RSS based Localization of Sensor Nodes by Learning Movement Model
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- Buddy Newman
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1 RSS bsed Locliztion of Sensor Nodes by Lerning Movement Model 1 R.ARTHI, 2 P.DEVARAJ, 1 K.MURUGAN 1 Rmnujn Computing Centre, Ann University, Guindy, Chenni, Indi 2 Deprtment of Mthemtics, College of Engineering, Guindy, Chenni, Indi 1 drthi73@gmil.com, 2 devrj@nnuniv.edu, 1 murugn@nnuniv.edu Abstrct: - Node Locliztion in Wireless Sensor Networks (WSNs) is widely used in mny pplictions. Locliztion uses prticle filter tht provides higher network trffic due to continuous updtes, which leds to high power consumption. The rticle presents rnge-bsed locliztion for Mobile Nodes (MN) tht builds up on Hidden Mrkov Model (HMM) lgorithm. The proposed work is bsed on MN nd the stte is hidden in the Received Signl Strength (RSS) for outdoor pplictions. Hidden sttes uses explicit knowledge of the observtion probbility obtined from two-ry ground propgtion model. HMM correltes these observtions to predict the hidden sttes. The stte trnsition nd the observtion of HMM help to estimte the most probble stte sequence nd the lst stte obtined is the predicted loction. This work uses vrious mobility models for the movement of nodes. Vrying the trnsmission rnge effectively controls the network connectivity. Results from simultion study hve reveled the possible reduction of network trffic nd power consumption with less estimtion error. In ddition, this work provides n efficient confidence intervl for the estimtion error. Key-Words: - Estimtion Error, Hidden Mrkov Model, Locliztion, Mobile Nodes, Received Signl Strength, Stte Estimtion, Wireless Sensor Networks. 1 Introduction Sensor networks re significntly different from trditionl d hoc networks. In generl, sensor nodes re densely deployed, prone to filures nd limited in power provision, computtionl complexity nd memory when compred to d hoc nodes. While most d hoc networks communicte on point-topoint bsis, sensor nodes minly use brodcst communiction prdigm [1]. In prticulr, loction-bsed pplictions of WSNs re employed for locting people nd trcking mobile objects in lrge buildings (e.g., wrehouses, hospitls) using GPS. However, very few studies hve indicted the use of WSN in outdoor environments to trck people in wide outdoor res, such s enemies in the bttlefield. The geogrphic loction of nodes in sensor network is determined for mny fetures of system opertion such s dt stmping, trcking, signl processing, querying, topology control, clustering, nd routing [2]. The selection of suitble lgorithm for given ppliction nd its performnce depends on severl key fctors such s the informtion vilble bout known loctions, difficulty in locting coopertive node, the dynmics of chnge of loction, the desired ccurcy, nd the constrints plced on hrdwre. The estimted position of ech MN (non-nchor node) cn be computed by communicting with the sttic node (nchor node). The position of the node is obtined using only rdio signls (RSS, n index of the received signl power). In relity, the nodes of the sttic network should be power-efficient when they re bttery-operted, helthy to pcket drop, esy to trck in ctul time, nd finlly, it should tolerte suitble locliztion ccurcy even in the cse of some sttic node filure. The prticle filter [3] solves the outdoor locliztion problem tht incorportes multiple sensory dt using both sttic nd mobile multihop network. The node moves with rndom velocity ttrcts norml distribution nd noise model re the prticle filter ssumptions to compre the results from RSS nd Angle of Arrivl (AOA, n estimte of the reltive ngles between nodes) sensor types. The simultion study nd nlysis revel tht n AOA sensor does not work when the network connectivity is low. The network contining 50 % of AOA nd RSS sensors thn the network dominted by individul-type sensors chieves better locliztion. Continuous updting t sufficient frequency to keep up with the node movement results in network trffic tht consumes high power; this is constrint in prticle filter. The current study proposes network-bsed locliztion system, which is modeled s HMM, nd the unobserved (hidden) stte sequence in the RSS hs been used to estimte MN loction. The hidden mrkov stte uses RSS nd the MN loction sequence to estimtes the most likelihood E-ISSN: Issue 11, Volume 12, November 2013
2 probbility nd the lst stte ttined is the estimted loction. The originl contributions provided in this pper re the cpbility to model nd hndle the rnge-bsed RSS through two-ry ground propgtion [4], node movement follows the rndom pttern of mobility model such s Rndom Wlk Model (RWM), Rndom Wypoint Model (RWP), nd Reference Point Group Mobility model (RPGM) [5] perceives less estimtion error. The proposed model emphsizes on outdoor locliztion using HMM nd the MN loction is estimted using the observtion probbility, which helps to minimize the trffic tht consumes less power for the locliztion process. The rest of the pper is orgnized s follows: section 2 summrizes the Existing locliztion methods nd Motivtion; the proposed model for locliztion is given in section 3, nd the performnce evlution is discussed in section 4. Section 5 concludes the pper nd discusses on the future work. 2 Existing Locliztion Methods nd Motivtion Sequentil Monte Crlo Locliztion (SMCL) is suitble for sensor networks, but it needs to ddress how the mobility model ffects the locliztion ccurcy [6]. In Improved MCL (IMCL), nchor constrint, neighbour constrint nd moving direction constrint re proposed [7] to confine the region of the vlid smples ner the ctul position of the norml nodes to improve the locliztion ccurcy. Improving MCL uses Genetic Algorithm, which reduces the precision of the locliztion ccurcy [8 ]. In the cse of indoor locliztion, Byesin Filtering [9] hs used RSS to estimte the loction on smple sets derived by Monte Crlo Smpling. The sttic pth-plnning problem of mobile becon to loclize sensors for uniformly deployed network pproch is considered in [10]. The locliztion procedure needs to djust the pth for dynmic pth plnning. The pproch for locliztion by using single mobile becon is delt [11], but inter-sensor locliztion methods cn be used fter the mobile becon exits the deployment re. A Fde-skew-level Lplce signl strength sttisticl model pplying prticle filter is used to estimte the loction [12] of moving nd sttionry people for wireless networks. RSS bsed sensor locliztion using unscented Trnsformtion is delt [13] for both coopertive nd non-coopertive scenrios. Incorporting multiple sensory dt in both sttic nd mobile multihop networks solves the locliztion problem using prticle filter [3]. The limittions re tht the continuous updting of the filter increses network trffic nd high power consumption. The model could be improved by lerning movement pttern (HMM) for mobile networks. HMM is used in speech recognition [14], nd directs the technique to be pplied to more dvnced speech recognition problems. For indoor environment, HMM method improves the ccurcy of locliztion [15] with respect to conventionl rnging methods, especilly in mixed LOS/NLOS conditions for ll rdio links. HMM is used s cscde model [16] for finding correltions mong sensory inputs to lern set of symbolic concepts for mobile robot. Multiuser decision feedbck [17] uses HMM in which liner filter bsed on the mximum trget likelihood criterion is derived to remove the interferences. The Byes Prticle filter frmework ws compred with Hidden Mrkov Model [18] using Semi Mrkov smooth mobility model nd it is seen tht the locliztion ccurcy ws improved for HMM. Though vrious techniques hve been proposed for locliztion, HMMs re the lerning movement models tht incorporte notion of time directly into the model through n underlying mrkov chin. The HMM is proposed to locte the nodes by improving the loction ccurcy using vrious mobility models for the node movement. 2.1 Motivtion WSN locliztion trgets to find the physicl loction of ll nodes deployed in the region. The objective of the locliztion lgorithm is to find the loction of non-nchor nodes with the help of nchor nodes. Prticle filtering is technique for executing recursive Byesin filtering by Monte Crlo smpling. Prticle filters llow Byesin estimtion to be crried out pproximtely in structured nd itertive mnner. The estimted position on the nodes is represented by probbility distribution. Byes Prticle filtering frmework cn be used for both sttic nd mobile nodes in sensor network locliztion [3]. The node movement drwn from rndom velocity follows norml distribution where RSSI uses free-spce propgtion model nd the mesured AOA is ffected by the noise model. The prticle filters re updted continuously t sufficient frequency leding to increse in network trffic nd high power consumption. E-ISSN: Issue 11, Volume 12, November 2013
3 This frmework ddresses the locliztion for mixed type of sensory cpcities, rther thn permitting individul RSSI or AOA sensor type. As recommended, this model could be improved by lerning the movement ptterns (models) for mobile networks. By using RSS sensor type in HMM, the loction is estimted using the stte sequence hidden in the signl strength bsed on the observtion probbility. 3 Proposed Model for Locliztion WSN locliztion is bsic need for mny pplictions. Node locliztion could involve trcking single node moving cross the plne or trying to identify the loction of fixed node. The proposed model ssumes tht the nchor nodes re sttic while the non-nchor nodes re moving dynmiclly over the network. The gol is to estimte the loctions of the MN with the help of HMM nd the following sections discusses bout this method. 3.1 Gthering RSS vlues of non-nchor nodes Limited number of nchor nodes use RSS cpcity to chieve node locliztion. To predict the received signl power of ech MN node, node locliztion uses two-ry-ground propgtion model. With the support of nchor node, the RSS of the MN is collected with the nodeid. Becuse of the continuous movement of the node, the non-nchor node hs mny RSS vlues. 3.2 Loction Estimtion Using HMM The proposed method loctes the rndomly scttered non-nchor nodes (MN) in the outdoor environment with the help of nchor nodes. The re of grid cell size n n for node movement follows the pttern of mobility models to move from one grid to nother. The server or bse sttion estimtes the loction of non-nchor nodes. To estimte HMM prmeters, ech stte represents loction in the discrete physicl observtion nd n observtion from stte represents n RSS reding from ssocited nonnchor node [19]. During the opertionl stge, RSS interprettion from ech non-nchor node nd the HMM prmeters re the necessry input to estimte the most probble sequence of sttes tht results in the estimted loction Estimtion of Probbility Mtrix in HMM HMMs extend mrkov models by ssuming tht the sttes of the mrkov chin re not observed directly. Hence, this model shows how the sttes (positions) relte to the ctul observtions (locliztions). HMM cn be used for locliztion process becuse it cn model sequentil stochstic processes or sttes, where probbility of stte depends on previous sttes. An HMM cn be represented s λ = (R,S,A,B,π) where: R = {R1,R2,R3,,RN} is the set of possible sttes,ech stte represents grid loction in the physicl spce. S = {S1,S2,S3,,SM} is the set of observtions from the model,ech observtion is n ordered pir of (non-nchor nodeid,rss). A = {ij} is the stte trnsition probbility mtrix,where ij = P[qt+1 = Sj qt=si], 1i, j N nd qt is the stte t time t. B = {bj(k)}is the observtion symbol probbility distribution in stte j, where bj(k) = P[Sk t t qt =Rj], 1 j N, 1 k M nd Sk re the output symbols t time t. π = { π i} is the initil distribution, where π i = P[q1 = Ri]. Therefore, the problem in brief: With given sequence of observtions O = (O1,,OT), where T is system prmeter nd ech Oi ϵ S, 1 i T, the most probble sequence of loction (sttes) Q = (q1,,qt), where ech qi ϵ R, 1 i T must be found. The purpose is to build the HMM nd estimte its prmeters for the locliztion. The stte trnsition mtrix is obtined by the rndom node movement either in forwrd, bckwrd, upwrd or downwrd direction nd ech stte represents loction in the grid. The node existence is identified by its trnsition probbility of signl strength. The trnsition sequence length prmeter is ssumed to be N. The trnsition probbility mtrix is denoted by An for the nth node nd it is of the form A n =. N N N 2N. NN (1) Further, the observtion mtrix (B) is ttined by the loction of nchor node to estimte the observtion probbility inside the cell. The nchor nodes direct the becon messges nd bsed on the response of RSS of the MN, B cn be obtined. The observtion sequence length prmeter is ssumed to be M. The observtion probbility mtrix is denoted by Bn for the nth node nd it is shown in (2) E-ISSN: Issue 11, Volume 12, November 2013
4 b 11 b12.. b1 M b21 b22.. b2 M B n = (2).... bn1 bn 2.. bnm Algorithm 1 is developed for itertively computing B n. Algorithm 1 Observtion mtrix Input: Set the loction of the trnsmitter coordinte T x, T y for ech nchor node in the grid cell. Output: Generte the observtion probbility mtrix for ech non-nchor node from the known nchor node loction coordintes in the grid cell. 1. Declre the vribles for the sttes s i, j, k=1. 2. Set the constnts G t, G r, h t, h r, P t, π, λ 3. Initilize n rry of grid cell size NxM for the observtion mtrix B[i][j] 4. begin 5. Divide the grid into smller cells to observe the movement of nodes 6. for i vrying from 1 to N sequence length do 7. for j vrying from 1 to M sequence length do 8. for (R Y = (i-1)*100; R Y < i * 100; R Y = R Y +0.1) i.e., receiver Y co-ordinte do 9. for (R X = (j-1)*100; R X < j * 100; R X = R X + 0.1) i.e., receiver X co-ordinte do 10. Compute the distnce d = sqrt ((R X - T X ) * (R X - T X ) + (R Y - T Y ) * (R Y - T Y )); 11. Compute crossover_dist = (4 * π * h t * h r ) / λ; 12. if (d <= crossover_dist),then 13. J = λ / (4 * π * d); 14. P r = (P t * G t * G r * (J * J)) / L; 15. else 16. P r = P t * G t * G r * (h r * h r * h t * h t ) / (d * d * d * d * L); 17. endif 18. rssi = 10*log 10(P r ); 19. rs = (int) rssi ; 20. B[k] [rs] + = 1; 21. end for 22. end for 23. Increment k by 1; 24. end for 25. end for 26. Find sum of ech row in observtion mtrix 27. Divide ech element in observtion mtrix with its respective sum 28. Generte the observtion probbility mtrix B[i][j] Once these fctors re clerly understood, the system is redy to find the loction estimte of the non-nchor node Evluting the Sequence using Forwrd- Bckwrd Algorithm The min pproch is to estimte the loction of the MN using RSS vlues. The observtion sequence is considered to find the loction where the non-nchor node exists t the end of the stte sequence. The sequence evlution is obtined by the probbility of the observtion, given the model λ, i.e. to find.the forwrd or bckwrd lgorithm is used to evlute the sequence for loction estimte [14]. The forwrd probbility clcultion is bsed on the grid cell, considering there re only N sttes (node loction t ech time in the grid), ll possible stte sequences will merge into those node loctions, no mtter how long the observtion sequence. The initil forwrd vrible is defined s where is the probbility of observing the prtil sequence ) such tht the stte is i. At times, there is need to clculte vlues of forwrd vrible, where ech clcultion involves only N previous vlues. The effect in forwrd nd bckwrd procedures is lmost identicl. The result P (O/λ) is minly used for trining the model Estimting the sequence using Viterbi Algorithm Given the observtion, the most likely stte sequence is obtined using the decoding problem by Viterbi lgorithm [14]. This lgorithm involves initiliztion, recursion nd termintion. The Viterbi lgorithm cretes better trjectory thn the trditionl lgorithm becuse it decides the rel stte tht depends on ll sttes nd the finl one is the most likelihood stte. The observtion sequence will keep on vrying bsed on the known nchor node loction. The focus is to compute the most probble stte sequence, hence the Viterbi decoding lgorithm is used to find the stte sequence with the help of observtion probbility. The stte sequence for ech node is found nd the lst stte estimted, i.e. qt is returned s the estimted user loction. By incresing the observtion sequence length tht dds more sttes, the loction estimtion ttins high ccurcy. As the locliztion process proceeds, ech non-nchor node loction is estimted nd converges fster to more concentrted loction estimte. E-ISSN: Issue 11, Volume 12, November 2013
5 The HMM Model uses the loction informtion from the nchors, which is implicitly contined in the observed stte sequence estimtion for ech unknown non-nchor node. The dvntge of our model is tht it uses the sequence of sttes to find the estimte loction tht does not require continuous smpling nd updtes s required by the prticle filter frmework. 4 Performnce Evlution The performnce of Byes Prticle Filter nd proposed HMM model with RWM, RWP nd RPGM model hve been evluted using NS2 simultion. Loction estimtion error, Control overhed nd Averge energy dissiption re considered [20] s the key metric for evluting locliztion schemes. (i) Loction Estimtion Error: It is the verge distnce between estimted loction nd ctul loction of ll sensor nodes. The loction error is scled s the percentge of trnsmission rnge. (ii) Control Overhed: It is the totl number of control pckets trnsmitted by the nchors to loclize n unknown node in ech locliztion process. (iii) Averge Energy Dissiption: It is the verge mount of energy spent by sensor node during communiction in the network. deployed with 100 nodes. The prticle filter hs totl number of 200 prticles t ech node. The trnsmission rnge is set to 150m tht leds to coverge of 100%. The trnsition sequence length prmeter N is fixed t 100 nd the observtion sequence length prmeter M is fixed t Simultion Results nd Anlysis The simultion results for the proposed HMM re nlyzed to study the effect of node vrition, vrying trnsmission rnges for connectivity nd vrious speeds Effect of vrying the number of nodes The evlutions on estimtion error or locliztion ccurcy over number of nodes re nlyzed for the proposed method. Increse in the number of nodes improves the locliztion ccurcy for different mobility models s shown in Fig 1. Tble 1: Simultion Prmeters Simultion re Antenn Type 1000m X 1000m Omni Directionl Propgtion Model Two-ry ground Trffic Type Speed Initil Energy Pcket size Puse Time CBR 2 10 m/sec 5.1 J 512 bytes 5 sec Mobility Model RWM, RWP, RPGM Tble 1 shows the simultion prmeters. The performnce metrics re nlysed for vlidting the lgorithm by vrying the node density, trnsmission rnge nd speed. 10% of the totl nodes re ssumed s nchor nodes [3] nd the network re is As expected, higher node density lowers the estimtion error. The error estimte of HMM RPGM proves to be better becuse ech node moves ner the other s group with lmost similr speed nd direction. E-ISSN: Issue 11, Volume 12, November 2013
6 Fig 1: Impct of Node density on Estimtion Error RWM RWP RPGM However, in comprison with other mobility models, it hs lowest reltive speed becuse ech node in group chooses rndom speed nd direction ccording to the group leder. This specifies tht for the proposed work, nodes with RSS tend to dpt mobility nd converge fster when compred with prticle filter. The performnce of control overhed over node density is shown in Fig 2. The nchor node trnsmits pcket within its rnge to gther informtion from the neighbouring node tht increses control overhed. Non-nchor nodes overhering this pcket reply their known informtion to nchor node. The simultion endorses tht HMM tkes 10% less compred to existing method becuse of the stte sequence rther thn continuous updting of filters. Fig 2: Impct of Node density on Control Overhed RWM RWP RPGM Overll, the mobility model behves s per the functionlity of the model, tking more overhed increses nodes density. The effectiveness of verge energy dissipted with respect to totl number of nodes is shown in Fig 3. The verge energy spent when in movement is more, but ctul energy spent in locliztion process is less. This shows tht energy consumption vries due to increse in the node density. It is observed tht for different mobility model, verge energy dissiption grdully decreses for lrger density of nodes. The existing method in the RPGM model consumes more energy due to the prticle size tht requires continuous updting of the filter. E-ISSN: Issue 11, Volume 12, November 2013
7 eventully propgte throughout the network of vrying trnsmission rnges nd llow non-nchor nodes to loclize themselves using the stte sequence estimtion provided by HMM. The estimtion error for HMM RPGM ppers to be better when compred with other mobility models. Fig 3: Impct of Node density on Averge Energy Dissiption RWM RWP RPGM Effect of the coverge The impct of estimtion error ginst coverge to trnsmission rnge of 150m for 100 nodes with the speed of 10m/s is shown in Fig 4. The effect of coverge becomes low when the network is dense, i.e., increse in trnsmission rnge. The estimtion error increses due to increse in the trnsmission rnge for higher node density. The network connectivity is efficiently controlled by vrying the trnsmission rnge. The nchors Fig 4: Impct of Coverge on Estimtion Error RWM RWP RPGM The control overhed pckets differ s shown in Fig 5 with increse in trnsmission rnge for vrying mobility models. The control overhed E-ISSN: Issue 11, Volume 12, November 2013
8 pcket grdully decreses for incresing trnsmission rnge for higher nodes. As nticipted, the estimted loctions become more ccurte s more informtion is exchnged mong neighbors. The overhed pckets re decresed to increse the node density for 80 to 100% of coverge. RPGM consumes more overhed pckets when compred to the other mobility model becuse the member nodes follow the leder node. The impct of coverge over the verge energy dissiption shows minor difference s shown in Fig 6. Fig 5: Impct of Coverge on Control Overhed RWM RWP RPGM Fig 6: Impct of Coverge on Averge Energy Dissiption RWM RWP RPGM As the becon node percentge vries over the deployment re, the verge energy dissipted indictes tht more nodes re loclized for vrying trnsmission rnge. The energy spent in proposed locliztion is less due to stte sequence compred to continuous updting in the existing work. It cn be seen tht the RPGM model consumes less energy E-ISSN: Issue 11, Volume 12, November 2013
9 when compred to other models becuse the members follow the leder nodes to be loclized Effect of vrying the Speed The effect of vrying speed over the estimtion error is shown in Fig 7. estimtion error obtined for HMM RWM is lesser thn the prticle filter with vrious moving speeds. RWP puses for few seconds nd chooses the speed to move to the next destintion. RPGM behves differently from the other two models by choosing the pproprite ngle nd speed devition, which controls the velocity of group members from tht of the leder. Vrition of speed over the control overhed is shown in Fig 8. The increse in the speed grdully decreses the control overhed. RWM nd RWP hve lower overhed when compred to RPGM. RPGM follows the speed nd ngle devition so tht the overhed ws slightly high t initil speed of 2m/s. Fig 7: Impct of Speed on Estimtion Error RWM RWP RPGM All the nodes in the network hve communiction rnge of 150m. As the speed increses, the locliztion error progressively decreses.the The performnce of verge energy dissiption for vrying speed is shown in Fig 9. The energy is grdully reduced due to the increse in speed for RWM. In ll the three mobility models, the energy drops down t higher speed. For RWP nd RPGM, since it puses for few seconds to tke decision for the next movement to rech the destintion, it spends more energy thn RWM. E-ISSN: Issue 11, Volume 12, November 2013
10 higher nchor rtio, higher speed produce better estimtions. Fig 8: Impct of Speed on Control Overhed RWM RWP RPGM Fig 9: Impct of Speed on Averge Energy Dissiption RWM RWP RPGM The estimtion error is clculted s the difference between the most probble estimted vlue nd the ctul loction. The χ² - test is used to test the sttisticl significnce of difference between estimted nd ctul loction; the dt collected for multiple runs clims 98 % level of confidence for RWM nd RWP, while 99 % for RPGM communicting bout the fct tht networks with Summrizing the bove observtions of the proposed work, the estimtion error reduces nd converges fster for vrying node density, vrious trnsmission rnges nd vrying speed for different mobility model. These observtions show tht the stte sequence estimtes for loction of non-nchor nodes re more ccurte nd converge fster by minimizing the trffic rte nd reducing the power dissiption using vrious mobility models. 5 Conclusion nd Future Work The knowledge of physicl loction of mobile nodes is more useful to geogrphicl routing in the wireless sensor network. Extensive literture is vilble for indoor sensor network wheres only miniml studies focused on outdoor. The current work helps to obtin better loction ccurcy in the outdoor environment through RSS mesurement by two-ry propgtion model using HMM. The proposed pproch exploits the RSS mesurements to estimte the position of mobile node. The network connectivity is controlled by vrying the trnsmission rnge; hence the trffic is voided by the stte sequence estimtion; longer the sequence, better the loction ccurcy. In ddition, through comprtive simultion study of vrious mobility models it hs been observed tht RPGM improves the loction ccurcy. The dvntge of the proposed work is rpid convergence of the stte sequence, which directly helps to reduce the trffic nd subsequently consumes low power consumption. This work cn be extended for E-ISSN: Issue 11, Volume 12, November 2013
11 uniform nd non-uniform deployment of the nodes using multiple sensory dt with other propgtion model. References: [1] I.F.Akyildiz, W.Su, Y.Snkrsubrmnim, nd E.Cyirci. : A Survey on Sensor Networks, IEEE Communiction Mgzine, Vol.40 No.8, pp , [2] Angelo Cenedese, Giuli Ortoln, nd Mrco Bertinto. : Low-Density Wireless Sensor Networks for Locliztion nd Trcking in Criticl Environments, IEEE Trnsctions on Vehiculr Technology, Vol. 59, No. 6,pp , [3] Rui Hung, Gergely V.Zrub. : Incorporting Dt from Multiple Sensors for loclizing nodes in Mobile Ad Hoc Networks, IEEE Trnsctions on. Mobile Computing, vol.6, No.9, pp , [4] T.S.Rppport. : Wireless Communictions: Principles nd Prctice, 2nd edition, Prentice Hll, [5] Bbk Pznd, Chris McDonld. : A Critique of Mobility Models for Wireless Network Simultion,Interntionl Conference on Computer nd Informtion Science, pp , [6] Weidong Wng, Qingxin Zhu. : Sequentil Monte Crlo Locliztion in Mobile Sensor Networks, Springer Science+Business Medi, LLC2007, Wireless Networks 15, pp , DOI /s , [7] Jng-Ping Sheu, Fellow, IEEE, Wei-ki Hu, Student Member, IEEE, Jen-chio Lin. : Distributed Locliztion Scheme for Mobile Sensor Networks, IEEE Trnsctions on Mobile Computing,Vol.9,No.4, pp , [8] Yuehu Liu, Ho Yu, Bin Chen, Yubin Xu, Zhihui Li, Yu Fng. : Improving Monte Crlo Locliztion Algorithm Using Genetic Algorithm Mobile WSNs, IEEE Interntionl Conference on Geoinformtics, pp:1-5, DOI: /Geoinformtics, [9] G.V.Zrub, M.Huber, F.A.Kmngr. : Indoor Loction trcking using RSSI redings from single Wi-Fi ccess point, Springer Science+Business Medi, LLC2007, Wireless Networks (2007), pp , DOI /s , [10] Rui Hung, Gergely V.Zrub. : Sttic Pth Plnning for Mobile Becons to Loclize Sensor Networks, IEEE Interntionl Conference on Pervsive Computing nd Communictions Workshops (PerComW 07), pp , [11] Rui Hung, Gergely V.Zrub. : Monte Crlo Locliztion of wireless sensor networks with single mobile becon, Springer Science+BusinessMedi, LLC2008, WirelessNetworks15, pp , DOI /s , [12] Joey Wilson, Nel Ptwri. : A Fde-Level Skew-Lplce Signl Strength Model for Device-Free Locliztion with Wireless Networks, IEEE Trnsctions on Mobile Computing, Vol. 11, No. 6,pp , [13] Gng Wng, Kehu Yng, Member, IEEE. : A New Approch to Sensor Node Locliztion using RSS Mesurements in Wireless Sensor Networks, IEEE Trnsctions on Wireless Communictions, Vol. 10, No. 5, pp , [14] Lwrence R. Rbiner, Fellow, IEEE. : A Tutoril on Hidden Mrkov Models nd Selected Applictions in Speech Recognition, Proceedings of the IEEE, Vol. 77 No. 2, pp , [15] Crlo Morelli, Monic Nicoli, Member, IEEE, Vittorio Rmp, nd Umberto Spgnolini,Senior Member, IEEE. : Hidden Mrkov Models for Rdio Locliztion in Mixed Los/ NLos Conditions, IEEE Trnsctions On Signl Processing, Vol. 55 No. 4, pp , [16] Kevin M. Squire, Member, IEEE, Stephen E. Levinson, Fellow, IEEE. : HMM-Bsed Concept Lerning for Mobile Robot, IEEE Trnsctions on Evolutionry Computtion, Vol.11 No.2, pp , [17] Fngjiong Chen, Sm Kwong, Senior Member, IEEE. : Multiuser Detection Using Hidden Mrkov Model, IEEE Trnsctions on Vehiculr Technology, Vol.58 No.1, pp , [18] R.Arthi, K.Murugn. : Locliztion in Wireless Sensor Networks by Hidden Mrkov Model, IEEE Interntionl Conference on Advnced Computing, pp , [19] Mohmed Ibrhim, Moustf Youssef. : A Hidden Mrkov Model for Locliztion Using Low-End GSM Cell Phones, IEEE Interntionl Conference on Communiction, pp. 1-5, [20] Sebstin Thurn, Dieter Fox, Wolfrm Burgrd, Frnk Dellert. : Robust Monte Crlo Locliztion for mobile robots, Artificil Intelligence Journl, 128(1-2), pp , E-ISSN: Issue 11, Volume 12, November 2013
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