008 Inernaoal Symposum on Telecommuncaons A cooperave sngle arge rackng algorhm usng bnary sensor neworks Danal Aghajaran, Reza Berang Compuer Engneerng Deparmen, Iran Unversy of Scence and Technology, Iran Absrac- Sensor neworks nclude large number of low cos sensor nodes wh small processng capables ha are deployed over an area n an aemp o do neres sensng ask. In hs paper we eamne he role of very smple and nosy sensors for dsrbued rackng problem ha s one of hese asks. We use a proposed bnary sensor model, where each sensor s value s convered relably o one b of nformaon only: wheher he objec s movng oward he sensor or away from and propose a cooperave dsrbued algorhm ha can be used n real-me rackng and s effcen n power and bandwdh. We show ha how an esmaor sensor use nformaon from s neghbors o esmae arge locaon more accuraely. Our eensve smulaons show low error n low densy sensor neworks. Key words- Cooperave arge rackng, Dsrbued algorhm, Sensor neworks I. Inroducon Sensor neworks nclude large number of low cos sensor nodes wh small processng capables ha are deployed over an area n an aemp o do neres sensng ask. The number of sensor nodes may be on he order of hundreds or housands. Dependng on he applcaon, he number may reach an ereme value of mllons []. Also he densy of he sensor nodes can range from few sensor nodes o few hundred n a regon, whch can be less han 0 m n dameer []. Sensor neworks have unque feaures and lmaons ha dsngush hem from oher neworks. Large number of sensor nodes, low processng capables and power lmaon are some of hese. Therefore many proocols and algorhms ha have been proposed for radonal wreless ad hoc neworks canno be used for sensor neworks. One of sensor nework s applcaon s arge rackng ha was nally nvesgaed 00[,3,4,5,6]. Targe rackng has been a classcal problem snce he early years of elecrcal sysems. In a gven feld of survellance neres, here s a arge ha arses n he feld a random locaon and a random me. The movemen of hs arge follows an arbrary bu connuous pah, and persss for a random amoun of me before dsappearng n he feld. The arge locaon s sampled a random nervals. The goal of he arge rackng problem s o fnd he movng pah for hs arge n he feld. Tradonal arge rackng sysems are based on powerful sensor nodes, capable of deecng and locang arges n a large range and all sensed daa were cenralzed n a powerful compuer for runnng rackng algorhms [7]. Wh he advances n he fabrcaon echnologes ha negrae he sensng and he wreless communcaon echnologes, ny sensor moes can be densely deployed n he desred feld o form a large-scale wreless sensor nework. The numbers of sensor nodes are wo o hree magnudes greaer han hose n radonal mulsensor sysems. On he oher hand, each sensor node can have only lmed sensng and processng ables. A arge rackng sysem n hs model can have several advanages [7]: ) he sensng un can be closer o he arge, and hus he sensed daa wll be of a qualavely beer geomerc fdely; ) he advances n wreless sensor nework echnques wll guaranee quck deploymen of such a sysem he sensed daa can be processed and delvered whn he nework, so ha he fnal repor abou he arge s accurae and mely; and 3) wh a dense deploymen of sensor nodes, he nformaon abou he arge s smulaneously generaed by mulple sensors and hus conans redundancy, whch can be used o ncrease he sysem s robusness and ncrease he accuracy of rackng. Challenges and dffcules, however, also es n a arge rackng sensor nework:. Trackng needs collaborave communcaon and compuaon among mulple sensors. The nformaon generaed by a sngle node s usually ncomplee or naccurae [7].. Each sensor node has very lmed processng power. Tradonal arge rackng mehods based on comple sgnal processng algorhms may no be applcable o he nodes 0 [] []. 3. Each node also has gh budge on energy source. Every node canno be always acve n sensng and daa forwardng. Thus, all he nework proocols for daa processng and rackng should consder he mpac of power savng mode n each node. 978--444-75-/08/$5.00 008 IEEE 75
4. The opology of a sensor nework may change very frequenly []. For a arge rackng sensor nework, he rackng scheme should be composed of wo componens [7]. The frs componen s he mehod ha deermnes he curren locaon of he arge. I nvolves localzaon as well as he racng of he pah ha he movng arge akes. The second componen nvolves algorhms and nework proocols ha enable collaborave nformaon processng among mulple sensor nodes. The goal of hs componen s o devse echnques for effcen and dsrbued schemes for collaboraons beween nodes of a sensor nework. Dsrbued algorhms for deecon and rackng of moble arges are desgned whn he consrans of varous resources (especally power consrans). In hs paper we propose a dsrbued algorhm n he cone of a rackng applcaon focused on bnary sensors model proposed n []. The bnary model assumpon s ha each sensor nework node has sensors ha can deec one b of nformaon. Ths b shows ha wheher an objec s approachng sensor or movng away from. We analyze hs bnary sensor nework n he cone of a rackng applcaon and derve a rackng algorhm ha can be used for real-me rackng n applcaons wh hgh speed velocy movemen. We also show ha a bnary sensor nework n whch sensors have only one b of nformaon do no have enough nformaon conen o denfy he eac objec locaon bu For many applcaons hs accuracy s enough for eample n rackng a flock of brds, a school of fsh, vehcle convoy. The remander of he arcle s organzed as follows. We dscuss relaed work n he ne secon. Used bnary sensor model for developmen of algorhm wll dscuss n secon 3. In secon 4 and 5 we descrbe man algorhm and some mplemenaon deals. We see smulaon resul n secon 6 and hen conclude our arcle n secon 7 and alk abou our fuure work n secon 8. II. Relaed work Targe rackng s concerned wh appromang he rajecory of one or more movng objecs based on some paral nformaon, usually provded by sensors. Targe rackng s necessary n varous domans such as compuer vson [8], sensor neworks [9], accal balefeld survellance, ar raffc conrol, permeer secury and frs response o emergences. A ypcal eample s he problem of fndng he rajecory of a vehcle by bearngs measuremen, whch s a echnque used by radars. Work n robocs has also consdered rackng arges from movng plaforms [0]. Several mehods for rackng have been proposed. Ths ncludes Kalman fler approaches or dscrezaon approaches over he confguraon space. A recen mehod ha shows grea promse s parcle flerng, whch s a echnque nroduced n he feld of Mone Carlo smulaons. In [] proposed a bnary algorhm based on parcle fler approach. The semnal paper n hs doman s [], whch saes he basc algorhm and properes. Snce hen many papers have addressed hs opc; among he mos mporan are he varance reducon scheme [] and he aulary parcle fler [3]. A survey of heorecal resuls concernng he convergence of parcle fler mehods can be found n [4]. Probablsc mehods have also been used n robocs for smulaneous localzaon and mappng (SLAM), n whch he robo aemps o rack self usng he sensed poson of several landmarks. For eample, n [5], parcle fler echnques were used for localzaon only when he radonal Kalman fler echnque had faled. These algorhms ypcally assume range and bearng nformaon beween he landmarks and racked vehcle, unlke he very smple sensors consdered here. A dsrbued proocol for arge rackng n sensor neworks s developed n [6]. Ths algorhm organzes sensors n clusers and uses 3 sensors n he cluser oward whch he arge s headed o sense he arge. The arge s ne locaon s predced usng he las wo acual locaons of he arge. We are nspred by hs prevous work and use a dsrbued mehod n he cone of he bnary sensor model. III. Sensor Nework model We assume ha he sensor nodes are scaered randomly n a geographcal regon. Each node s aware of s locaon. Locaon s nformaon can be gahered usng an on-board GPS recever. Absolue locaon s nformaon s, however, no needed. Many localzng echnques can be used wh varyng degree of hardware compley and accuracy. See, for eample,error! Reference source no found.error! Reference source no found.. The sensor nodes are saonary n our model; hs makes he localzaon problem somewha smpler. We use a bnary sensor nework model. Each sensor node n hs nework consss of sensors ha can each supply one b of nformaon only. In hs arcle we assume ha he sensor nodes have only one bnary sensor ha can deec wheher he objec s approachng or movng away. The deecon s performed as follows. Each sensor performs deecon 75
and compares s measuremen wh a precompued hreshold (e.g., lkelhood rado es). If he probably of presence s greaer han he probably of absence, also called he lkelhood rao, he deecon resul s posveerror! Reference source no found.. The model assumes ha sensors can denfy wheher a arge s movng away from or owards In each sep, all sensors ha repor approachng arge o self form a se ha we wll call hem, plus sensors and we wll call sensors ha repor movng away, mnus sensorserror! Reference source no found.. We can formulae hese defnons as equaon() : Plus sensors = { S s =+ } Mnus sensors = { S s = } Where S means h sensor and s means value of h sensor. In Error! Reference source no found. represened some sensor nework geomery properes ha show he locaon of he racked objec s ousde he conve hull of he plus sensors (we call hs conve hall as plus conve hull) and also ousde he conve hull of he mnus sensors (mnus conve hull). We use hs propery n nalzaon phase n our algorhm laer. IV. The rackng algorhm As In hs secon we descrbe our rackng algorhm. A. Algorhm deals Our rackng algorhms make hree assumpons. Frs, for each arge ha eners he regon we suppose s velocy s fed ( V ). For he sake of smplcy we also suppose sensors know hs velocy. For eample f we deploy some speed deecon sensors n he edges of he regon, when arge eners he regon from an arbrary drecon, hese sensors can esmae s speed and broadcas o oher sensor nodes. Ths does no have a heavy communcaon cos for he nework, because he speed deecon operaon s done only once for each arge. Also he number of speed deecon sensors s neglgble wh respec o he number of man sensors, addng he speed deecon sensors does no () nfluence he cos of whole sensor nework. Our second assumpon s ha movemen of he arge n he regon s under mld pah (a each sensor readngs he drecon of he racked objec can vary from he prevous one wh a mos π /6). We descrbe laer abou use of hs assumpon. The hrd assumpon s ha all sensor nodes are me synchronzed. We suppose ha when a arge eners he range of a sensor, he sensor sars sensng and savng wo consecuve sensor readng values. When here s a change n he readng (we call hs poson he crcal pon hereafer), he sensor node can esmae he poson of he arge and broadcas boh poson and s readng me o he nework. Each sensor keeps prevous esmaon and s me (we call hem ˆ and T respecvely). In he followng we wll dscuss and prove ha he esmae refers o wo dfferen posons locaed on a crcle, C, cenered on he prevous arge poson ˆ wh a radus of r ha s arge s dsplacemen beween prevous esmaon and he curren one. Theorem. Le be an arbrary sensor, locaed a poson S.Also Le and be wo mes so ha s =+ ands = where s and s are sensor readng s values a mes respecvely. Whou loss of generaly, and suppose < T < and arge move on sragh lne. If lm = 0 hen T s me ha sensor readng value for sensor change. Then lnes S and are perpendcular n pon. T Proof. S Le angel beween lnes T and Assume by conradcon haα 90. Therefore here are wo saes. α > 90 And α < 90. Frs consderα > 90. In fgure we see hs sae. T α. 753
Le S α = S and T = and S = = d and T T = and Changng sensor value n pon o condons(): < < j j j Fgure - arge moves from T Γ c S T T o sensor value changed. S T =. can be convered and n () velocy. Dsplacemen ( d ) beween wo crcal pons n whch he readng values change s calculaed from(3). d = v ( T T ) (3) Ths dsplacemen gves us a crcular locus, C, for he ne locaon, T, wh he cener ˆ and he radus d. On he oher hand, we know from heorem ha he arge rajecory and he connecng lne beween he sensor S (reporng sensor) and he crcal pon are perpendcular. These gve wo possble posons for he arge, ha are angen pons of he lnes from he sensor S (he reporng sensor) o he crcle, C, as shown n fgure. We can represen hese pons as: { y ys y and y sonc } (4) In wrng hese condons we suppose frs arge moves oward sensor and hen gong away. α > 90 S < 90 And because < T hen S 90 T < S T <. In S T we have and are less han 90 herefore alude lne from T alude nersec S s nsde rangle. We suppose hs a pon c (see fgure ). In T Sc T angel c s 90 and herefore > Sc and hs s on he conrary wh second condon n(). Therefore α > 90. α < n he same manner For he case 90 conradc wh(), herefore α = 90. Ths heorem can be used o locae he arge, assumng ha a sragh lne pah and a fed Fgure - Locaon esmaon of arge based on heorem. pons _ and _ can be an esmaon for locaon of arge ha algorhm calculae mddle of hese wo pon on he crcle for fnal esmaon of arge. As here s no furher nformaon o dsrc beween hese wo pons, esmaor sensor wh cooperave manner can ncrease accuracy of esmaon n each sep. By combnng daa from neghborng sensors, algorhm can reach a rackng 754
resul wh a resoluon hgher han ha of he ndvdual sensors beng used. In each sep, he sensor ha esmaes poson sends a vongmessage o s neghbors. Ths message conans wo ne poson locus and d of esmaor sensor. Each node afer recevng hs message, check s readngs wh hese wo pons and send a new message o esmaor node. If each wo pons have no conssency wh s readng ha node doesn send any message because hs condon has no any nformaon for esmaon. Ths s power effcen manner. Also f each wo pons have conssency wh sensor readng, node doesn send any message. Ths s because of power effcency oo. In wo reman condons here s an acceped pon and a rejeced pon and node sends a message o esmaor node. Ths message conans d of sender and acceped pon. Esmaor node was for a me ou afer sendng vongmessage. Then esmae new poson accordng o receved messages as follow. Suppose C s number of messages ha esmaor receved and valdaes _ and C s number of valdaon messages for pon _ hen: Esmaor node choose _ as ne poson _ f C-C>. Esmaor node choose _ as ne poson _ f C-C>. Oherwse _ choose as mddle pon of _ and _ on crclec. Ths pon depc as _ on fgure. New algorhm can be rewre as below: = y 0 = 0 Inalze 0 whle (arg e s n range ) y = sensor readngvalue f y y hen d = VT ( T ) calculae and oncrcle d (, ) send vongmessage ( d,, ) o neghbers recevevaldaonmessage for ameou se C = number of messages ha valdae se C = number of messages ha valdae f C C > hen se se = elsef C C hen broadcas (, T ) > se = else = + end f end whle = average of and as new poson on crcle end f B. Epermens To evaluae our approach, we mplemened our rackng Algorhm n MATLAB and performed smulaons. For each pon n he plo, we run our algorhm for 00 rajecores and random sensor neworks and average resuls. The Fg. 3 s based on Absolue Mean Error (AME). Suppose r(k) s acual poson of he objec n me k and E(k) s esmaon of algorhm AME error model calculaed as equaon(8). 755
n Error = r ( k ) E ( k ) AME (5) n k = Where n s number of locaon esmaons. Each plo n fgure 3 s concern wh sensor range. When a sensor range s R, mean ha he sensor can deecs always he arge wh dsance d ha d < R 0.and deecs somemes n ranges R 0. d R + 0.. wh longer range esmae arge locaon wh bgger AME error. IV. Conclusons In hs paper we suded a new arge rackng algorhm for wreless sensor neworks. We assume ha node n he neworks have sensors ha can gve one b of nformaon whch dsnc abjec s approachng or movng away from sensors. We proof The plos n fgure 3 show esmaon error s sored wh sensor range. Ths means ha sensors 0.06 0.05 0.04 0.03 0.0 0.0 AME Absolue Mean Error R=0.05 R=0.06 R=0.07 R=0.08 R=0.09 R=0.0 0 5 36 49 64 8 00 44 69 96 5 56 Number of sensors Fgure 3 The plo shows AME error for rackng algorhm. The plo show number of sensors s no nfluenced accuracy of algorhm hardly. Lle decreasng n error s because of nalzaon phase. a geomerc heorem ha gves us condons for deermne objec locaon locus as wo pons on a crcle. We use hs propery n our rackng algorhm for esmang he arge locaon. The smulaon resuls show ha he accuracy of algorhm s no nfluenced hardly by number of sensors. Ths s because n each sep locaon esmaon s down only by a sensor node and ncreasng number of sensors n he feld, ncrease number of esmaon ( means ha decrease he me beween wo esmaons). Number of sensors nfluence more, nalzaon phase of algorhm ha cause a lle mprovemen n accuracy. Because hs propery of algorhm s well sued for usng n low densy sensor nework. Usng hs algorhm n hgh densy sensor neworks causes more effcency n power and bandwdh of nework, because algorhm dose no need o acvae all sensors for overlappng deecon of arge a a me. In he end of our paper we descrbe some of he open ssue ha we plan o consder hese n our fuure work. One mporan aspec of fuure work s nose. Real world sensors are nfluenced by nose. We can ncorporae nose n our model by addng a Gaussan varable o he sgnal srengh graden a sensor and hen quanze as -, 0 or. A 0 repors a a 756
ceran me means ha he sensor s sgnal srengh graden s below a ceran hreshold and hus no relable enough, whch can also be regarded as a emporarly shudown of he sensor. The Gaussan varable ε has zero mean, bu s varance should be deermned from real daa reflecng sensors characerscs. Also n our algorhm we suppose nodes know velocy of objec ha s a drawback. Because n some applcaons knowng velocy s non-realsc assumpon alhough n many applcaon velocy of objec s fed and known or we can esmae velocy wh some speed deecon sensors n edge of sensor nework feld. Anoher drawback of our algorhm s ha can appled o rackng a sngle objec only, alhough an eenson for rackng mulple objecs usng group managemen schemes s dscussed n our fuure works In he near fuure we wll nvesgae how o add hese conceps o our algorhm and how o eend our algorhms o suppor mulple arge rackng. VI. References [] Ian F.Akyldz and Welan Su, A survey on Sensor Nework, IEEE Trans. Communcaon magazne, Vol.40, No.4, pp0-4 00. [] J. Aslam, Z. Buler, V. Cresp, G. Cybenko, and D. Rus, Trackng a movng objec wh a bnary sensor nework, Proc. ACM In. Conf. Embedded Neworked Sensor Sysems (SenSys), 003. [3] R. R. Brooks, P. Ramanahan, and A. M. Sayeed, Dsrbued arge classfcaon and rackng n sensor nework, Proc. IEEE, 9(8) (003). [4] J. Lu, M. Chu, J. Lu, J. Rech, and F. Zhao, Dsrbued sae represenaon for rackng problems n sensor neworks, Proc. 3rd In. Symp. Informaon Processng n Sensor Neworks (IPSN), 004. [5] K. Mechov, S. Sundresh, Y. Kwon, and G. Agha, Cooperave Tracng wh Bnary-Deecon Sensor Neworks, Techncal repor UIUCDCS-R- 003-379, Compuer Scence Dep., Unv. Illnos a Urbaba Champagn, 003. [6] F. Zhao, J. Shn, and J. Rech, Informaon-drven dynamc sensor collaboraon for rackng applcaons, IEEE Sgnal Proces. Mag. (March 00). [7] Rajeev Shorey, A. Ananda, Mun Choon Chan and We Tsang Oo, Moble, wreless and sensor Neworks echnology, applcaons and fuure drecons, a john wley & sons, INC.,Pblcaons, pp 73-94 006. [8] W.E.L. Grmson, C. Sauffer, R. Romano, and L. Lee. Usng adapve rackng o classfy and monor acves n a se. In Proc. of IEEE In l Conf. on Compuer Vson and Paern Recognon, 9,998. [9] F. Zhao, J. Shn, and J. Rech. Informaon-drven dynamc sensor collaboraon for rackng applcaons. IEEE Sgnal Processng Magazne, 9():6 7, March 00. [0] Lynne E. Parker. Cooperave moon conrol for mul-arge observaon. In Proc. of IEEE Inernaonal Conf. on Inellgen Robos and Sysems, pages 59 7, Grenoble, Sep. 997. [] P. Clfford, J. Carpener and P. Fearnhead. An mproved parcle fler for non-lnear problems. In IEE proceedngs - Radar, Sonar and Navgaon, I46: 7, 999. [] D. Salmond, N. Gordon and A. Smh. Novel approach o nonlnear/non-gaussan bayesan sae esmaon. In IEE Proc.F, Radar and sgnal processng,40():07 3, Aprl 993. [3] Mchael K. P and Nel Shephard. Flerng va smulaon: Aulary parcle flers. Journal of he Amercan Sascal Assocaon, 94(446), 999. [4] D. Crsan and A. Douce. A survey of convergence resuls on parcle flerng for praconers, 00. [5] Eduardo Nebo, Favo Masson, Jose Guvan, and Hugh Durran-Whye. Robus smulaneous localzaon and mappng for very large oudoor envronmens. In Epermenal Robocs VIII, 00 9. Sprnger, 00. [6] H. Yang and B. Skdar, A Proocol for Trackng Moble Targes usng Sensor Neworks, Proceedngs of IEEE Workshop on Sensor Nework Proocols and Applcaons, 003. [7] Nrupama Bulusu, John Hedemann, and Deborah Esrn. GPS-less low cos oudoor localzaon for very small devces. IEEE Personal Communcaons, Specal Issue on Smar Spaces and Envronmens, 7(5):8 34, 000. [8] K. Whehouse and D. Culler. Calbraon as parameer esmaon n sensor neworks. In Proceedngs of he Frs ACM Inernaonal Workshop on Wreless Sensor Neworks and Applcaons(WSNA), pages 59 67, 00. 757