudy he updae cos and locaion accuracy of he proposed localizaion updae algorihms in differen mobiliy paerns. Secion 5 concludes he paper. 2 Relaed Work Locaion updae schemes generally can be classified as 1 ime-based updaes are made a fixed ime inervals, 2 movemen-based updaes are made whenever he number of cell-boundary crossings since he las updae exceeds a specified hreshold, 3 disance-based a mobile updaes is locaion whenever is disance from an expeced locaion exceeds a specified value since is las updae [9], 4 dead reckoning a scheme o predic a locaion based on velociy componens calculaions from previous locaions, and 5 mobiliy-aware-based updaes are made based on he mobiliy paern. As an example of ime-based scheme, saic fixed rae (SFR performs he localizaion periodically wih a fixed ime period T [1]. The energy consumpion of he SFR mehod is independen of mobiliy. However, he accuracy of he locaion varies wih he mobiliy of he sensor. Dynamic velociy monoonic (DVM [1] is an example of dead reckoning. In DVM, a sensor node adaps is localizaion period as a funcion of is mobiliy speed. Based on he speed value a node schedule he nex ime o localize. A parameer α is se o represen he arge maximum error. For each localizaion measuremen, he speed value is compared wih α o esimae how much ime needed o reach he arge maximum error if he node coninues on he same speed. The nex localizaion is scheduled afer ha ime period. Noe ha he assumpion is for consan velociy be-

3 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks 3 ween wo measuremen poins and his could affec he scheduling ime for localizaion such ha a node reaches values of error higher han he arge maximum error (hreshold error. To accommodae for exremely low/high speeds, DVM assigns an upper and lower limi for localizaion periods. A more complex mehod is called mobiliy aware dead reckoning driven (MADRD [1]. MADRD uses he dead reckoning model (DRM [3, 8] o calculae he Euclidean disance beween he prediced locaion and he acual curren locaion. If he difference exceeds a predeermined hreshold error he process moves ino a low confidence sae where localizaion is performed wih a higher frequency. Oherwise, he process moves ino a high confidence sae where localizaion is performed wih a lower frequency. Since MADRD essenially is based he predicion echnique, is complexiy inherenly limis is wide use. Recenly, Song e al. proposed an algorihm o rack moving objecs in locaion-based services [2]. In heir design, he mobiliy paern is divided ino hree ypes: Pause, Linear, and Random. Differen localizaion updae policies are used for differen mobiliy paerns. However, his design in [2] is more suiable for cellular neworks. For example, he disance is defined in erms of he number of cells. 3 Mobiliy-Paern Based Localizaion Updae Algorihms 3.1 Main Ideas Moivaed by Song s work in [2], we divide he mobiliy paern of mobile sensors ino hree saes: Pause, Linear, and Random. A modified ime-based scheme is used for Pause sae since here is no disance or movemen involved in a pause. The localizaion period is increased as he pause ime increase. To preven a long wai ime here is a maximum period of wai ime ha canno be exceeded. Dead reckoning scheme is mos suiable for linear mobiliy paern since i works for predicive movemen paern where here is no change of velociy or unprediced change of direcion. The localizaion period is incremened as long as he disance beween he prediced locaion and real locaion is wihin a predefined hreshold. The localizaion is se o he iniial localizaion period if he error exceeds he hreshold value. The mos suiable policy for he random movemen paern is disance-based scheme. Our disance-based scheme is differen han he one used in [2]. In [2] he disance is beween he las updae in he las cell and he curren cell. The idea in our design is no o acually measure he disance beween las updae and curren posiion bu raher o predic when he node will cross he limi of his disance based on he acceleraion value measuremen of he node. The acceleraion a is measured periodically. The localizaion period is hen measured as ˆ = d a hresh where d hresh denoes he disance limied o localize. Afer he node localizes, d hresh will be as he radius lengh of a circle where he node is on he origin. The value of (1

4 4 Mohammad Y. Al-laho, Min Song, Jun Wang d hresh will depend on he applicaions. Applicaions ha need more accuracy will have smaller d hresh. For simulaion of discree ime inervals, ˆ should be convered o discree ime inervals by using (2. n= ˆ imeslo During he n ime inervals he locaions are esimaed as follows, ( x = x + v + v imeslo (3 ˆ 1 x ( y y v v imeslo ˆ = 1 + y + where x and y are he new esimaed posiion coordinaes, and x -1 and y -1 are he previous posiion coordinaes, v x and v y are he velociy componens. Since a equals o he incremen or decremen of velociy per second, a is muliplied by he imeslo period o ge he incremen or decremen in velociy vecor for each ime inerval, ˆv = a imeslo. (2 (4 3.2 Mobiliy Models The mobiliy model used in his sudy is Gaussian Markovian Random Waypoin [6]. I is a hybrid of he Random Waypoin and Gaussian Markovian models. In Random Waypoin model he Mobile node chooses a random desinaion in he simulaion area and a speed ha is uniformly disribued. When i reaches he chosen desinaion, i pauses for a specific period of ime. Then he node chooses a random desinaion again. All desinaions are randomly chosen from wihin a predefined area. In Gaussian Markovian model each node iniially is assigned a curren speed and direcion. The speed (s and direcion (d are updaed a fixed inervals as follows: s = αs 1 + (1 α s + 1 α s 2 n n x n 1 (5 d = αd 1 + (1 α d + 1 α d 2 n n x n 1 (6 where α is a value from o 1 and i is he uning parameer used o vary he randomness: α = leads o very random moion, while α = 1 leads o compleely linear moion; s and d are he mean value of speed and direcion as n ; dx n 1 sx n 1 are wo random variables following a Gaussian disribuion. A each ime inerval he nex locaion is calculaed as follows: x = x + s cos d (7 n n 1 n 1 n 1 and

5 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks 5 y = y + s sin d (8 n n 1 n 1 n 1 The idea of Gaussian Markovian Random Waypoin is o use random waypoin a he macro level and use Gaussian Markovian a he micro level o provide a noisy behavior. Tha is, he mobile node sill chooses a random desinaion locaion and speed, and hen compues he direcion of ravel. However, i follows he model presened in equaions (5 and (6 o ravel in his direcion in small ime seps. The model is iniialized wih s and d being equal o he chosen speed and direcion. The node ravels following his model for an amoun of ime (T equal o wha i would ake for i o reach he curren desinaion using he chosen speed. The mobile node may no reach he desinaion, bu possibly a locaion close o i depending on he amoun of noise. Afer he ime T he node pauses according o a given pause ime, chooses a random desinaion locaion, and repeas he above process. In our sudy, we use he Gaussian Markovian Random Waypoin wih some aleraion. For Linear sae we se α value equal o 1 in equaions (5 and (6 so i behaves as pure linear movemen. However, he dn-1 in (6 should be recalculaed o he new locaion. In Random sae he α value is se for values beween.1 and.9, because a value of zero will make i a compleely random and memoryless model ha does no depend on he previous speed and direcion. Whenever he mobile node goes in pause ime, i auomaically swiches o he pause sae for ha amoun of ime. 3.3 Analyical and Sysem Models Condiions o move from one sae o anoher will be esed in he curren sae so he updae policy is changed wih a sae change. Fig. 1 (a shows he iniial and hree mobiliy paern saes. In he acual algorihm he main es o ransi from sae o anoher is based on velociy informaion. A es for he pause sae is o have same locaion deeced wo imes in a row. A same locaion means he velociy value equals o zero. In Linear sae velociy should be he same for cerain ime, which is consan velociy or equivalenly acceleraion value equals o zero. For Random sae, he es is o have velociy change which indicaes random mobiliy paern. Fig. 1 (b shows he sae-based mobiliy model. We have he seady-sae ransiion probabiliy vecor π for each sae: PP LP RP + PP LP RL + PP LR RP π P = ( PPR PLR( PLP + PLR + PRL + ( PLP + PLR + PPL( PRP + PRL + PLR PPRPLP + PPRPLR + PLRPPL π R = ( PPR PLR( PLP + PLR + PRL + ( PLP + PLR + PPL( PRP + PRL + PLR PPRPRL + PRPPPL + PRLPPL π L = ( PPR PLR( PLP + PLR + PRL + ( PLP + PLR + PPL( PRP + PRL + PLR (9 (1 (11

6 6 Mohammad Y. Al-laho, Min Song, Jun Wang Equaions (9, (1, and (11 are used o calculae he performance measuremen specified in Secion 3.5. Iniial (Deecs curren mobiliy paern Linear (L P LL Localizaion updae saes Velociy change P LR Linear Consan velociy Random P PL P LP P RL Consan velociy Velociy = Velociy change Velociy = P PP Pause (P P PR Random (R P RR P RP Pause Fig. 1. (a Mobiliy paern ransiion diagram, (b sae-based mobiliy model 3.4 Pseudo-codes of he Algorihms Iniial Sae Algorihm 1. define Ini_updaeime // one ime slo 2. define max_ime //maximum updae waiing ime 3. define Lin_hresh 4. define d_hresh 5. main 6. loc1 loc_updae 7. wai for Ini_updaeime // (x 1, y 1 8. loc2 loc_updae // (x 2, y v1 ((x 1 x 2 2 +(y 1 y 2 2 /( 2 1 if (v1= hen 11. sae Pause sae(, v, loc1 12. else 13. wai for Ini_updaeime 14. loc3 loc_updae // (x 3, y v2 (x2 x3²+(y2 y3²/( if (v1=v2 hen 17. sae Linear sae(, loc else 19. sae Random sae(, v -1, loc -1 Pause Sae Algorihm 1. Pause sae(, v -1, loc updae ime Ini_updaeime 3. loop 4. wai for updae ime 5. loc o loc_updae // Localize 6. calculae v o // from loc -1 and loc o 7. if (v o!= for wo consecuive imes hen 8. if v -1!= v o 9. sae Random sae

7 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks 7 1. else 11. sae Linear sae if (updae_ime < max_ime hen updae_ime++ Linear Sae Algorihm 1. Linear sae(, loc updae_ime Ini_updaeime 3. loc o loc_updae // ( x o, o y Localize 4. calculae v loop // from loc -1 and loc o 6. compue velociy componens vx, vy perform predicion (dead reckoning //(x pred, y pred wai for updae_ime 9. loc o loc_updae // ( x o, y o 1. calculae v o // v -1 is saved from las calculaion 11. if (v o!= v -1 hen 12. if (v o = hen 13. sae Pause sae 14. else 15. sae Random sae 16. compue d beween prediced loc and real loc 17. if (d < Lin_hresh hen updae_ime++ else 2. updae_ime Ini_updaeime Random Sae Algorihm 1. Random sae(, v -1, loc updae_ime Ini_updaeime 3. loop 4. loc o loc_updae // ( x o, y o localize 5. calculae v o // from loc o and loc calculae a // acceleraion from v o and v if (v o = v -1 hen 8. if (v o = hen 9. sae Pause sae 1. else 11. sae Linear sae 12. ˆ = d a hresh 13. n = ˆ ( imeslo 14. ˆv= a imeslo 15. for (updae_ime=n,updae_ime>, updae_ime compue velociy componens v x + ˆv, v y + ˆv 17. perform predicion // (x pred, y pred

8 8 Mohammad Y. Al-laho, Min Song, Jun Wang 3.5 Performance Measuremens The wo performance measuremens are he localizaion updaes cos C u and he locaion imprecision cos C e. The imprecision cos is he average of he Euclidean disance beween he acual locaion and he esimaed locaion. We have C C = π c (12 i u i u i S = π c (13 i e i e i S where c u i and c e i are he normalized updae cos and imprecision cos for each sae, which are defined as follows: where n is he number of ime slos, oherwise. n 1 i cu = c n n 1 = (14 c is 1 if he updae occurs a ime slo and { } i c = d k, i L, R e = (15 n 1 { } i c = d l, i P e = (16 where d is he Euclidean disance beween he esimaed locaion and he real locaion a ime slo. k is he number of predicions occurred for Linear and Random saes policies. For Pause sae policy he imprecision cos equaion is calculaed differenly since Pause sae policy does no have predicions, so in (16 l is he number of updaes occurred during Pause sae duraion ime. 3.6 An Example Consider ransiions from sae o sae for 15 ime slos as following: PPPPPPRRRRRRRRLLLLLLLLLLLRRRRRRPPPPPPPPPLLLLLLLLLLLLLL PPPPLLLLLLRRRRRRRLLLLLRRRRRRRRRPPPPPPRRRRRRRPPPPPP Couning he number of ransiions N ij from sae i o sae j gives P L R P [ Nij ] i, j S = L R

9 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks 9 The sae ransiion probabiliy Pij can be esimaed as: ˆ Nij Pij = Calculaing each sae ransiion probabiliy we ge he following N k S ik marix: P L R P Pˆ = L R We obain π P =.288, π L =.346, and π R =.366 as esimaes of residence probabiliies of each movemen sae. Given he mobiliy paern a each sae, we can easily have he performance measuremens using equaions (12 hrough (15. 4 Simulaion Resuls Wih he mobiliy-paern based localizaion updae algorihms (MBLUA, we make a rade-off beween updae cos and imprecision cos. We expec ha when updae cos is low (no updaing oo much, imprecision cos will increase indicaing oo much error as a node moves. On he oher hand, if updae cos is high (updae oo ofen, he imprecision cos will decrease indicaing a low error. Our experimen is divided ino wo pars. The firs par concerns he simulaion of he node s acual movemen. Our model is based on GMRW mobiliy model [6]. In order o analyze he algorihms, we modify BonnMoion [1], and use our mobiliy model o generae he workload for differen mobiliy paern scenarios. The nex mobiliy paern (he nex sae is randomly chosen. However, he probabiliy ha he nex mobiliy paern is Linear or Random is higher han he probabiliy of Pause hrough he enire simulaion. The probabiliy of Linear or Random is.4 for each, and he probabiliy of Pause is.2. The second par is localizaion updae algorihms, and hey are run over he workload generaed from he mobiliy model. Localizaion updae algorihms include algorihm for hree saes combined using he Sae-based Mobiliy Model (SMM, and algorihm for each movemen sae. The purpose of each sae algorihm alone is o compare i wih MBLUA. We use a simulaion area of 2 by 2 meers and simulae he mobiliy model over 1 nodes for 9 seconds. The localizaion scheme should no affec our proposed model, since he model akes care of he localizaion period only and i is mobiliy based dependen. Fig. 2 (a and (b show he race resuls for one slow node and one fas node, respecively, including he acual movemen race from modified GMRW model and he MBLUA race from localizaion updae algorihms for wo differen speed ranges. For slow node, he speed range is form.5 m/s o 1 m/s; for fas node, he speed range is from 2 m/s o 4 m/s. The maximum pause ime is 6 seconds. The resuls indicae a perfec mach beween acual movemen and MBLUA race when he movemen is

10 1 Mohammad Y. Al-laho, Min Song, Jun Wang linear and i ends o have some mismach when he node urns abruply. In Fig. 2 (b, he error increases for fas node. Mobiliy Trace Mobiliy Trace 2 Acual MBUA 2 Acual MBLUA Y(m 1 Y(m X(m (a Slow speed (.5-1 m/s (Max pause ime 6 sec. (max_ime = 5 ime slos, Lin_hresh = 4m, and d_hresh = 5m Fig. 2. Mobiliy race for slow and fas speeds X(m (b Fas speed (2-4 m/s (Max pause ime 6 sec. (max_ime = 5 ime slos, Lin_hresh = 4m, and d_hresh = 5m Table 1 shows he updae and imprecision coss for hree updae policies and our model for he fas and he slow movemen wih he same parameers. Pause sae policy has he leas updae cos bu he mos imprecision cos. Depending on he mobiliy moion percenage, if he moion is more linear, hen he lowes imprecision cos is Linear sae policy; and if he moion is more random, hen he lowes imprecision cos is Random sae policy. However, our MBLUA has considerably low updae cos wih an accepable imprecision cos beween Linear and Random policies. Table 1. Policies updae and imprecision coss comparison Policy Fas node (2-4 m/s Slow node (.5-1 m/s Updae cos Imprecision cos Updae cos Imprecision cos MBLUA Pause-sae Linear-sae Random-sae Fig. 3 (a and (b show he updae and imprecision coss for MBLUA model when varying he d_hresh. I was observed ha, when d_hresh is low, he updae cos is high indicaing more frequen updaes, and he imprecision cos is low since locaion knowledge is updaed more frequen. As d_hresh increases, he updae cos decreases and he imprecision cos increases, since a larger d_hresh value resuls in larger wai ime o localize. We have found ha changing Lin_hresh only have lile impac on he resuls because Linear sae policy increase he waiing ime o he maximum ime as long as he predicion error is less han Lin_hresh, which is he case ha he error value is close o zero for linear movemen. From he resuls of Fig. 3, i is observed ha any d_hresh value greaer han 5 does no have effec on he updae cos meanwhile imprecision cos does increase. The reason is ha he maximum ime (max_ime o localize is fixed in he simulaions. As a

11 Mobiliy-Paern Based Localizaion Updae Algorihms for Mobile Wireless Sensor Neworks 11 a resul, when d_hresh is greaer han5, he sensor node will localize afer max_ime period no maer how large d_hresh value is, which sabilizes he updae cos. Consequenly, when he updae cos sabilizes, he main facor of changing he imprecision cos is he acceleraion value. Updae cos Disance hreshold (m Slow node Fas node (a Updae cos vs. d_hresh (max_ime=5 ime slos and Lin_hresh=4m Imprecision cos Disance hreshold (m Slow node Fas node (b Imprecision cos vs. d_hresh (max_ime=5 ime slos and Lin_hresh=4m Fig. 3. Updae and imprecision cos as a funcion of d_hresh Updae cos Slow node Fas node Maximun waiing ime slos (a Updae cos vs. max_ime (Lin_hresh=4m, d_hresh=5m Imprecision cos Maximum waiing ime slos Slow node Fas node (b Imprecision cos vs. max_ime (Lin_hresh=4m, d_hresh=5m Fig. 4. Updae and imprecision coss as a funcion of maximum waiing ime slos (max_ime Fig. 4 shows he updae and imprecision coss for MBLUA model when varying he maximum wai ime o localize. Wih low value of maximum wai ime, he updae cos is high and he imprecision cos is low since we force he algorihm o localize very ofen. As he maximum ime increases he updae cos decreases and he imprecision cos increases because he algorihm will have more possible ime o increase he wai ime o localize and hence will decrease he localizaion updae frequency. Bu his causes more error as he wai ime increases.

12 12 Mohammad Y. Al-laho, Min Song, Jun Wang Our experimens show ha fas movemen has more updae and imprecision coss. When a mobile node moves faser, he esimaion deviaes from he real locaion in higher raes, which causes larger esimaion errors. Moreover, as long as he error value exceeds he predefined error hresholds (d_hresh or Lin_hresh, a node will localize more frequenly. 5 Conclusions We designed hree mobiliy-paern based localizaion updae algorihms for mobile wireless sensor neworks. The main idea is o divide sensor movemens ino hree saes, Pause, Linear, and Random. Based on he naure of each movemen paern, differen localizaion updae algorihm is adoped a each sae. To verify he design, we have performed boh mahemaical analysis and simulaions. The resuls demonsrae how he localizaion cos is minimized and how he locaion accuracy is improved. This research is significan o conserve he power consumpion in sensor nodes and o rack he locaion of mobile sensors in a real-ime manner. References 1. S. Tilak, V. Kolar, N. B. Abu-Ghazaleh, and K. D. Kang, Dynamic Localizaion Conrol for Mobile Sensor Neworks, Proc. of IEEE Inernaional Workshop on Sraegies for Energy Efficiency in Ad Hoc and Sensor Neworks, Apr M. Song, K. Park, J. Ryu, and C. Hwang, Modeling and Tracking Complexly Moving Objecs in Locaion-Based Services, Journal of Informaion Science and Engineering, vol. 2, no. 3, pp , May V. Kumar, and S. R. Das, Performance of dead reckoning-based locaion service for mobile ad hoc neworks, Wireless Communicaions and Mobile Compuing Journal, vol. 4, no. 2, pp , Mar L. Hu, and D. Evans, Localizaion for Mobile Sensor Neworks, Proc. of Tenh Annual Inernaional Conference on Mobile Compuing and Neworking, pp , Sep I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor neworks: a survey, Compuer Neworks, vol. 38, no. 4, pp , Mar T. Camp, J. Boleng, and V. Davies, A Survey of Mobiliy Models for Ad Hoc Nework Research, Wireless Communicaion & Mobile Compuing, Special issue on Mobile Ad Hoc Neworking: Research, Trends and Applicaions, vol. 2, no. 5, pp , Apr A. Savvides, C. C. Han, and M. B. Srivasava, Dynamic fine-grained localizaion in ad-hoc neworks of sensors, Proc. of he 7h ACM/IEEE Inernaional Conference on Mobile Compuing and Neworking (MobiCom, pp , Jul A. Agarwal, and S. R. Das, Dead reckoning in mobile ad hoc neworks, Proc. of he IEEE Wireless Communicaions and Neworking Conference, Mar V. W. S. Wong, and V. C. M. Leung, An adapive disance-based locaion updae algorihm for nex-generaion PCS neworks, IEEE J. Selec Areas on Communicaions, vol. 19, no. 1, pp , Oc BonnMoion, hp://web.informaik.uni-bonn.de/iv/miarbeier/dewaal/bonnmoion/