1756 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY Silent Positioning in Underwater Acoustic Sensor Networks

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1 1756 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO., MAY 008 Slent Postonng n Underwater Acoustc Sensor Networks Xuzhen Cheng, Member, IEEE, Hanng Shu, Student Member, IEEE, Qlan Lang, Senor Member, IEEE, and Davd Hung-Chang Du, Fellow, IEEE Abstract In ths paper, we present a slent postonng scheme termed UPS for underwater acoustc sensor networks. UPS reles on the tme dfference of arrvals locally measured at a sensor to detect range dfferences from the sensor to four anchor nodes. These range dfferences are averaged over multple beacon ntervals before they are combned to estmate the -D sensor locaton through trlateraton. UPS requres no tme synchronzaton and provdes locaton prvacy at underwater vehcles/sensors whose locatons need to be determned. To study the performance of UPS, we model the underwater acoustc channel as a modfed ultrawdeband Saleh Valenzuela model: The arrval of each path cluster and the paths wthn each cluster follow double Posson dstrbutons, and the multpath channel gan follows a Rcan dstrbuton. Based on ths channel model, we perform both theoretcal analyss and smulaton study on the poston error of UPS under acoustc fadng channels. The obtaned results ndcate that UPS s an effectve scheme for underwater vehcle/sensor self-postonng. Index Terms Localzaton, navgaton, UnderWater Acoustc Sensor Networks UWA-SNs), underwater Global Postonng System GPS), underwater postonng, ultrawdeband UWB) Saleh Valenzuela S-V) model. I. INTRODUCTION UNDERWATER Acoustc Sensor Networks UWA-SNs) consst of a varable number of sensors and vehcles the unmanned underwater vehcle UUV), the autonomous underwater vehcle AUV), etc.) to perform collaboratve montorng tasks over a gven area. The man motvaton for UWA-SNs s ther relatve ease of deployment snce they elmnate the need for cables, and they do not nterfere wth shppng actvtes. UWA-SNs are envsoned to enable applcatons for envronmental montorng of physcal and chemcal/bologcal ndca- Manuscrpt receved March 5, 007; revsed July 6, 007 and September 1, 007. The work of X. Cheng was supported n part by the Natonal Scence Foundaton NSF) under Grants CNS and CNS The work of H. Shu and Q. Lang was supported n part by the NSF under Grant CNS and n part by the Offce of Naval Research under Grants N and N The revew of ths paper was coordnated by Prof. X. Shen. X. Cheng s wth the Department of Computer Scence, The George Washngton Unversty, Washngton, DC 005 USA e-mal: cheng@ gwu.edu). H. Shu and Q. Lang are wth the Department of Electrcal Engneerng, The Unversty of Texas at Arlngton, Arlngton, TX USA e-mal: shu@wcn.uta.edu; lang@uta.edu). D. H.-C. Du s wth the Department of Computer Scence and Engneerng, Unversty of Mnnesota, Mnneapols, MN USA e-mal: du@cs.umn.edu). Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Object Identfer /TVT tors, tactcal survellance, dsaster preventon, undersea exploraton, asssted navgaton, etc. Locaton dscovery for underwater vehcles/sensors s nontrval n the oceanc medum. Propagaton delays, motonnduced Doppler shft, phase and ampltude fluctuatons, multpath nterference, etc. are all sgnfcant factors n locaton measurement. The well-known Global Postonng System GPS) recevers, whch may be used n terrestral systems to accurately estmate the geographcal locatons of sensor nodes, do not work properly underwater [7]. Some localzaton schemes based on receved sgnal strength RSS), tme of arrval ToA), or angle of arrval AoA) could be used. Nevertheless, the bandwdth constrant, sensor moblty, and unpredcted varaton n channel behavor make many of these approaches naccurate or unapplcable [15]. For example, the Doppler shft ntroduced by moblty affects the AoA algorthm, and the underwater power loss model dependng on dstance and frequency) makes the RSS-based estmaton results ambguous. Moreover, the accuracy of the localzaton relates to the bandwdth of the sgnal and the sgnal-to-nose rato at the recever [5, p. 49]. The lower lmt for σ estmaton n the presence of addtve whte Gaussan nose s gven by the Cramer Rao lower bound,.e., σ =N 0 / + πf) pf) df ), whch ndcates that σ s nversely proportonal to the bandwdth. Unfortunately, the bandwdth of UWA-SNs s sgnfcantly lmted, whch theoretcally demonstrates that acoustc postonng n UWA-SNs s very challengng. Intutvely, ToA- or tme dfference of arrval TDoA)-based localzaton should be preferable. Nevertheless, ToA or TDoA approaches requre tme synchronzaton f one-way sound flyng tme s counted on; otherwse, a png-pong-style roundtrp propagaton delay needs to be measured. In UWA-SNs, precse tme synchronzaton s hard to acheve due to the characterstcs of sound when travelng n water [9]. In addton, the low bandwdth of acoustc sgnals s shared by navgaton and data communcaton n UWA-SNs [6]; therefore, the pngpong-style alternatve may sgnfcantly decrease the network throughput. For the same reason, schemes requrng a large number of anchor nodes whose locatons are known apror are prohbtve to UWA-SN. In ths paper, we propose UPS, whch s a ToA-based slent underwater postonng scheme, to carefully address the concerns and challenges prevously mentoned. The major contrbuton of ths paper les n three aspects: Frst, we propose UPS,.e., a slent postonng scheme for UWA-SNs, and demonstrate our algorthm by smulaton /$ IEEE

2 CHENG et al.: SILENT POSITIONING IN UNDERWATER ACOUSTIC SENSOR NETWORKS 1757 Second, we nvestgate the propagaton delay and multpath channel. We found that, n acoustc underwater networks wth large propagaton delays, a multpath channel can be modeled as a modfed ultrawdeband UWB) Saleh Valenzuela S-V) model: The arrval of each cluster and the paths wthn each cluster follow double Posson dstrbutons, and the multpath channel gan follows a Rcan dstrbuton. Thrd, we analyze the theoretcal performance of our scheme n propulson nose envronments and dentfy the possble sources of errors wth measures to help mtgate them. Compared to exstng schemes proposed n the context of UWA-SNs, UPS has fve characterstcs and advantages. 1) UPS utlzes very few anchor nodes four anchors n our study) and requres no specal hardware to provde -D localzaton. ) UPS requres no tme synchronzaton. All tme dfferences are computed from the measurements by a local tmer. ) UPS provdes slent postonng. Underwater vehcles and sensors do not actvely transmt any beacon sgnal. They just passvely lsten to the broadcasts of the anchor nodes for self-postonng. 4) UPS has low computaton overhead. It s based on smple algebrac operatons on scalar values. 5) As evdenced by our smulaton study, UPS has low poston error. It s applcable to both localzaton and navgaton n UWA-SNs. The slent postonng feature of UPS deserves further emphass. Frst, t can sgnfcantly conserve bandwdth and, therefore, mprove network throughput snce sensors/vehcles do not transmt any beacon for postonng purpose. Ths s partcularly true when a large number of vehcles and sensors need to be postoned n a UWA-SN. Second, UPS s applcable to asymmetrc UWA-SNs where the transmsson from an underwater vehcle or sensor could not reach four or more anchor nodes. Thrd, slent postonng provdes strong locaton prvacy, whch can help protect sensors/vehcles from beng detected n crtcal applcatons. Ths paper s organzed as follows: Secton II summarzes the major related works n UWA-SNs. Secton III proposes UPS,.e., a slent underwater postonng scheme for UWA-SN. Underwater acoustc channel modelng and theoretc performance analyss are gven n Secton IV. Smulaton results are reported n Secton V. We conclude our paper and report our future research n Secton VI. II. RELATED WORK Sensor self-postonng has been extensvely studed for typcal ndoor and outdoor sensor networks [16], [0]. In ths secton, we brefly overvew the localzaton technques proposed n UWA-SNs. For a more detaled lterature survey, see [15] and the references theren. Underwater acoustc localzaton can be broadly classfed nto two categores: 1) range-based and ) range-free. Rangebased schemes frst measure or estmate dstances or angles to a small number of anchor nodes va ToA, RSS, AoA, or even network connectvty and then apply trangulaton or multlateraton to transform ranges nto coordnates. Range-free schemes explore the local topology, and the poston estmate s derved from the locatons of the surroundng anchor nodes. Generally speakng, range-based schemes have hgher poston accuracy, whereas range-free schemes provde coarser locaton estmaton. An area-based range-free underwater postonng area localzaton scheme, ALS) s proposed n [14]. ALS reles on the varable power levels of anchor nodes to partton the plan nto areas. Each anchor node has ts own nonoverlappng partton. A vehcle/sensor receves ts poston estmate from a central server after provdng all the areas one for each anchor node) where t resdes. UPS s a range-based scheme wth much hgher poston accuracy. Range-based underwater localzaton requres ether longrange or short-range anchors. Snce a short-range beacon covers a smaller space, a larger number of anchor nodes are nvolved; therefore, t s unfavorable n underwater envronment. Motvated by terrestral GPS, underwater GPS, such as GPS ntellgent buoys GIBs) [9] and PARADIGM [8], has been proposed. Even though PARADIGM s able to compute locaton onboard, GIB reles on a centralzed server to compute locaton for underwater vehcles/sensors. These two methods requre tme synchronzaton for ToA measurement between anchor nodes and underwater vehcles/sensors. Hahn and Rce [18] propose a png-pong-style scheme to measure the round-trp delay for range estmaton. All these long-range-based methods requre underwater vehcles/sensors to nterrogate wth multple surface buoys, whch contrbutes to network throughput degradaton compared to UPS s slent postonng. If there s no drect communcaton between anchor nodes and sensors, network connectvty can be explored for range estmaton. In [5], three range detecton methods based on network connectvty have been proposed: 1) DV-hop; ) DV-dstance; and ) Eucldean. A comparson study n [5] ndcates that Eucldean performs best n ansotropc topologes wth a tradeoff of larger computaton and communcaton overheads. Zhou et al. [] have extended the Eucldean method to -D UWA-SN and studed ts performance. Ths method reles on a relatvely larger number of anchor nodes, whch results n hgher deployment cost. Zhang and Cheng [1] propose UR- PLACE,.e., a protocol for underwater robot self-postonng that explots the multhop connectvty to anchor nodes va beacon floodng. The extensve local communcaton n [] and the global floodng n [1] worsen the bandwdth shortage problem n UWA-SN, whch unavodably degrades the network throughput. As a comparson, our UPS requres no actve transmsson from underwater vehcles/sensors. III. UPS: AN UNDERWATER POSITIONING SCHEME In ths secton, we propose UPS,.e., a slent acoustc postonng scheme for underwater vehcle/sensor localzaton. UPS s motvated by our prevous work presented for -D terrestral sensor networks [16], [], [0], whch rely on the ToA of RF sgnals from three anchor nodes for locaton estmaton. The propagaton characterstcs of RF sgnals n free space and those of acoustc sgnals underwater are sgnfcantly dfferent,

3 1758 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO., MAY 008 Fg. 1. Sensor S wll measure the arrval tmes of beacon sgnals from anchor nodes A, B, C, and D locally. S wll also receve the turn-around delay nformaton from B, C, and D. B s transmsson wll start after t receves A s beacon sgnal. C s transmsson wll start after t receves the beacon sgnals of both A and B. In addton, D s transmsson wll start after t receves the beacon sgnals of A, B, and C. Ths procedure wll be repeated once every T seconds. whch fundamentally affect the performance of any poston algorthm. UPS conssts of two steps: The frst step detects the dfferences of sgnal arrval tmes from four anchor nodes. These tme dfferences are transformed nto range dfferences from the underwater vehcle/sensor to the anchor nodes. In the second step, trlateraton s performed to transform these range estmates nto coordnates. In the followng, we frst dscuss the network model under our consderaton. A. Network Model We assume that a UWA-SN conssts of moble underwater vehcles e.g., UUVs or AUVs) and statonary sensors. UUVs and AUVs move about at a typcal speed of about m [6] wthn a confned space, whch also covers all nonmoble sensors. To ease our elaboraton, herenafter, we use sensor to denote both a moble vehcle or a statonary sensor. There exst at least four noncospace anchor nodes wth long-range beacons, whose locatons are known apror. Each of them s equpped wth an acoustc transmtter that can cover the whole actvty space. No three anchors are collnear. An example layout of anchor nodes s llustrated n Fg. 1. B. Tme-Based Locaton Detecton Scheme Gven the locatons x a,y a,z a ), x b,y b,z b ), x c,y c,z c ), and x d,y d,z d ) of anchor nodes A, B, C, and D, respectvely, we are gong to determne the locaton x, y, z) of sensor S, asshown n Fg. 1. Let d j be the dstance between and j, where, j {a, b, c, d, s}, representng the four anchor nodes and sensor S. We have d ab = x a x b ) +y a y b ) +z a z b ) d ac = x a x c ) +y a y c ) +z a z c ) d ad = x a x d ) +y a y d ) +z a z d ). The frst step of UPS computes the range dfferences between d sa and d sb, d sc, and d sd, respectvely. Step 1 Range Dfference Computaton: Let A be the master anchor node, whch ntates a beacon sgnal every T seconds. Each beacon nterval begns when A transmts a beacon sgnal. Consderng any beacon nterval, attmest 1, t b, t c, and t d, sensor S and anchor nodes B, C, and D receve A s beacon sgnal, respectvely. At tme t b, whch s t b, B reples to A wth a beacon sgnal conveyng nformaton t b t b = t b. Ths sgnal reaches S at tme t. After recevng beacon sgnals from both A and B, at tme t c, C reples to A wth a beacon sgnal conveyng nformaton t c t c = t c. Ths sgnal reaches S at tme t. After recevng beacon sgnals from A, B, and C, at tme t d, D reples to A wth a beacon sgnal conveyng nformaton t d t d = t d. Ths sgnal reaches S at tme t 4. Based on trangle nequalty, t 1 <t <t <t 4. Lettng t 1 = t t 1, t = t t 1, and t = t 4 t 1, we obtan whch gves d ab + d sb d sa + v t b = v t 1 1) d ac + d sc d sa + v t c = v t ) d ad + d sd d sa + v t d = v t ) d sb = d sa + v t 1 d ab v t b = d sa + k1 4) d sc = d sa + v t d ac v t c = d sa + k 5) d sd = d sa + v t d ad v t d = d sa + k 6) where d sa, d sb, d sc, and d sd are postve real numbers; v s the speed of the ultrasound; and k1 = v t 1 v t b d ab 7) k = v t v t c d ac 8) k = v t v t d d ad. 9) Averagng k 1, k, and k over I ntervals gves [ I k 1 = v I =1 [ I k = v I =1 [ I k = v I =1 t 1 t ) ] b d ab 10) t t ) ] c d ac 11) t t ) ] d d ad. 1) We are gong to apply trlateraton wth k 1, k, and k to compute coordnates x, y, z) for sensor S n the next step. Remarks: 1) All arrval tmes, ncludng t j, where j =1,,, 4, and t j, where j {b, c, d}, are based on the local tmers of the anchor nodes and sensor S. No tme synchronzaton s requred. ) We requre A to perodcally ntate the beacon sgnal transmsson to decrease the measurement error and to facltate navgaton.

4 CHENG et al.: SILENT POSITIONING IN UNDERWATER ACOUSTIC SENSOR NETWORKS 1759 Step Locaton Computaton: From 4) 6) and 10) 1), we have d sb = d sa + k 1 1) d sc = d sa + k 14) d sd = d sa + k. 15) Based on trlateraton, we obtan four equatons wth four unknowns x, y, z, and d sa, where d sa > 0,.e., x x a ) +y y a ) +z z a ) = d sa 16) x x b ) +y y b ) +z z b ) =d sa + k 1 ) 17) x x c ) +y y c ) +z z c ) =d sa + k ) 18) x x d ) +y y d ) +z z d ) =d sa + k ). 19) Wthout loss of generalty, we assume that the four anchor nodes are located at 0, 0, 0), x b, 0, 0), x c,y c, 0), and x d,y d,z d ), respectvely, where x b > 0, y c > 0, and z d > 0. Note that we can always transform real postons to ths coordnate system through rotaton and translaton. From 16) 19), we have x + y + z = d sa 0) x x b ) + y + z =d sa + k 1 ) 1) x x c ) +y y c ) + z =d sa + k ) ) x x d ) +y y d ) +z z d ) =d sa + k ). ) Solvng these equatons, we obtan where d 1) sa d ) sa = β β 4αγ α 4) = β + β 4αγ α 5) x = A x d sa + B y 6) y = A y d sa + B y 7) z = A z d sa + B z 8) α = A x + A y + A z 1 9) β =A x B x + A y B y + A z B z ) 0) γ = B x + B y + B z 1) A x = k 1 x b ) Fg.. Transecton of the feasble space where z =0. B x = x b k 1 x b ) A y = k 1x c x b y c k y c 4) B y = x c + y c x b x c + x ck 1 x b k y c 5) ) A z = k 1x d k y k1 x c d x b k 6) x b z d z d y c z d B z = x d + y d + z d x bx d + xdk 1 x b k y dx c y c z d + y cy d + x bx c y d y c k 1 x cy d x b y c + k y d y c z d. 7) We have conducted extensve smulaton to study the feasble space where d sa > 0 s unque. It s nterestng to observe that when S s not close to any anchor node and when t s not behnd any anchor node, 4) provdes a unque feasble soluton. In addton, the correct poston can be computed va 4) f a sensor resdes n the enclosed space by the four anchor nodes, even when t s close to an anchor node. Fgs. 4 report the three transectons z =0, 5, 10) of the feasble space the gray area) when the four anchor nodes A, B, C, and D resde n 0, 0, 0), 10, 0, 0), 0, 10, 0), and 0, 0, 10), respectvely. IV. CHANNEL MODELING AND THEORETICAL PERFORMANCE ANALYSIS In ths secton, we study the poston error of UPS that resulted from the acoustc fadng channel. In the followng, we frst propose a modfed UWB S-V model to characterze the underwater acoustc fadng channel; then, we apply ths model to study the poston error of UPS. Major sources of poston errors are also dentfed. Note that, to the best of our

5 1760 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO., MAY 008 Fg.. Transecton of the feasble space where z =5. Fg. 4. Transecton of the feasble space where z =10. knowledge, there s no standard channel model for underwater so far, and our modfed UWB S-V model s a reasonable model based on the study on outdoor UWB channel detaled n [1]. A. Channel Modelng for Underwater Sensor Networks The underwater acoustc channel exhbts phenomena such as sgnal fadng and phase and ampltude fluctuaton due to the nteractons wth the boundares and the scatterng from nhomogenetes wthn the ocean medum. The speed of sound underwater s approxmately 1500 m/s, whch leads to large propagaton delays and moton-nduced Doppler effects. Phase and ampltude fluctuatons may nduce hgh bterror probablty, compared to most rado channels. Multpath nterference s another mportant phenomena n UWA networks, causng frequency-selectve fadng n underwater channels. There has been much effort to model the underwater acoustc fadng channels and estmate ther performance. Early research [1], [8] assumes Raylegh fadng n nature, but t s later observed n [17] that Raylegh fadng exhbts only n lmted cases. Geng and Zelnsk [17] propose that, n an underwater acoustc channel, there can be several dstnct paths egenpaths) over whch a sgnal can propagate from transmtter to recever egenpath sgnals). Each egenpath sgnal contans a domnant stable component and many smaller randomly scattered components sub-egenpath or egenray components). The envelope of the egenpath sgnal can therefore be descrbed usng a Rce fadng model. Such an egenpath or egenray concept was frst ntroduced n [19]. The egenray arrval angles, as well as the ampltude and phase fluctuatons, are all statstcally modeled and are assumed to be ndependent of each other. The number of egenrays reachng the recever s a Posson dstrbuton wth a mean number calculated from the Ray Theory. Enlghtened by the pror research on underwater acoustc channel modelng, we propose a modfed UWB S-V channel model [7] for underwater acoustc networks, whch can be valdated n three consderatons: Frst, UWB comes from the UWB radar world and refers to the electromagnetc waveforms that are characterzed by an nstantaneous fractonal energy bandwdth greater than about In an underwater acoustc channel, the communcaton frequency range s nferor to 10 khz. In short-range transmsson, the carrer frequency s 550 Hz n shallow water and khz n deep water. The carrer frequency for long-range transmsson s 1500 Hz. In all cases, the fractonal bandwdth f H f L )/f H + f L )/) s much greater than Therefore, the underwater acoustc channel can be modeled as a UWB channel. In July 00, the Channel Modelng subcommttee of study group IEEE SGa publshed the fnal report regardng the UWB ndoor multpath channel model []. It s a modfed verson of the ndoor S-V channel model [7]. Second, multpath channels can be modeled as an S-V model n UWB communcatons. The S-V model s based on the observaton that, usually, multpath contrbutons generated by the same pulse arrve at the recever grouped nto clusters. Such a channel behavor s analogous to the aforementoned egenpath/ sub-egenpath concept n underwater networks. Thrd, smlar to [19], two Posson models are employed n the modelng of the path arrvals n UWB communcatons. The frst Posson model s for the frst path of each path cluster, and the second Posson model s for the paths or rays wthn each cluster. Applyng the S-V model nto underwater acoustc channels, the arrval of clusters s modeled as a Posson arrval process wth rate Λ, whereas, wthn each cluster, subsequent multpath contrbutons or rays also arrve accordng to a Posson process wth rate λ see Fg. 5). We defne the followng. T l s the arrval tme of the frst path of the lth cluster. τ k,l s the delay of the kth path wthn the lth cluster relatve to the frst path arrval tme T l. Λ s the cluster arrval rate. λ s the ray arrval rate,.e., the arrval rate of the paths wthn each cluster.

6 CHENG et al.: SILENT POSITIONING IN UNDERWATER ACOUSTIC SENSOR NETWORKS 1761 Fg. 5. Channel mpulse response. By defnton, we have τ 0l = T l. The dstrbutons of the cluster arrval tme and the ray arrval tme are gven by pt l T l 1 )=Λexp ΛT l T l 1 ), l > 0 p τ k,l τ k 1),l ) = λ exp λ τk,l τ k 1),l )), k > 0. 8) In the UWB S-V model, the magntude of the kth path wthn the lth cluster s denoted by β kl. It follows a Raylegh dstrbuton. However, n underwater acoustc networks, the channel wthn the communcaton frequency range does not behave lke a Raylegh channel. Based on the dscusson n [17] and [19], t s rather approprate to model the multpath channel gan as a Rcan dstrbuton. Then, n the underwater S-V model, the gan of the kth path wthn the lth cluster s a complex random value wth a modulus β kl and a phase θ kl.we assume that the β kl values n a underwater acoustc channel are statstcally ndependent and are Rcan-dstrbuted postve random varables, whereas the θ kl values are assumed to be statstcally ndependent unform random varables over [0, π). We have β kl = β 00 exp T l/γ) exp τ kl /γ) 9) where the term β 00 represents the average energy of the frst path of the frst cluster, whereas Γ and γ are the power decay coeffcents for clusters and multpath, respectvely. Accordng to 9), the average power decay profle s characterzed by an exponental decay of the ampltude of the clusters and a dfferent exponental decay for the ampltude of the receved pulses wthn each cluster, as shown n Fg. 6. In [], based on many expermentatons carred out by Loubet and Faure wth the French Navy, t was shown that the Raylegh fadng model s not ft for underwater transmssons. They proposed the underwater channel model usng ray tracng by great determnstc propagaton paths macromultpath) assocated wth random fluctuatons mcromultpaths). The macromultpaths are very smlar to the clusters n our model, and the mcromultpaths are very smlar to the rays wthn each cluster n our model. Fg. 6. Double exponental decay of the mean cluster power and the ray power wthn clusters. B. Theoretcal Error Analyss In ths secton, we study the poston error of S that resulted from the acoustc fadng channel, whch has been modeled as a modfed UWB S-V model n Secton IV-A. The trlateraton equatons 16) 19) compute the coordnates x, y, z) for sensor S based on the measured values k 1, k, and k, whch are determned by the tme-related measurements at the sensor t 1, t, and t ) and anchor nodes B t b ), C t c), and D t d ) over beacon nterval [see 10) 1)]. Therefore, the errors of x, y, and z result from the measurng errors of t 1, t, t, t b, t c, and t d. Snce the error of t b t c, t d ) plays the same role as that of t 1 t, t ) n the computaton of k 1 k,k ) and anchor node B C, D) and can have more sophstcated hardware to precsely estmate t b t c, t d ), we consder the errors of t 1, t, and t only, whch are computed from the arrval tmes of the beacon sgnals transmtted from anchor nodes A, B, C, and D at beacon nternal t 1, t, t, and t 4, respectvely. Assume that the underwater sensor always lstens to the frst ray of the transmtted sgnal and records the arrval tmes, whch, n our case, are t 1, t, t, and t 4. Due to the underwater multpath effect, as llustrated n Fg. 6, these arrval tmes contan an error wth an exponental dstrbuton. Let δt 1, δt, and δt be the measurng errors of t 1, t, and t, respectvely. It s reasonable to assume that δt 1, δt, and δt are ndependent from each other. Gven t 1, the condtonal probablty densty functons of δt 1, δt, and δt are exponental wth parameters λ 1, λ, and λ, respectvely,.e., P e δ t1 t ) 1 = λ1 exp λ 1 δt ) 1 P e δ t t ) 1 = λ exp λ δt ) P e δ t t 1) = λ exp λ δt ). 40) To smplfy the elaboraton, we consder the case when anchor nodes A, B, C, and D are located at 0, 0, 0), R,0,0), 0, R, 0), and 0, 0, R), respectvely. To further smplfy the analyss, we consder the case when S resdes n a small area wth a dameter R) whose center s equdstant to all anchor nodes. The general case can be smlarly analyzed.

7 176 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO., MAY 008 From 10) 1), k 1, k, and k are the averaged results over I beacon ntervals, and based on the central lmt theorem, k 1, k, and k are approxmately normally dstrbuted when I s large. Therefore, we may assume that k 1, k, and k are dstrbuted accordng to N µ 1,σ 1), N µ,σ ), and N µ,σ ), respectvely. Deducng from 10) 1), we have ) 1 k 1 : µ 1 = v + ν 1 R, σ 1 = v λ 1 Iλ 1 ) 1 k : µ = v + ν R, σ = v λ Iλ ) 1 k : µ = v + ν R, σ = v λ Iλ 41) where ν 1, ν, and ν are the mean of the accurate values for t 1, t, and t, respectvely. Based on these assumptons, we have µ 1 /R 0, µ /R 0, and µ /R 0. Pluggng x b = y c = z d = R and other zero coordnates nto 4) and smplfyng ts soluton by approxmatng k 1/R, k /R, and k /R wth 0, we end up wth R +k 1 + k + k ) d sa k 1 + k + k ). 4) Substtutng the precedng equaton nto 6) yelds x R k 1 R k 1 R +k 1 +k +k ) k 1 +k +k ). R 4) Now, replacng k 1 k /R )=k 1 /R)k /R), k 1 k /R )= k 1 /R)k /R), and k k /R )=k /R)k /R) by 0, we obtan x R + k 1 R k + k ) k 1 = R + k 1k, 44) where k, =k + k )/R /. Smlarly, from 7) and 8), we have y R + k R k 1 + k ) k = R + k k1, z R + k R k 1 + k ) k = R + k k1, 45) where k 1, =k 1 + k )/R /, and k 1, =k 1 + k )/ R /. Snce x, y, z) s used to estmate the locaton of S, the error n the estmaton must be addressed. There are several ways to do ths. The followng s a common practce, where the varance of each varable s computed, and the sze of the varance or standard devaton s used as a measure of the estmaton error. As k 1 has a Gaussan dstrbuton wth mean µ 1 and varance σ1, k has a Gaussan dstrbuton wth mean µ and varance σ, and k has a Gaussan dstrbuton wth mean µ and varance σ, the lnear combnaton k1, has a Gaussan dstrbuton wth mean µ 1 + µ )/R / and varance σ1 + σ)/4r, k1, has a Gaussan dstrbuton wth mean µ 1 + µ )/R / and varance σ1 + σ)/4r, and k, has a Gaussan dstrbuton wth mean µ + µ )/R / and varance σ + σ)/4r. Denote by EX) and V X) the mean and varance of random varable X. We have, from 44) V x) V k 1 k, ) = E k 1 k,) [ E k1 k, )] = E k1 ) ) k, [ E k 1 k,)]. 46) By the ndependence between k 1, k, and k,wehave E k 1 k,) = Ek1 )E k, ) E k1 ) ) k, = E k1 ) E k, ) = [V k 1 )+Ek 1 )) ] 47) [ V k, ) )) ] + E k,. 48) Therefore, substtuton gves V x) V k 1 ) [ E k, )] ) + V k, [Ek1 )] = σ 1 + V k 1 )V k, ) µ + µ R ) + σ + σ 4R µ 1 + σ1 σ + σ 4R = σ 1µ + µ ) + ) σ + σ µ 1 + σ1 σ + σ) 4R + σ1 µ ) + µ. 49) R Snce µ 1 /R 0 and µ /R 0, pluggng n 4), the precedng equaton reduces to V x) σ 1 + σ + σ ) R [ = v v ] Iλ + 1 IRλ + λ ). 50)

8 CHENG et al.: SILENT POSITIONING IN UNDERWATER ACOUSTIC SENSOR NETWORKS 176 Smlarly, we have V y) V k1,) [Ek )] + V k ) [ E k1, )] + V k1,) V k ) + σ 1 + σ ) R σ = v Iλ [ + v IRλ 1 + λ ) ]. 51) V z) V k1,) [Ek )] + V k ) [ E k1, )] + V k1,) V k ) + σ 1 + σ ) R σ = v Iλ [ + v IRλ 1 + λ ) ]. 5) From the precedng analyss, we make the followng observatons: Frst, the varances of x, y, and z depend on ray arrval rates λ 1, λ, and λ. Second, λ 1 contrbutes more to the varance of x than λ and λ, λ contrbutes more to the varance of y than λ 1 and λ, and λ contrbutes more to the varance of z than λ 1 and λ. Thrd, when R s large, V x) σ 1/ =v /Iλ 1, V y) σ / =v /Iλ, and V z) σ / =v /Iλ, showng that the varance of x s dependent on that of k 1, the varance of y s dependent on that of k, and the varance of z s dependent on that of k. Fourth, f λ 1 = λ = λ, the varances of x, y, and z can be treated the same n practce. Note that the precedng analyss well explans our smulaton results, whch ndcate that poston errors strongly depend on the arrval rates of double exponental dstrbutons. C. Sources of Errors There are three major sources of errors for tme-based locaton detecton schemes n UWA-SNs: 1) the recever system delay; ) the underwater multpath fadng; and ) the varable acoustc speed underwater. The recever system delay s the tme duraton from whch the sgnal hts the recever antenna untl the sgnal s accurately decoded by the recever. Ths tme delay s determned by the recever electroncs. Usually, t s constant or vares n very small scale when the recever and the channel are free from nterference. Ths system delay can be predetermned and used to calbrate the measurements. For example, anchor nodes B, C, and D can always elmnate the system delay from t b, t c, and t d before these values are conveyed to the sensors n ther reply messages to A s beacon sgnal. Meanwhle, as t 1, t, and t are measured by one sensor, the effect of recever system delay may cancel out. Thus, n our model, f anchor nodes B, C, and D can provde precse aprornformaton on recever system tme delays, the effect of these delays wll be neglgble. The underwater multpath fadng channel wll greatly nfluence the locaton accuracy of any locaton detecton system. Major factors nfluencng terrestral multpath fadng [6] nclude multpath propagaton, speed of the recever, speed of the surroundng objects, and the transmsson sgnal bandwdth.in the underwater envronment, other mportant factors nclude water temperature and clarty, moton behavor of recever and underwater objects, and transmsson range. In our tmebased locaton scheme, we assume that the moton of the underwater vehcles s relatvely small such that the motonnduced Doppler effect can be gnored. There are two mportant characterstcs of multpath sgnals: Frst, the multple nondrect path sgnals wll always arrve at the recever antennas later than the drect path sgnal, as they must travel a longer dstance. Second, n the lne-ofsght transmsson model, nondrect multpath sgnals wll normally be weaker than the drect path sgnal, as some sgnal power wll be lost from scatterng. If nonlne-of-sght exsts, the nondrect multpath sgnal may be stronger, as the drect path s hndered n some way. Based on these characterstcs, scentsts can always desgn more senstve recevers to lock and track the drect path sgnal. For example, multpath sgnals usng a pseudorandom code arrvng at the recever later than the drect path sgnal wll have neglgble effects on a hgh-resoluton drect-sequence bnary phase-shft keyng recever [11]. Our locaton detecton scheme mtgates the effect of multpath fadng by measurng TDoA over multple beacon ntervals and modelng the multpath arrval tmes as the double exponental dstrbuton. TDoA measurements have been very effectve n fadng channels, as many detrmental effects caused by multpath fadng and processng delay can be canceled [1]. Another source of poston error s the varable speed of sound, whch sgnfcantly affects the precson of all localzaton systems that assume a constant acoustc speed. The velocty of underwater acoustcs depends on temperature, salnty, and depth [4]. In future research, we wll nvestgate the nfluence of the varable speed of sound on our postonng scheme. V. S IMULATION In ths secton, we are gong to study the performance of UPS n UWA-SNs. We make the same assumptons as those n Secton IV-B; for a gven t 1, the measurng errors of t, t, and t are ndependent exponental dstrbutons wth arrval rates λ 1, λ, and λ, respectvely, and the underwater vehcle/sensor measures the arrval tme of the frst ray of the frst cluster only n a multpath fadng channel. We further assume that the measurng errors of t b, t c, and t d are neglgble, as justfed n Secton IV-C. Therefore, λ 1, λ, and λ can be assumed to be equal, and ths value s denoted by λ. We wll nvestgate the nfluence of λ on poston error. Another factor that we wll nvestgate s the number of beacon ntervals I used to compute k 1, k, and k. Snce we also consder the localzaton of moble underwater vehcles, we choose to average over a small number of beacon ntervals. We use Matlab to code UPS. Ths tool provdes procedures to generate normally dstrbuted and unformly dstrbuted random numbers. Note that we do not use the sqrt functon n Matlab. Instead, we use Newton s method []. We have found that four

9 1764 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO., MAY 008 Fg. 7. Poston errors versus real postons when λ =0.1n the x = y plane wth z =5. Fg. 8. Poston errors versus real postons when λ =.5n the x = y plane wth z =5. teratons generally yeld good results. In addton, 4) wll be adopted for poston estmaton snce, n our smulaton, sensors wll be placed wthn the space enclosed by four anchor nodes. Frst, we study the dstrbuton of poston errors over a -D montored space. In ths smulaton scenaro, the four anchor nodes are located at 0, 0, 0), 0, 0, 0), 0, 0, 0), and 0, 0, 0), respectvely. Sensors are placed at grd ponts +0.5,j + 0.5,k+0.5), where, j, k =0, 1,...,19. The errors of t 1, t, and t are exponentally dstrbuted wth parameters λ 1 = λ = λ = λ. We average the sensor locaton estmaton over 1000 trals. For each tral, I =16. In addton, we smulate dfferent λ settngs and obtan smlar results. Nevertheless, we report the cases of λ =0.1 and λ =.5 only n ths paper. Fgs. 7 and 8 llustrate the x=y plane poston errors versus the real postons of the sensors for z =5. Results from the x=z and y = z planes are close to those reported for the x = y plane. We observe that a lower arrval rate gves a better estmaton snce a hgher arrval rate may brng moton-nduced Doppler shft n the channel and cause jtterng n the measurement. We also observe that, as the dstances from a sensor to all four anchor nodes become larger, the poston errors wll Fg. 9. Poston errors versus λ where BAC =90. correspondngly become larger; when the sensor s closer to any of the four anchor nodes, the errors become larger. Notce that, n Fg. 7, the sensor at locaton 9.5, 9.5, 5.0), whch s close to the ntersecton of the three angle bsectors of ABC, has the smallest poston error and that the sensors at ts neghborng area also demonstrate qute low poston errors. Interestngly, Bulusu et al. [10], Cheng et al. [16], and Naspur and L [4] provde smlar results n ther smulaton study. Intutvely, ths s because the geometry of the ntersecton of the range crcles s poor when the sensors are far away from any anchor node or when the sensors are close to any anchor node. From ths analyss, we conclude that the poston error s related to the placement of anchor nodes. Careful studes wll be conducted n the future as the results can be appled to gude the deployment of anchor nodes for better performance. For these reasons, n the followng smulaton, we ntentonally enforce an allowable shortest dstance 1.0 unt) from any randomly generated sensor to any anchor node. Ths means that the four anchor nodes are placed some dstance away from the boundary of the montored area. Next, we consder the scenaro when sensors are randomly deployed n a cubc space wth lower left corner 1, 1, 1) and upper rght corner 19, 19, 19). The four anchor nodes are stll located at 0, 0, 0), 0, 0, 0), 0, 0, 0), and 0, 0, 0), respectvely. For each λ value, we try 000 random sensor postons. The averaged results are reported n Fg. 9. Note that, n ths paper, I s selected from {1,,, 4} to demonstrate the effectveness of UPS when appled to postonng moble underwater vehcles. We obtan three observatons from Fg. 9: Frst, as I ncreases, poston error decreases. Ths s because averagng over a larger number of beacon ntervals to compute k 1 k and k can better smooth out the effects of measurng errors n t 1, t, and t and, thus, produce an mproved result. A detaled theoretcal explanaton comes from Secton IV-B. As I ncreases, σ 1, σ, and σ wll decrease, and thus, V x), V y) and V z) wll decrease. Then, the errors from estmatng the coordnates of sensors by x, y, and z wll decrease, mplyng that the poston error wll become smaller. Second, poston

10 CHENG et al.: SILENT POSITIONING IN UNDERWATER ACOUSTIC SENSOR NETWORKS 1765 VI. CONCLUSION AND FUTURE RESEARCH In ths paper, we propose UPS, a slent underwater postonng scheme for UWA-SNs. UPS s superor to exstng systems n many aspects, such as lack of synchronzaton and low computaton overhead. To evaluate the performance of UPS, we model the underwater acoustc channel wth a modfed UWB S-V model and conduct both theoretcal analyss and a smulaton study. Our scheme s smple and effectve. For future research, we wll study the mpact of the channel modelng error on the poston error of UPS. In addton, we ntend to desgn a general framework based on projecton such that localzaton algorthms proposed for -D terrestral sensor networks can be easly talored to -D UWA-SNs. By ths approach, the anchor node at the seabed s expected to be saved. Fg. 10. Poston errors versus λ where BAC 90. error ncreases as λ ncreases. Ths s reasonable n the underwater acoustc channel, n whch a hgher λ comes from an even hgher transmsson rate when asymmetry commonly exsts between the transmtter and the recever. Such a characterstc of the underwater medum brngs sgnfcant multpath nterference at the recever and causes jtterng, as shown n Fg. 8. Agan, ths can be well explaned by Secton IV-B. In fact, f λ ncreases, whch means that v ncreases at an even larger pace, v /λ ncreases. As a result, V x), V y), and V z) ncrease, so that the errors from estmatng the coordnates of the sensor by x, y, and z ncrease. Thus, the larger the arrval rate, the larger the poston error. Thrd, n the stuaton of small λ, e.g., λ 0.5, as shown n Fg. 9, the locaton errors vary very lttle wth the number of beacon ntervals I. When λ s relatvely hgh, I plays a more mportant role. The hgher the λ, the bgger the dfference nduced from I. Ths observaton s analogous to the terrestral wreless communcaton channels, n whch coherent tme s ntroduced to depct a perod of tme where the channel behavor or model can be consdered as statonary. For underwater wreless communcatons, not only temporal coherence but also spatal and frequency coherences [19] are sgnfcant parameters for sgnal propagaton through acoustc channels wth multple paths. Based on the thrd observaton, λ n underwater communcatons should not be neglected n estmatng the coherence parameters. Note that, by rotatng the square-cube montored space wthn the open space formed by anchor nodes A, B, C, and D, we obtan very smlar results. In the followng, we report the smulaton results when BAC 90. In ths smulaton, the four anchor nodes are located at 0, 0, 0), X B,Y B, 0), X C,Y C, 0), and 0, 0, Z D ), respectvely, where X B, Y B, X C, Y C, and Z D are randomly drawn from [5, 0]. Two thousand sensors are randomly placed wthn the overlappng space formed by the anchor nodes A, B, C, D) and the cube space wth corners 0, 0, 0) and 0, 0, 0). Fg. 10 reports the poston error versus λ. Note that the observatons from Fg. 10 are very smlar to those from Fg. 9. Nevertheless, for the same λ, the acute angle case performs slghtly better than the rght angle case. REFERENCES [1] Global Postonng System Standard Postonng Servce Specfcaton, Jun., [] IEEE SGa, Channel Modelng Sub-Commttee Report Fnal, Feb. 00. [] MIT Books, Square Roots by Newton s Method. [Onlne]. Avalable: [4] Underwater Acoustcs Techncal Gudes Speed of Sound n Seawater. [Onlne]. Avalable: soundseawater/speedsw.pdf [5] M. G. D Benedetto and G. Gancola, Understandng Ultra Wde Band Rado Fundamentals, ser. Prentce-Hall Communcatons Engneerng and Emergng Technology. Englewood Clffs, NJ: Prentce-Hall, 004. [6] T. S. Rappaport, Wreless Communcatons: Prncples and Practce, nd ed. Englewood Clffs, NJ: Prentce-Hall, 00. 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Zhou, Localzaton for large-scale underwater sensor networks, Unv. Connectcut, CSE Tech. Rep.: UbNet-TR06-04, Dec Xuzhen Susan) Cheng M 0) receved the M.S. and Ph.D. degrees n computer scence from the Unversty of Mnnesota, Mnneapols, n 000 and 00, respectvely. In 006, she was a Program Drector wth the Natonal Scence Foundaton NSF) for sx months. She s currently an Assstant Professor wth the Department of Computer Scence, The George Washngton Unversty, Washngton, DC. Her current research nterests nclude wreless and moble computng, sensor networkng, wreless and moble securty, and approxmaton algorthm desgn and analyss. Dr. Cheng has served on the edtoral boards of several techncal journals and n the techncal program commttees of varous professonal conferences/ workshops. She was the Program Cochar of the frst Internatonal Conference on Wreless Algorthms, Systems, and Applcatons WASA06). She was the recpent of the NSF CAREER Award n 004. Hanng Shu S 04) receved the B.S. degree n electroncs and nformaton systems from Pekng Unversty, Bejng, Chna, n 1996, the M.S. degree n electrcal engneerng from the Unversty of Texas at Dallas, Rchardson, n 00, and the Ph.D. degree n electrcal engneerng from The Unversty of Texas, Arlngton, n 007. Pror to the master program, she was a System Engneer wth the Telecom Plannng and Research Insttute, Bejng. She s currently wth the Department of Electrcal Engneerng, The Unversty of Texas at Arlngton. Her research nterests nclude fuzzy logc systems and applcatons, dstrbuted source codng, sensor networks, and collaboratve radar systems. Qlan Lang M 01 SM 05) receved the B.S. degree from Wuhan Unversty, Wuhan, Chna, n 199, the M.S. degree from Bejng Unversty of Posts and Telecommuncatons, Bejng, Chna, n 1996, and the Ph.D. degree from the Unversty of Southern Calforna USC), Los Angeles, n 000, all n electrcal engneerng. In August 00, he joned the Department of Electrcal Engneerng, The Unversty of Texas at Arlngton UTA). He was a member of Techncal Staff wth Hughes Network Systems Inc., San Dego, CA. He has publshed more than 10 journal and conference papers and sx book chapters. He s the holder of sx pendng U.S. patents. Hs research nterests nclude sensor networks, wreless communcatons, wreless networks, communcaton systems and communcaton theory, sgnal processng for communcatons, fuzzy logc systems and applcatons, and collaboratve and dstrbuted sgnal processng. Dr. Lang was the recpent of the 00 IEEE TRANSACTIONS ON FUZZY SYSTEMS Outstandng Paper Award, the 00 U.S. Offce of Naval Research Young Investgator Award, and the 005 UTA College of Engneerng Outstandng Young Faculty Award. Davd Hung-Chang Du S 81 M 81 SM 95 F 98) receved the B.S. degree n mathematcs from Natonal Tsng Hua Unversty, Hsnchu, Tawan, R.O.C., n 1974 and the M.S. and Ph.D. degrees n computer scence from the Unversty of Washngton, Seattle, n 1980 and 1981, respectvely. He s currently a Qwest Char Professor wth the Department of Computer Scence and Engneerng, Unversty of Mnnesota, Mnneapols. He has authored and coauthored more than 190 techncal papers, ncludng 90 referred journal publcatons n hs research areas. He has also graduated 48 Ph.D. and 80 M.S. students. Hs research nterests nclude cyber securty, sensor networks, multmeda computng, storage systems, hgh-speed networkng, hgh-performance computng over clusters of workstatons, database desgn, and computer-aded desgn for very-large-scale ntegraton crcuts. Dr. Du s a Fellow of the Mnnesota Supercomputer Insttute. He s currently servng on a number of journal edtoral boards. He has also served as guest edtor for a number of journals, ncludng IEEE Computer, and Communcatons of ACM. He has also served as Conference Char and Program Commttee Char for several conferences n the multmeda, database, and networkng areas.