WIRELESS positioning technologies for estimating the

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1 350 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 Cooperatve Self-Navgaton n a Mxed LOS and NLOS Envronment Po-Hsuan Tseng, Member, IEEE, Zh Dng, Fellow, IEEE, and Ka-Ten Feng, Member, IEEE Abstract We nvestgate the problem of cooperatve self-navgaton (CSN) for multple moble sensors n the mxed lne-of-sght (LOS) and nonlne-of-sght (NLOS) envronment based on measurng tme-of-arrval (TOA) from the cooperatve sensng. We frst derve an optmzed recursve Bayesan soluton by adoptng a multple model samplng-based mportance resamplng partcle flter for the development of CSN. It can accommodate nonlnear sgnal model and non-gaussan poston movement under dfferent levels of channel knowledge. We also utlze a Rao-Blackwellzaton partcle flter to splt the orgnal problem by trackng the channel condton wth a grd-based flter and estmatng the poston wth a partcle flter. The CSN wth poston and channel trackng exhbts advantage over the noncooperatve methods by utlzng addtonal cooperatve measurements. It also shows mprovement over the methods wthout channel trackng. Smulaton results valdate that both schemes can take the advantage of cooperatve sensng and channel condton trackng n mxed LOS/NLOS envronments, whch motvates future research of cooperatve gan for navgaton and localzaton n a more general envronment. Index Terms Self-navgaton, cooperatve localzaton, tme-of-arrval (TOA), nonlne-of-sght (NLOS), partcle flter Ç 1 INTRODUCTION WIRELESS postonng technologes for estmatng the poston of moble devces have attracted a lot of attenton over the past decade. Self-navgaton and target trackng are the two man applcatons. In an envronment where GPS coverage s ether weak or blocked, wreless navgaton and localzaton for moble users have varous practcal applcatons. In partcular, there are ncreasng demands for commercal applcatons to utlze devce locaton nformaton wthn system desgns, such as selfnavgaton, target trackng, locaton-based bllng, electronc healthcare, wreless sensor networks (WSNs) [1], [2], and ntellgent robotc or transportaton control management. Wth rsng nterests n locaton-and-stuaton-aware servces, localzaton algorthms wth enhanced precson become crtcal for varous applcatons under potentally challengng crcumstances. For self-navgaton, a moble unt needs to determne ts own coordnate poston based on ts recepton of sgnals from multple rado statons of known postons. These rado statons are known as anchors. In fact, the self-navgaton problem s euvalent to the source localzaton problem whose goal s to estmate source locaton based on sgnals receved by multple sensors [3]. A number of wreless postonng methods have been wdely studed wth varous. P.-H. Tseng s wth the Department of Electronc Engneerng, Natonal Tape Unversty of Technology, 1, Sec. 3, Chung-Hsao East Road, Tape, Tawan E-mal phtseng@ntut.edu.tw.. Z. Dng s wth the Department of Electrcal and Computer Engneerng, Unversty of Calforna, Davs, 2064 Kemper Hall, 1 Shelds Avenue, Davs, CA Emal zdng@ece.ucdavs.edu.. K.-T. Feng s wth the Department of Electrcal and Computer Engneerng, Natonal Chao Tung Unversty, 1001 Ta Hsueh Rd., Hsnchu, Tawan 300. E-mal ktfeng@mal.nctu.edu.tw. Manuscrpt receved 23 July 2011 revsed 17 Apr accepted 30 Nov publshed onlne 4 Jan For nformaton on obtanng reprnts of ths artcle, please send e-mal to tmc@computer.org, and reference IEEECS Log Number TMC Dgtal Obect Identfer no /TMC sgnal measurements. Representatve sgnal models for wreless postonng ncludes dstance measurements [4], tme-of-arrval (TOA) [5], tme dfference-of-arrval (TDOA) [6], angle-of-arrval (AOA) [7], and the receved sgnal strength (RSS) [8]. Because the AOA and RSS measurements can be hghly naccurate under complex ndoor envronment n practce, we focus on the TOA measurement for self-navgaton n ths work. For moble self-navgaton, the moble sensor (MS) unt moves dynamcally. The TOA measurement s made seuentally and the moble state s estmated or updated to facltate locaton estmate for next nstant. We note that the measurement-error (nose) model of the TOA depends on whether the path between a rado anchor and the moble recever s a drect lne-of-sght (LOS) path or nonlne-of-sght (NLOS) path. The NLOS refers to a transmsson path obstructed by structures whch cause substantal bas to the sgnal travel tme/dstance. The NLOS stuatons [9], [10], [11], whch occurs mostly under urban or ndoor envronment, can substantally affect the precson n most locaton estmaton schemes. Tradtonal schemes locate the poston of a moble sensor based on ts receved rado sgnals from the anchors only. Instead, we study the problem of cooperatve navgaton, n whch multple sensors can exchange ther receved sgnals or ther estmated postons to ontly mprove the accuracy of ther ndvdual postons. Despte the lack of accurate poston nformaton at all the sensors, cooperatve navgaton and postonng have been shown to mprove the estmaton results from the perspectve of Fsher nformaton matrx or Cramer-Rao bound [12]. Fg. 1 llustrates the concepts of cooperatve selfnavgaton (CSN) and cooperatve trackng. In CSN, each MS lstens to the sgnal broadcast by the anchors and estmates ts own poston from the downlnk TOA measurement. Each MS exchanges certan belef nformaton wth other MSs for CSN. In partcular, each MS can /14/$31.00 ß 2014 IEEE Publshed by the IEEE CS, CASS, ComSoc, IES, & SPS

2 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 351 Fg. 1. Transmsson and measurement procedure of (a) cooperatve self-navgaton (CSN), and (b) cooperatve trackng. re-estmate ts own poston after recevng sgnals from the anchors and belefs from other MSs. In cooperatve trackng, the archtecture becomes complex, snce the data center needs to collect all measurements to generate a poston estmate. Not only the belef nformaton, but also the cooperatve measurements should be transmtted to the data center. In general, cooperatve self-navgaton keeps low transmsson overhead by only sendng the belef of ts poston. In fact, a known work on cooperatve localzaton usng sum-product algorthm s the so-called SPAWN of [13] whch adopted nonparametrc belef propagaton [14] for nformaton exchange among moble sensors of unknown postons.wymeersch et al. [13] demonstrated superor performance of SPAWN wth a recursve Bayesan estmaton over both the noncooperatve scheme and the cooperatve least-suares scheme. However, the assumpton that ether the channels are known to be LOS or NLOS lmts the practcal applcablty of SPAWN. Specfcally, n a dynamc system, channels would swtch between LOS or NLOS over tme because of MS movement and the other movng obects. Hence, we do not know a pror whether a gven channel s LOS or NLOS at a partcular tme. To model the channel evoluton n tme and space, a Markov model has been proposed n [15]. Several papers deal ths problem by ntroducng an nteractng multple model (IMM) [16], [17], [18]. The IMM method estmates all possble modes n parallel and mxes the estmaton result accordng to mode probablty. Lao and Chen [16], and Chen et al. [17] utlzed the IMM method on the sgnal models, where each dstance measurement conssts two modes ncludng LOS and NLOS. One IMM and two Kalman flters are utlzed to smooth each TOA [16] measurement, thereby leadng to better poston estmate. Chen et al. [17] further proposed an extended Kalmanflter-based IMM to smooth the RSS that combnes wth the TOA va data fuson. Instead of applyng an IMM on each measurement, Frtsche et al. [18] used one IMM on the poston estmate. Assumng that there are total N anchors, there are 2 N modes whch capture all the combnatons of LOS/NLOS condtons, for example, N ¼ 3 wth eght modes contanng flos LOS LOSg flos LOS NLOSg... fnlos NLOS NLOSg. The poston s estmated accordng to LOS/NLOS combnatons n dfferent modes. The ntegraton of poston estmates for dfferent modes enhances the performance at the expense of computatonal complexty. On the other hand, Morell et al. [19] and Ncol et al. [20] consdered a ont channel condton and poston trackng problem based on the hdden Markov model. The grd based [19] and partcle flter [20] methods are employed for the problem. Chen et al. [21] consdered a Rao-Blackwell partcle-flter method by estmatng the channel condton wth partcle flter, and then applyng extended Kalman flter for the poston estmaton. As s clear from the lterature survey, there are a number of researches on the locaton estmaton n mxed LOS/NLOS envronment. Stll, no study based on cooperatve sensng has been nvestgated. Most exstng research works on cooperatve localzaton focus on dscussng whether the uncertanty of MS poston lmts the cooperatve performance. However, t s wellknown that the NLOS nose can degrade the localzaton performance sgnfcantly n all locaton estmaton schemes. Cooperatve localzaton can become neffectve under the exstence of NLOS bas on the dstance measurements. Our work s the frst to nvestgate how cooperatve measurement sensng can mprove self-navgaton n a mxed LOS/NLOS channel condton. The maor contrbuton of ths paper s the dervaton of optmzed recursve Bayesan solutons for CSN from two perspectves. In partcular, we present CSN wth ont poston and channel trackng (named ont CSN), and CSN wth separate poston and channel trackng (named separate CSN). Snce, the channel condton s nondetermnstc, and s obvously non-gaussan, we adopt the use of multple model samplng mportance resamplng (SIR) partcle flter [22], [23] to approxmate the assocated nonlnear and non- Gaussan recursve Bayesan problem, and to develop a ont CSN method for ont poston and channel trackng. On the other hand, the Rao-Blackwellzaton partcle flter [24], [25] has been developed to partton the states nto two sets the poston states and the channel condton states. Thus, the poston states, whch are of key nterest, can be tracked by a SIR partcle flter wth lower number of state estmaton by margnalzng the channel condton. The channel condton states can be analytcally updated by grd-based flter. Though ont estmaton keeps all the nformaton for calculaton, samplng n hgh-dmensonal spaces becomes computatonally cumbersome for partcle flter. Gven lmted number of partcles, the Rao-Blackwellzaton partcle flter can acheve better performance wth reduced number of state estmaton. Our results demonstrate good performance for both schemes under cooperatve localzaton scenaro. Moreover, the separate CSN outperforms the ont CSN especally under the scenaro when channel condtons freuently swtch between LOS and NLOS states. Ths paper conssts of fve sectons. In Secton 2, we descrbe our problem formulaton by presentng our measurement model and a model of channel state transton n self-navgaton. In Secton 3, we propose the ont CSN and the separate CSN for the estmaton of channel condton

3 352 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 and MS s poston. Secton 4 presents numercal smulaton results that are followed by the concluson n Secton 5. 2 PROBLEM FORMULATION 2.1 Problem Descrpton Consder a synchronous network of N transmttng anchors fxed at the known postons. Ther postons are denoted by a set of m-dmensonal vectors a ¼½a 1 a 2...a N Š T, respectvely. Although m ¼ 2 and m ¼ 3 are both possble, wthout loss of generalty, we consder m ¼ 2 n ths manuscrpt. Our goal s to estmate the unknown postons of M MSs at tme nstant t, whch are denoted by a set of m-dmensonal vectors x ¼½x 1 x 2...x other words, based on the known postons of the transmttng anchors, the moble unts wsh to estmate ther postons at dfferent tme nstants. There are typcal movement of sensors between the samplng tme nstants t and t þ 1. When the th anchor broadcasts ts sgnal, the th MS M ŠT.In receves a measurement y. Meanwhle, the MS cooperates wth each other by transmttng ts belef poston to others. Hence, the th MS also receves cooperatve measurement from the th MS to the th MS. We assume that y z and z are orthogonally multplexed possbly n freuency or n code such that the two types of sgnals do not nterfere wth each other s recepton by the th MS. By collectng measurements from tme ndex 1 to t from the anchors to the th MS (.e., y ð1tþ ¼½y ð1tþ 1...y ð1tþ N ŠT ) and the cooperatve measurements from the other mobles to the th MS (.e., z ð1tþ ¼½z ð1tþ 1...z ð1tþ 1 zð1tþ þ1...zð1tþ M ŠT ), the goal s for the th MS to generate an estmate x of ts poston. Consderng that the channel condtons are unknown to the th MS, we can estmate the poston and channel condtons wth the followng two problems. Frst, we estmate the poston by solvng the poston and channel condton ontly, whch corresponds to the followng problem. Problem 1 (Jont Poston and Channel Condton Estmaton Problem). By collectng measurements y ð1tþ from the anchors and cooperatve measurements z ð1tþ from the other mobles, the goal s for the th MS to estmate ts poston x and channel condton ontly for the self-navgaton. On the other hand, we can decouple ths problem nto two subproblems the channel condton estmaton and the poston estmaton problems. Problem 2 (Separate Poston and Channel Condton Estmaton Problem). By collectng measurements y ð1tþ from the anchors and cooperatve measurements z ð1tþ from the other mobles, we estmate the channel condton based on the nformaton of the poston. Gven the estmaton of channel condton along wth the collected measurements, the goal s for the th MS to estmate ts poston x. 2.2 Measurement Model As explaned earler, we focus on the TOA measurement model. For notatonal smplcty, the TOA measurement from the anchor to the MS s multpled by the speed of lght c. Thus, the effectve TOA measurement s y ¼ a x þ s ð1þ where kk denotes the eucldean dstance and s the measurement nose at tme t. Smlarly, the TOA measurement between moble statons are z ¼ x x þ l ð2þ where represents the addtve measurement error/ nose. The dfference between LOS and NLOS models les n the nose dstrbutons. In the paper, both LOS and NLOS stuatons are consdered. Thus, the nose dstrbuton of each lnk can be ether LOS or NLOS dstrbuton. The channel condton s hdden n the measurement. Though we are prmarly nterested n estmatng the poston of the MS, the estmaton of the channel condton s necessary to dentfy dfferent nose dstrbutons. We, therefore, denote the channel state between the th anchor and the th MS as s 2f0 1g and denote the cooperatve channel condton from the th MS to the th MS s as l 2f0 1g. LOS corresponds to state 0, whereas NLOS s denoted by state 1. For the convenence, we denote all the noncooperatve channel states to the th MS as a N-dmensonal vector s ¼½s 1... s N Š.We also denote all the cooperatve channel states to the th MS as a vector of l ¼½l 1...l 1 l þ1...l M Š. 2.3 State Transton Model For a self-navgaton problem, both the poston and the channel condton of the MS change from tme to tme n a perod from tme ndex 1 to T. To model the correlaton of the poston and the channel condton between dfferent tme nstant, a hdden Markov process of order 1 s adopted as the state model. The poston of the th MS s consdered as a Markov process from tme ndex t 1 to t, x ¼ x þ T s v ð3þ where v denotes the m 1 vector of the th MS velocty at tme t. T s represents the samplng nterval. We model 2D (m ¼ 2) MS movement as random walks whch leads to the state euaton n (3) as v ¼ v cos sn T where v s the speed of the MS movement and represents the movng drecton. Meanwhle, the channel condton s modeled as a Markov chan wth the LOS and the NLOS states. The transton probablty s modeled as P l ¼ a l ¼ b ¼ P s ¼ a s ¼ b 8 p 0 a ¼ 0 b ¼ 0 >< 1 p 0 a ¼ 1 b ¼ 0 ð5þ ¼ 1 p 1 a ¼ 0 b ¼ 1 > p 1 a ¼ 1 b ¼ 1 3 PROPOSED COOPERATIVE SELF-NAVIGATION METHOD The proposed cooperatve self-navgaton (CSN) method s frst presented n the optmal recursve Bayesan estmaton representaton n Secton 3.1. Secton 3.2 descrbes how the ð4þ

4 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 353 partcle flter approxmates the probablty densty functon of the Bayesan estmaton n practce and how the MS collects the measurements wth the proposed CSN method. 3.1 Optmal Recursve Bayesan Estmaton Jont Poston and Channel Condton Trackng In the recursve Bayesan estmaton Problem 1, the mportant process s to calculate the ont poston and channel condton posteror dstrbuton, P x s l y ð1tþ z ð1tþ 1 ¼ P y z x s l fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} lkelhood y ð1t 1Þ z ð1t 1Þ P x s l fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} pror where the denomnator acts lke a normalzng constant as ¼ P y ¼ X s z X Z l P x y ð1t 1Þ P y z s l z ð1t 1Þ y ð1t 1Þ x s l z ð1t 1Þ dx The predcton nformaton n (6) can be derved as P x s l y ð1t 1Þ z ð1t 1Þ ¼ X P s s P s y ð1t 1Þ z ð1t 1Þ s fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} noncooperatve channel condton predcton X P l l P l y ð1t 1Þ z ð1t 1Þ l fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Z cooperatve channel condton predcton P x dx P x x y ð1t 1Þ z ð1t 1Þ fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} poston predcton Pðx y ð1t 1Þ z ð1t 1Þ Þ In ths paper, the poston and channel condton are assumed to be ndependent, and the predcton can be performed separately. Euaton (8) can be calculated through the known ntal condton and the known state model n (3) and (5). Note that all lnks ncludng the and the cooperatve measurements z are consdered ndependent. The lkelhood n (6) can be wrtten as noncooperatve measurements y P y z ¼ Y k x P y s k x l s k fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} noncooperatve lkelhood Y P z x l fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} cooperatve lkelhood ð6þ ð7þ ð8þ ð9þ From (6)-(9), the posteror functon n (6) can be rewrtten as P x s l y ð1tþ z ð1tþ ¼ 1 P x y ð1t 1Þ z ð1t 1Þ ½BŠ ½CŠ fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} poston predcton ð10þ where B refers to the terms related to noncooperatve lkelhood and channel condton predcton, and C represents the terms related to cooperatve lkelhood and channel condton predcton. For the noncooperatve term, the TOA measurement s affected by the MS poston and the channel condton,.e., B ¼ Y k X P y s k P s k s k k x s k P s k y ð1t 1Þ z ð1t 1Þ ð11þ For the cooperatve term, the TOA measurement s affected by the source poston (.e., the other MS poston), the MS poston, and the channel condton,.e., C ¼ Y X Z P z l P l l x P l k x l y ð1t 1Þ P x z ð1t 1Þ dx ð12þ The extra ntegraton n (12) s reured for the cooperatve measurement, whch also ncreases the computatonal complexty. Note that the source poston s a known parameter for noncooperatve term n (11). However, for cooperatve term n (12), we can only calculate P ðx Þ through the belef of the th MS based on the measurement from tme 1 to t 1 as P x b x ¼ P x y ð1t 1Þ z ð1t 1Þ ð13þ Therefore, the coordnates of anchors and each moble s belef record are avalable for all moble statons to ontly estmate ther postons. Note that the transmsson of frst belef nformaton exchange s chosen as the pror nformaton as n (13) before the measurement update at tme t. Wth the measured TOA and belef nformaton from cooperatng mobles, each MS can estmate ts own poston accordng to the recorded channel condton. The MS can update the belef to ts posteror nformaton as bðx Þ¼ Pðx y ð1tþ z ð1tþ Þ wth (6)-(12). Followng the belef propagaton concept n [14], the MS refnes ts estmate and broadcasts ts own belef nformaton teratvely to further enhance the ont locaton accuracy Separate Poston and Channel Trackng The estmated states of Problem 1 can be decoupled nto two subsets by factorzng the ont poston and channel condton posteror dstrbuton as P x s l ¼ P s l y ð1tþ x z ð1tþ yð1tþ z ð1tþ P x y ð1tþ z ð1tþ ð14þ Condtoned on the poston x, the channel condton states s and l can be margnalzed and the channel condton s analytcally tractable through a grd-based method. Wth the knowledge of channel dstrbuton, we focus on estmatng the poston dstrbuton P ðx y ð1tþ z ð1tþ Þ to solve Problem 2, whch can reduce the number of state estmaton owng to the decoupled archtecture. The above two strateges are proposed for the CSN, whch are also named as ont CSN (A1) and separate CSN (A2), respectvely, n the rest of ths paper. To clearly llustrate

5 354 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 Fg. 2. A flow chart about the samplng mportance resamplng (SIR) partcle flter. how the recorded channel condton affects the estmate, the followng two strateges are developed to ntegrate channel condton knowledge for cooperatve lnks No Knowledge of Channel Condton In ths case, the orgnal CSN method does not take the channel condton nto account. In other words, there s no nformaton about P ðl l Þ and P ðl z Þ. The lkelhood functon becomes P z X x ¼ P z l x l P l ð15þ Therefore, we can only assume that the LOS or the NLOS happens wth the same probablty Pðl Þ¼ Perfect Knowledge of Channel Condton In ths stuaton, the channel condton s known at every tme nstant,.e., Pðl Þ s a drac delta functon n (15). Note that the knowledge of channel condton can be obtaned through the LOS/NLOS classfcaton. To acheve accurate classfcaton, there s an extra overhead needed for LOS/ NLOS detecton. Ths stuaton can serve as an upper bound for the proposed method. 3.2 Partcle Flter Representaton Fundamental Concepts of Partcle Flter The concept of the partcle flter s to use a set of partcles f½x Š ½s Š ½l Š gn ¼1 assocated wth ts weghtng ½w Š to denote a random measure of the posteror dstrbuton P x XN s l ¼1 s y ð1tþ w x z ð1tþ s l x l ð16þ Here N denotes for the number of partcles, ½x Š represents the th partcle of the th m-dmensonal MS poston x at tme t, and ½s of the noncooperatve lnk condton s Š represents the th partcle receved by the Fg. 3. A flow chart about the partcle flter for CSN. th MS. Furthermore, ½l Š represents the th partcle of the cooperatve lnk condton l receved by the th MS, and ½w Š denotes the mportance weghts assocated to the th partcle. The SIR partcle flter [22], [23] s one of the represented method and s adopted n our method as shown n Fg. 2. Note that the Bayesan recursve estmaton can be classfed as the state update and the measurement update. In the state update stage, the mportance densty of SIR flter s chosen to be the transton pror to draw samples (.e., partcles). Note that there are two lkelhood functons, one for LOS channel and one for NLOS channel condton, respectvely. By substtutng the poston samples nto the lkelhood functon accordng to channel condton samples, the weghts of the correspondng partcles can be obtaned. The assocated weghts are regarded as the approxmatons to the posteror P N ¼1 ½w probabltes of the partcles such that Š ¼ 1. Therefore, for mportance samplng, the mnmum mean suare error estmaton (e.g., poston) can be obtaned from a weghted average as E x y ð1tþ Z z ð1tþ ¼ XN ¼1 P x w y ð1tþ z ð1tþ x x dx ð17þ To overcome the degeneracy problem, whch denotes partcles wth neglgble weghts after teratons, the resamplng of the partcles s necessary. The dea of the resamplng algorthm s to remove the partcles wth small weghts and ncrease the partcles wth large weghts by makng several copes to fll the place of the deleted partcles. Therefore, the weghts would be adusted to 1=N, whch means there s no need to record the weghts for every tme nstant Partcle Flter for Jont Poston and Channel Trackng Fg. 3 and Algorthm 1 llustrate how to update the partcles and the assocated weghts recursvely wth the proposed CSN method for the th MS.

6 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 355 Algorthm 1. Proposed Jont CSN Method for th MS. 1 ntal state ½x ð0þ Š, ½s ð0þ Š, ½l ð0þ Š 8 2 for t ¼ 1 to T do 3 for ¼ 1 to N do 4 mportance samplng x P x x l 5 end for ð0þ, s P l ð0þ P s l 6 broadcast self-belef f½x Quantzaton n Secton 4.3 Šð0Þ ð0þ s, g N ¼1 percent 7 receve noncooperatve measurement y and assocated coordnates a receve cooperatve measurement z belefs f½x Š ð0þ and assocated g N ¼1 ( ¼ 1...þ 1...N) 8 weghts computaton accordng to (18) 9 calculate ½^x Šð0Þ accordng to (20) 10 update self-belef f½x Šð1Þ ½s ½l resampleðf½x Šð0Þ 11 for d ¼ 1 to N d do ½s Šð0Þ ½l 12 broadcast self-belef f½x Quantzaton n Secton 4.3 Šð0Þ Šð1Þ ŠðdÞ ½w Šð1Þ g N ¼1 ¼ Šð0Þ g N ¼1 Þ g N ¼1 percent 13 receve belefs from other MSs f½x Š ðdþ 1...þ 1...N) 14 weghts computaton accordng to (18) 15 calculate ½^x ŠðdÞ accordng to (20) 16 update self-belef f½x Šðdþ1Þ ½l Šðdþ1Þ g N ¼1 ¼ resampleðf½x ½l ŠðdÞ ½w ŠðdÞ g N ¼1 Þ ½s Šðdþ1Þ ŠðdÞ 17 end for 18 update estmaton at tme t ^x ¼½^x ^s ¼½^s ŠðNdÞ ^l ¼½^l ŠðNdÞ n (20) 19 for ¼ 1 to N do 20 update partcles ½x ½s Š ¼½s 21 end for 22 end for ŠðN dþ1þ ½l ½s ŠðdÞ ŠðNdÞ Š ¼½x ŠðN dþ1þ Š ¼½l ŠðN dþ1þ g N ¼1 ð ¼ We assume pror knowledge (or estmate) on the startng poston and channel condton P ðx ð0þ Þ, P ðs ð0þ Þ, and P ðl ð0þ Þ and draw partcles ð0þ x s ð0þ l ð0þ N ¼1 accordngly. At every sample tme t, the SIR partcle flter draws the mportant densty usng the transton pror,.e., x P x x s P s s and ½l Š Pðl ½l Š Þ8. The noncooperatve source broadcasts ts coordnates. At the same tme, the cooperatve nodes transmt ther poston belefs wth the partcle representaton f½x Šð0Þ g N ¼1 n parallel. Both the noncooperatve and cooperatve channel condtons are only recorded by local MS. After the MS receves the noncooperatve measurements, the anchors coordnates, the cooperatve measurements, and the partcles from the cooperatve nodes, we can then calculate the weghts as ~w / P y z ¼ Y k P y k x x s l s Y k P z x l ð18þ where the weghts should be normalzed by ½w Š ¼ ½ ~w Š =N ¼1 ½ ~w Š. Note that for the cooperatve measurements, the partcle flter expresson can be further derved as P z x l ¼ XN p¼1 P z x x ðdþ p l ðdþ w p ð19þ Therefore, the mnmum mean-suare error estmate can be generated va ^x ¼ N ¼1 w x ð20þ The channel condton partcles are mantaned as the probablty that the correspondng lnk was n LOS or NLOS. The systematc resamplng algorthm [26] s performed to adust the partcles nto an eual weght set. Snce there s uncertanty about the coordnates of the moble unts, teratve calculaton among cooperatve mobles s adopted. We let cooperatve MS transmt ts belef N d tmes between the tme t to t þ 1. ½x ŠðdÞ denotes the th partcles of the th MS poston calculated at the dth teraton whch happens between tme nstants t and t þ 1. For notatonal convenence, ½Š ðdþ represents the th partcle of the unknown varable at the dth teraton. To estmate the poston of the th MS, we have to obtan f½x Š ðdþ ½w Š ðdþ g from the th cooperatve moble unt n advance accordng to (19). However, we can only sample from each MS s pror nformaton ½x Š ð0þ Pðx ½x Š Þ to calculate the ntal estmaton at tme nstant t. Note that ths ntal estmaton s essental for cooperatve localzaton. Though the pror belef s exchanged once, the opertaton s defned as the teraton number N d ¼ 0. After the ntal estmaton s calculated, we can obtan the posteror ½x Š ð1þ after resamplng to obtan a more accurate result over the pror belef. As shown n (19), the posteror belef can be exchanged. Thus, teratve belef refnement wll be reured for the cooperatve par to obtan a more accurate result. In each teraton, the MS frst broadcasts ts own belef. After recevng the others belefs, the whole measurement process s performed to update ts belef. Before the noncooperatve source broadcasts the sgnal at next tme t þ 1, the cooperatve MS can exchange ther updated belef, recalculate the ½w the estmaton. ŠðdÞ and resamplng teratvely to refne Partcle Flter for Separate Poston and Channel Trackng The basc structures of both ont and separate poston and channel trackng are smlar, except for n separate CSN only the poston states estmaton follows the procedure as shown n Fg. 3 and Algorthm 1. The channel states

7 356 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 correspondng to each poston partcle are analytcally tractable by the grd-based method. After the factorzaton n (14), we track the poston state wth a SIR partcle flter, P x y ð1tþ z ð1tþ X N ¼1 w x whch allows us to derve channel condton as P s l y ð1tþ z ð1tþ XN ¼1 w P s l x yð1tþ x ð21þ z ð1tþ ð22þ To reduce the samplng complexty, the proposal dstrbuton for the poston trackng s adopted as the transton pror as ½x Š p P ðx ½x Š p Þ. Therefore, the weghts n (21) can update accordng to ~w / ~w P y z x s l ð23þ At tme nstant t, the condtonal probablty of the channel condton P ðs l x yð1tþ z ð1tþ Þ can be estmated by the grd-based method. The predcton and update euatons of the grd-based method are lsted as follows 8 < P ½s Š x P yð1tþ 1 p¼0 m s s P l x P zð1tþ 1 p¼0 f l l 8 < P s P ½l Š where 8 < ðtt 1Þ m ðtt 1Þ f y ð1t 1Þ P 1 ðtt 1Þ p¼0 m z ð1t 1Þ P 1 ðtt 1Þ p¼0 f ¼ 4 P 1 p¼0 m ¼ 4 P 1 p¼0 f The notatons ½m Š s l P s P l s l s l and ½f Š represent the weghts for the posteror probablty of channel condtons up to tme t of state p for noncooperatve and cooperatve lnks, respectvely, wth the th poston partcle. Note that the channel state s condtoned on the poston state, and the channel condton can be updated by usng the grd-based method va m ¼ 4 f ¼ 4 P 1 p¼0 m ðtt 1Þ P 1 p¼0 m ðtt 1Þ f ðtt 1Þ f ðtt 1Þ P y P z P y P z x x s x l x s l From the channel states estmaton of the grd-based method, the weghts n (23) for the poston states estmaton are further derved as P y z ¼ X1 p¼0 X1 p 0 ¼0 x P y P z s x x s l l ðp 0 Þ ðtt 1Þ m ðtt 1Þ ðp f 0 Þ ð24þ Note that the weghts n (23) should be normalzed by ½w Š ¼½~w Š =N ¼1 ½ ~w Š. The poston estmaton s generated based on the weghts as n (20). 4 SIMULATIONS AND RESULTS In ths secton, we provde several examples to llustrate the performance and effectveness of the proposed cooperatve navgaton strateges. We name the proposed cooperatve navgaton method as CSN. We wll test the four dfferent strateges (A1), (A2), (A3), and (A4) descrbed n Secton 3.1 to deal wth channel condtons. In addton, as a comparson, we also test the JMS-PF gven by [20] as the noncooperatve self-navgaton method n conuncton wth ont channel condton estmaton. We set N ¼ 500 partcles and teraton number N d ¼ 0. Recall that zero teraton number represents only predcton nformaton exchanged between the MSs, where the noncooperatve and cooperatve measurements update once per samplng nterval. We wll further examne the teratve refnement effect n Example 4. We consder a random ntalzaton n our smulaton examples. In Examples 1 and 2, we set up the network area sze as 50 m 50 m, whle the area sze s chosen as 100 m 100 m n Examples 3-7. In all examples, we partton the area of consderaton nto grds of 5m5m. At the start t ¼ 0, we assume to know whch grd the MSs are, but not ther exact postons. Thus, we draw ntal poston partcles unformly wthn the grd. We assume to know channel condtons wthn a 90 percent confdence nterval,.e., Pðs ð0þ Þ¼Pðl ð0þ Þ¼09, where we draw partcles unformly wth 90 percent of channel condton partcles n the true channel state. We wll further examne the mperfect knowledge of ntal poston and channel condton n Examples 5 and 6. The samplng nterval s chosen as T s ¼ 1 second. We model MS movement as random walks n the smulatons by assumng to know the speed of the MS movement based on a pedometer but not ts drecton. The velocty v n (4) s sampled from a truncated Gaussan dstrbuton v Nð0 1Þ over nterval 0 v 1 to smulate random walk behavor, but wth known value. The movng drecton s assumed unknown and s unformly dstrbuted wth U½0 2Þ. Therefore, the partcles of MS poston are unformly generated on the crcle centered at x wth known radus of v. We adopt the measurement model from [13], whch was establshed by performng round-trp TOA dstance estmaton wth commercal UWB rados. Note that for notatonal smplcty ths round-trp TOA measurement s multpled by the speed of lght c. Ths round-trp TOA model s a Gaussan dstrbuton P ðy s ÞNð 2 Þ based on the true dstance d ¼ka x k. The mean and varance of the

8 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 357 Gaussan dstrbuton accordng to the sght condton are parameterzed n the form of d 2 þ d þ whch are lsted n Table 1. Note that P ðz l Þ also possesses the same dstrbuton as P ðy Þ though t depends on the s true dstance between x and x,.e., d ¼kx x k. We use the outage probablty of the MS poston error [13] as the performance measure. In other words, we calculate the average probablty that the MS poston error exceeds a threshold e th P outðe th Þ¼ XP X M ¼1 ¼1 I x ^x >eth =ðm PÞ ð25þ where IðÞ denotes the ndcator functon. Note that the outage probablty averages over M mobles n P trals. At the same tme, we also adopt the root mean suare error (RMSE) to assess the performance of proposed strateges as RMSE ¼ TABLE 1 TOA Measurement Model [13] " # XP X M 1=2 2 =ðm P Þ ð26þ ¼1 ¼1 x ^x Each smulaton example lasts T ¼ 20 s. 4.1 Fxed Number of Noncooperatve Measurements In ths secton, we place three anchors as the fxed noncooperatve nodes n a 2D network topology at a 1 ¼ ½5 50Š, a 2 ¼½50 50Š, and a 3 ¼½50 5Š. Four mobles are located at x 1 ¼½20 25Š, x 2 ¼½25 20Š, x 3 ¼½25 30Š, and x 4 ¼½30 25Š. The number of smulaton trals s P ¼ The noncooperatve channel condton are nvestgated n two cases followng a Markov chan accordng to (5) wth p 0 ¼ p 1 ¼ 09 and p 0 ¼ p 1 ¼ 05. Note that the state transton p 0 ¼ p 1 ¼ 09 s more sutable to descrbe the channel varaton n the WSN case [15], whle p 0 ¼ p 1 ¼ 05 s also tested for performance comparson. Thus, we focus on the dscusson about the p 0 ¼ p 1 ¼ 09 case n the smulaton secton. On the other hand, the cooperatve channel condton s modeled as LOS throughout the smulaton perod. Recall that the LOS/ NLOS settng n the smulaton s to examne how LOS cooperatve measurements can provde assstance n the cooperatve localzaton problem. Example 1 (1 Noncooperatve Measurement). In ths example, each MS only receves one noncooperatve measurement from the anchor whch s nsuffcent measurement n tradtonal localzaton problem. The number of cooperatve measurements for the MSs are selected as one, two, and three n the smulatons, respectvely, and are labeled as 1MS, 2MSs, and 3MSs. At t ¼ 20, Fgs. 4 and 5, respectvely, llustrate the outage probablty and the RMSE of the JMS-PF, CSN wth 1MS, CSN wth 2MSs, and CSN wth 3MSs based on four dfferent strateges (A1), (A2), (A3), and (A4). Note that the outage probablty ncreases wth tme owng to the random walk by the MS and the transton of channel condtons between LOS and NLOS. We observe that snce strategy (A3) has no knowledge on the channel state, t results n the worst performance gven the same number of cooperatve measurements. The reason s that wthout the knowledge of channel state, we can only assume that LOS or NLOS occurs wth 1/2 probablty. Therefore, method (A3) can provde as an upper bound of the outage probablty for the proposed schemes (A1) and (A2). On the other hand, strategy (A4) s based on known channel, thereby provdng a lower bound for the performance of (A1) and (A2). Our proposed method, ether ont or separate poston and channel estmaton scheme, s a compromse between accurate poston estmate and channel state estmate. Fg. 4. Performance of the locaton estmaton n terms of outage probablty for Example 1.

9 358 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 Fg. 5. Performance of the locaton estmaton n terms of RMSE for Example 1 wth strateges (A1), (A2), (A3), and (A4). The smulaton results llustrate lttle dfference among the three strateges of the JMS-PF scheme. The reason s that a sngle noncooperatve measurement s suffcent for estmatng moble postons even wth the avalable channel state nformaton. On the other hand, ont and separate CSN schemes can provde addtonal channel nformaton whch effectvely reduce the RMSE of the MS. For example, as shown n Fg. 5a, strategy (A1) of the proposed CSN 3MS scheme can reduce the RMSE by about 22 m versus that of strategy (A3). Furthermore, there s a crossover between the JMS-PF and the CSN 1MS schemes as observed from Fg. 4a, whch ndcates that the CSN 1MS scheme leads to hgher outage probablty under larger MS s poston error. The reason s that the belef exchange among mobles on estmated poston can become neffcent n cases when the estmates are poor. Wth the ncreasng number of cooperatve measurements, the dversty of measurement nputs can lower the effect of poor MS locaton estmaton. As llustrated n Fg. 4, compared to other schemes, CSN 3MS acheves better outage performance especally under larger MS s poston error. Smlar results can be observed from the RMSE performance of Fg. 5a. The proposed CSN 3MS scheme n (A1) can provde around 29 m lower RMSE compared to JMS-PF. For the case of p 0 ¼ p 1 ¼ 09 when the state varaton s smaller, the ont CSN scheme n (A1) outperforms separate CSN scheme n (A2). As shown n Fg. 5a, CSN 1MS scheme n (A1) can provde around 05 m lower RMSE compared to CSN 1MS scheme n (A2). The separate CSN scheme n (A2) performs better when the state transton s hgher (p 0 ¼ p 1 ¼ 05). As shown n Fg. 5b, CSN 1MS scheme n (A2) can provde around 04 m lower RMSE compared to CSN 1MS scheme n (A1). The performance dfference between the ont and separate CSN wll be further dscussed n Example 7. Example 2 (2 Noncooperatve Measurements). In ths case, each MS receves measurement from two anchors. The number of cooperatve moble sgnals s 1 and 2, respectvely, denoted as 1MS and 2MS n Fg. 6. Under known channel condton, the performance dfference between the noncooperatve and cooperatve cases are nsgnfcant n ths example compared to that n Fg. 6. Performance of the locaton estmaton n terms of outage probablty for Example 2.

10 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 359 Fg. 7. Performance of the locaton estmaton n terms of RMSE for Example 2 wth strateges (A1), (A2), (A3), and (A4). Example 1. Ths s because the extra noncooperatve measurement n ths example can provde addtonal nformaton for estmatng moble locatons. As shown n Fg. 7, smlar RMSE performance s obtaned for strategy (A4) n all three schemes whle sgnfcant performance dfference s acured n the schemes wth strategy (A1) or (A2). The proposed CSN scheme can stll provder better performance compared to the JMS-PF method, for example, the CSN 2MSs (A1) case wll provde around 05 mless n RMSE n comparson wth the JMS-PF scheme as n Fg. 7a. By comparng Fgs. 5a and 7a, we can observe that the separate CSN (A2) starts to outperform the ont CSN (A1) when the number of sgnal sources ncreases. 4.2 A Sensor Network Scenaro Example 3. In ths example, a sensor network topology s confned n a 100 m 100 m space as shown n Fg. 8. There are 13 fxed anchors randomly dstrbuted wth known poston and 50 dynamcally movng mobles durng the smulaton perod. The transmsson ranges for all the anchors and mobles are lmted to 20 m. For ths topology, dstrbutons of the average avalable number of noncooperatve and cooperatve measurements for the 50 mobles are shown, respectvely, n top and bottom plots of Fg. 9. Note that both the noncooperatve and the cooperatve measurements can be LOS or NLOS accordng to the Markov model. All other condtons reman the same as n prevous examples. As shown n Fgs. 10 and 11, the proposed CSN can acheve lower outage probablty and smaller RMSE n comparson wth JMS-PF. For example, compared to JMS-PF, the CSN (A1) reduces outage probablty by 0.32 for e th ¼ 3mn Fg. 10a and lowers the RMSE by 35 mn Fg. 11. From Fg. 10a, we can conclude that the CSN results n substantal mprovement over the noncooperatve scheme n sensor networks. As ndcated n Example 1, the cooperatve scheme provdes mprovement over the nsuffcent measurement case. Even wth the possblty of NLOS cooperatve measurements n ths example, both ont and separate CSN schemes can stll provde effectve channel trackng, resultng n better locaton estmaton performance. Example 4. In ths example, we study the number of teratons of belef propagaton wthn each samplng Fg. 8. Network topology of Example 3 red suares represent the postons of the anchor green crcles represent the postons of the MS. Fg. 9. The dstrbutons for the average avalable numbers of noncooperatve and cooperatve measurements for the 50 MSs n Example 3.

11 360 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 Fg. 10. Performance of the locaton estmaton n terms of outage probablty for Example 3. Fg. 11. Performance of the locaton estmaton n terms of RMSE for Example 3 wth strateges (A1), (A2), (A3), and (A4). nterval. Here, we lmt some of the random terms by consderng t ¼ 1 to clearly llustrate the effect of belef propagaton. Frst, the JMS-PF (A1) represents the noncooperatve scheme, where no belef propagaton takes places. The N d ¼ 0 case actually propagates the belef once, whch s obtaned from the pror nformaton of source. The N d ¼ 1 case represents the stuaton that the posteror belef s obtaned for each MS. For N d > 1, the teratve belef propagaton s regarded as the belef refnement, whch shows small mpact on the localzaton performance. The belef propagaton effect s sgnfcant for both CSN (A1) and CSN (A2) at teraton N d ¼ 0, where the pror belef propagaton and at N d ¼ 1, where the posteror belef propagaton takes place. In Table 2, the mprovement acheved by gong TABLE 2 Iteratve Belef Propagaton Impact for Example 4 [RMSE ð1þ (m)] from zero to one teratve refnement s obvous. However, further ncrease of teraton number does not appear to substantally mprove the performance over N d ¼ 1. Thus, one or two teratons would typcally be suffcent. Example 5. We test the effect of ntal poston n ths example. The test scenaro n Example 3 s reconsdered, except for changes of ntal poston. In Table 3, we assgn the ntal partcles as the true MS s poston n the deal case, for example, ½x ð0þ Š ¼ ðx ð0þ Þ8. We draw ntal partcles unformly wth a larger grd n a 10 m 10 m layout partton. As expected, the RMSE error ncreases for the noncooperatve and cooperatve case as the ntal estmaton error ncreases. TABLE 3 Intal Poston Impact for Example 5 [RMSE ð20þ (m)]

12 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 361 TABLE 4 Intal Channel Condton Impact for Example 6 [RMSE ð20þ (m)] TABLE 5 State Transton Model Impact for Example 7 [RMSE ð20þ (m)] Example 6. In ths example, we test the mpact of ntal channel condton. The test scenaro n Example 3 s retested, except for the change of ntal channel condton. In Table 4, we assgn the ntal partcles as the true MS s poston n the perfect case, for example, ½s ð0þ Š ¼ ðs ð0þ Þ8. The RMSE error ncreases for the noncooperatve and cooperatve case as the channel condton error ncreases. Example 7. The test scenaro n Example 3 s retested, except for the state transton probablty. The transton probablty parameters p 0 and p 1 are chosen from 0.5 to 0.9 and the results are summarzed n Table 5. Note that the ont CSN (A1) track both the poston and channel ontly. Samplng n hgher dmenson causes degeneraton for the partcle flter, especally wth lmted number of partcles. For example, wth the state transton probablty euals to 50 percent, only 50 percent of poston partcles are useful for the ont CSN (A1). The performance of hgher channel state varaton wll be worse than that of smaller varaton for ont CSN (A1). On the other hand, opposte performance trend s observed for separate CSN (A2) scheme. The separate CSN (A2) can adapt to hgher channel state varaton due to ts separate estmaton archtecture. 4.3 Sgnalng of Cooperatve Navgaton Recall that cooperatve navgaton reures addtonal nformaton exchange among mobles by lettng mobles broadcast ther belefs. Unlke the case nvolvng only anchored nodes, MS moves and should broadcast ts belef to other mobles n each tme nstant. Ths sgnalng reures communcaton overhead. To lower the reured bandwdth for belef broadcastng, we assume n ths secton that the moble belefs are uantzed nto fnte bts before broadcastng. Ths s ncorporated nto Algorthm 1. To demonstrate the effect of such uantzaton on moble navgaton, the test scenaro n Example 3 s reconsdered usng uantzed belefs. Note that there s no belef propagaton, and hence no uantzaton error for the noncooperatve JMS-PF scheme. On the other hand, the full CSN algorthm broadcasts the full belef message wthout uantzaton, hence usng nfnte bandwdth. Quantzng the poston partcles results n the uantzaton error whch degrades the performance of the proposed CSN scheme. But uantzaton of belefs wll be better than no belef exchange at all. Thus, the RMSE results of CSN and JMS schemes wth strateges (A1) and (A2) n Example 3 are provded n Table 6 as benchmarks for the uantzed CSN performance. In Example 3, the x- and y-coordnates le n ½0 100Š. We adopt the measure of relatve resoluton for a fxed-sze layout to nvestgate the tradeoff between bandwdth reurement and estmaton accuracy. Therefore, the uantzed unt for the number of uantzed bts Q s chosen accordng to the sze of grd partton as ¼ 100=2 Q, for example, the uantzaton unt s ¼ 039 for Q ¼ 8. The uantzaton s performed by roundng, whch causes the uantzaton error to be unformly dstrbuted. Thus, pffffffffffffffffffffff the uantzaton error has standard devaton of 2 =12 ¼ for Q ¼ 8. The communcaton overhead (T o ) s calculated accordng to the number of poston partcles and ther uantzed bts transmtted per second as T o ¼ N m Q ðn d þ 1Þ, for example, the communcaton overhead for a 2D poston vector wth 500 partcles for Q ¼ 8 s T o ¼ ¼ 16 kbps. As shown n Table 6, cooperatve estmaton s better than the noncooperatve (JMS) scheme when more than 5 uantzaton bts are assgned. In fact, the performance of CSN wth strateges (A1) and (A2) gven Q ¼ 8 uantzaton bts can acheve the nearly dentcal performance to the nonuantzaton result. Accordng to [27], IEEE can be supported data rate up to 250 kbps. If Q ¼ 8, a small communcaton overhead of 16 kbps s feasble even for low rate sensor networks. Ths example reaffrms the practcalty of the proposed cooperatve navgaton under lmted sensor node bandwdth. 5 CONCLUSION In ths work, we nvestgate the problem of CSN n a mxed LOS/NLOS envronment. We develop a method for CSN for a team of moble unts. We frst propose to apply multple model SIR partcle flter for ont estmaton of moble poston and ther channel condtons. We then apply Rao-Blackwellzaton technues to track the poston TABLE 6 Communcaton Overhead for Quantzed Belef Sharng and Estmaton Accuracy for Secton 4.3

13 362 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 2, FEBRUARY 2014 wth the SIR partcle flter and the channel condton wth the grd-based flter. We show the mportance of channel condton trackng n a mxed LOS/NLOS envronment for cooperatve self-navgaton. Our results demonstrate the sgnfcant performance advantage of CSN over noncooperatve methods, especally n envronment where LOS cooperatve measurement can complement NLOS noncooperatve measurements. Wthout a complex LOS/NLOS dentfcaton algorthm, our proposed schemes can provde feasble locaton estmaton performance for moble sensors n a hghly dynamc sensor network scenaro. ACKNOWLEDGMENTS Ths work was n part funded by NSC E , NSC E , Amng for the Top Unversty and Elte Research Center Development Plan, the Meda- Tek research center at Natonal Chao Tung Unversty, and the Telecommuncaton Laboratores at Chunghwa Telecom Co. Ltd, Tawan. Ths materal s also based on works by Z. Dng supported n part by the Natonal Scence Foundaton Awards and REFERENCES [1] N. Patwar, J.N. Ash, S. Kyperountas, A.O. Hero III, R.L. Moses, and N.S. Correal, Locatng the Nodes Cooperatve Localzaton n Wreless Sensor Networks, IEEE Sgnal Processng Magazne, vol. 22, no. 4, pp , July [2] S. Gezc, Z. Tan, G.B. Gannaks, H. Kobayash, A.F. Molsch, H.V. Poor, and Z. Sahnoglu, Localzaton va Ultra-Wdeband Rados A Look at Postonng Aspects for Future Sensor Networks, IEEE Sgnal Processng Magazne, vol. 22, no. 4, pp , July [3] A. Sayed, A. Targhat, and N. Khaehnour, Network-Based Wreless Locaton Challenges Faced n Developng Technues for Accurate Wreless Locaton Informaton, IEEE Sgnal Processng Magazne, vol. 22, no. 4, pp , July [4] C. Wang and L. Xao, Sensor Localzaton under Lmted Measurement Capabltes, IEEE Network, vol. 21, no. 3, pp , May/June [5] J.-Y. Lee and R. Scholtz, Rangng n a Dense Multpath Envronment Usng an UWB Rado Lnk, IEEE J. Selected Areas Comm., vol. 20, no. 9, pp , Dec [6] E. Xu, Z. Dng, and S. Dasgupta, Reduced Complexty Semdefnte Relaxaton Algorthms for Source Localzaton Based on Tme Dfference of Arrval, IEEE Trans. Moble Computng, vol. 10, no. 9, pp , Sept [7] D. Nculescu and B. Nath, Ad Hoc Postonng System (APS) Usng AOA, Proc. IEEE INFOCOM, vol. 3, pp , [8] C. Meng, Z. Dng, and S. Dasgupta, A Semdefnte Programmng Approach to Source Localzaton n Wreless Sensor Networks, IEEE Sgnal Processng Letters, vol. 15, pp , [9] E. Xu, Z. Dng, and S. Dasgupta, Target Trackng and Moble Sensor Navgaton n Wreless Sensor Networks, IEEE Trans. Moble Computng, vol. 12, no. 1, pp , Jan [10] P.-H. Tseng, K.-T. Feng, Y.-C. Ln, and C.-L. Chen, Wreless Locaton Trackng Algorthms for Envronments wth Insuffcent Sgnal Sources, IEEE Trans. Moble Computng, vol. 8, no. 12, pp , Dec [11] P.-H. Tseng and K.-T. Feng, Geometry-Asssted Localzaton Algorthms for Wreless Networks, IEEE Trans. Moble Computng, vol. 12, no. 4, pp , Apr [12] Y. Shen, H. Wymeersch, and M.Z. Wn, Fundamental Lmts of Wdeband Localzaton Part II Cooperatve Networks, IEEE Trans. Informaton Theory, vol. 56, no. 10, pp , Oct [13] H. Wymeersch, J. Len, and M.Z. Wn, Cooperatve Localzaton n Wreless Networks, Proc. IEEE, vol. 97, no. 2, pp , Feb [14] A.T. Ihler, J.W. Fsher III, R.L. Moses, and A.S. Wllsky, Nonparametrc Belef Propagaton for Self-Localzaton of Sensor Networks, IEEE J. Selected Areas Comm., vol. 23, no. 4, pp , Apr [15] M. Hedar and K. Pahlavan, Markov Model for Dynamc Behavor of Rangng Errors n Indoor Geolocaton Systems, IEEE Comm. Letters, vol. 11, no. 12, pp , Dec [16] J.-F. Lao and B.-S. Chen, Robust Moble Locaton Estmator wth NLOS Mtgaton Usng Interactng Multple Model Algorthm, IEEE Trans. Wreless Comm., vol. 5, no. 11, pp , Nov [17] B.-S. Chen, C.-Y. Yang, F.-K. Lao, and J.-F. Lao, Moble Locaton Estmator n a Rough Wreless Envronment Usng Extended Kalman-Based IMM and Data Fuson, IEEE Trans. Vehcular Technology, vol. 58, no. 3, pp , Mar [18] C. Frtsche, U. Hammes, A. Klen, and A.M. Zoubr, Robust Moble Termnal Trackng n NLOS Envronments Usng Interactng Multple Model Algorthm, IEEE Int l Conf. Acoustcs, Speech, and Sgnal Processng (ICASSP 09), pp , Apr [19] C. Morell, M. Ncol, V. Rampa, and U. Spagnoln, Hdden Markov Models for Rado Localzaton n Mxed LOS/NLOS Condtons, IEEE Trans. Sgnal Processng, vol. 55, no. 4, pp , Apr [20] M. Ncol, C. Morell, and V. Rampa, A Jump Markov Partcle Flter for Localzaton of Movng Termnals n Multpath Indoor Scenaros, IEEE Trans. Sgnal Processng, vol. 56, no. 8, pp , Aug [21] L. Chen, S. Al-Lytty, R. Pch, and L. Wu, Moble Trackng n Mxed Lne-of-Sght/Non-Lne-of-Sght Condtons Algorthm and Theoretcal Lower Bound, Wreless Personal Comm., vol. 65, no. 4, pp , [22] M.S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, A Tutoral on Partcle Flters for Onlne Nonlnear/Non-Gaussan Bayesan Trackng, IEEE Trans. Sgnal Processng, vol. 50, no. 2, pp , Feb [23] S. McGnnty and G. Irwn, Multple Model Bootstrap Flter for Maneuverng Target Trackng, IEEE Trans. Aerospace Electronc Systems, vol. 36, no. 3, pp , July [24] A. Doucet, N.D. Fretas, K.P. Murphy, and S.J. Russell, Rao- Blackwellsed Partcle Flterng for Dynamc Bayesan Networks, Proc. 16th Conf. Uncertanty n Artfcal Intellgence (UAI 00), pp , 2000, [25] T. Schon, F. Gustafsson, and P.-J. Nordlund, Margnalzed Partcle Flters for Mxed Lnear/Nonlnear State-Space Models, IEEE Trans. Sgnal Processng, vol. 53, no. 7, pp , July [26] G. Ktagawa, Monte Carlo Flter and Smoother for Non-Gaussan Nonlnear State Space Models, J. Computatonal and Graphcal Statstcs, vol. 5, no. 1, pp. 1-25, [27] LAN/MAN Standards Commttee of the IEEE CS, IEEE Standard for Part 15.4 Wreless Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons for Low Rate Wreless Personal Area Networks (LR-WPANs), IEEE, Po-Hsuan Tseng receved the BS and PhD degrees n communcaton engneerng from the Natonal Chao Tung Unversty, Hsnchu, Tawan, n 2005 and 2011, respectvely. Snce August 2012, he has been an assstant professor n the Department of Electronc Engneerng and Graduate Insttute of Computer and Communcaton Engneerng, Natonal Tape Unversty of Technology, Tawan. From January 2010 to October 2010, he was a vstng researcher at the Unversty of Calforna at Davs. Hs research nterests nclude sgnal processng for networkng and communcatons, ncludng locaton estmaton and trackng, cooperatve localzaton, and moble broadband wreless access system desgn. He s a member of the IEEE.

14 TSENG ET AL. COOPERATIVE SELF-NAVIGATION IN A MIXED LOS AND NLOS ENVIRONMENT 363 Zh Dng receved the PhD degree n electrcal engneerng from Cornell Unversty n He s the Chld Famly Endowed professor of engneerng and entrepreneurshp at the Unversty of Calforna, Davs. He also holds a ont appontment as a thousand-talent professorshp at Southeast Unversty, Nanng, Chna. From 1990 to 2000, he was a faculty member of Auburn Unversty, Alabama, and later, the Unversty of Iowa, Des Mones. He has held vstng postons at the Australan Natonal Unversty, the Hong Kong Unversty of Scence and Technology, the NASA Lews Research Center, and the US Ar Force Wrght Laboratory. He has actve collaboraton wth researchers from several countres ncludng Australa, Chna, Japan, Canada, Tawan, Korea, Sngapore, and Hong Kong. He was an assocate edtor for the IEEE Transactons on Sgnal Processng from 1994 to 1997 and 2001 to 2004, and an assocate edtor of IEEE Sgnal Processng Letters 2002 to He was the techncal program char of the 2006 IEEE GlobeCom. He s also an IEEE dstngushed lecturer (Crcuts and Systems Socety, 2004 to 2006 Communcatons Socety, 2008 to 2009). He s a coauthor of Modern Dgtal and Analog Communcaton Systems, fourth edton, Oxford Unversty Press, He was a member of the Techncal Commttee on Statstcal Sgnal and Array Processng and a member of the Techncal Commttee on Sgnal Processng for Communcatons from 1994 to He s a fellow of the IEEE and has been an actve member of the IEEE, servng on techncal programs of several workshops and conferences. Ka-Ten Feng receved the BS degree from the Natonal Tawan Unversty, Tape, n 1992, the MS degree from the Unversty of Mchgan, Ann Arbor, n 1996, and the PhD degree from the Unversty of Calforna, Berkeley, n Between 2000 and 2003, he was an n-vehcle development manager/senor technologst wth OnStar Corporaton, a subsdary of General Motors Corporaton, where he worked on the desgn of future telematcs platforms and nvehcle networks. Snce August 2011, he has been a full professor wth the Department of Electrcal and Computer Engneerng, Natonal Chao Tung Unversty (NCTU), Hsnchu, Tawan, where he was an assocate professor and assstant professor from August 2007 to July 2011 and from February 2003 to July 2007, respectvely. From July 2009 to March 2010, he was a vstng scholar wth the Department of Electrcal and Computer Engneerng, Unversty of Calforna at Davs. Snce October 2011, he has been servng as the drector of the Dgtal Content Producton Center at the same unversty. Hs current research nterests nclude broadband wreless networks, cooperatve and cogntve networks, smartphone and embedded system desgns, wreless locaton technologes, and ntellgent transportaton systems. He receved the Best Paper Award from the Sprng 2006 IEEE Vehcular Technology Conference, whch ranked hs paper frst among the 615 accepted papers. He also receved the Outstandng Youth Electrcal Engneer Award n 2007 from the Chnese Insttute of Electrcal Engneerng and the Dstngushed Researcher Award from NCTU n 2008, 2010, and He has served on the techncal program commttees of several conferences. He s a member of the IEEE and the IEEE Computer Socety.. For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at