Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 Sensors & ransducers 213 by IFSA http://www.sensorsportal.com A Relatve Postonng echnque wth Spatal Constrants for Multple argets Based on Sparse Wreless Sensor Network Wemng U, aodong YIN, Zhuz HE, anyang LIU Department of Hydrography and Cartography, Dalan Naval Academy, 11618, Dalan, Laonng, P. R. Chna el.: +86-411-858-56438 E-mal: xwm5@mals.tsnghua.edu.cn Receved: 18 September 213 /Accepted: 25 October 213 /Publshed: 3 November 213 Abstract: Many applcatons of wreless sensor network requre precse knowledge of the locatons of nodes. Conventonal sparse wreless sensor network, whch s formed by a restrcted number of nodes, has two drawbacks,.e., low connectve rato and hop count lmted, whch probably cause the network lnk falure and/or low locatng performance. o mprove the relatve poston precson and relablty of multple targets based on the sparse wreless sensor network, a relatve locatng method wth spatal constrants s proposed accordng to the dfferent network confguraton and nter-range between target nodes for the sparse wreless sensor network, of whch the spatal constrant benchmarks nclude two categores of datum, namely, the spatal absolute dsplacement datum and drecton rotaton datum. In partcular, t s proven on the bass of the prncple of survey adjustment that the nodes poston ambguty, whch s caused by the rank defcency, could be solved whle the estmatng precson of the target nodes poston s unchanged. he smulaton results show that compared to the conventonal tme-varyng flterng, e.g. Kalman Flterng, the proposed constrant poston method may rapdly respond to network-lnk communcaton falure, and ncrease relatve postonng precson about 32.9 % va ntroducng the spatal constrant benchmarks. Copyrght 213 IFSA. Keywords: Wreless sensor network, Multple targets, Relatve poston, Spatal constrant, Poston benchmark, Kalman Flterng. 1. Introducton Wth the rapd development of mcroelectromechancal system, wreless communcaton system and low-power embedded system, wreless sensor network (WSN) come nto beng [1], of whch sea-surface wreless sensor network (S 2 WSN) are regarded as a specal communcaton networks consstng of a number of shps and buoys, namely, multple targets, accordng to a certan communcaton protocols. hrough rado technology, these targets communcate wth each other, whch may mplement cooperatve observaton, cooperatve communcaton and cooperatve remote sensng for envronment n tmes of exteror locaton benchmarks (lke global postonng system, GPS) outages or n these benchmarks dened sea areas. hese WSN are expected to form the backbone of future ntellgent networks for a broad range of applcatons such as underwater survellance and traffc montorng. For most applcatons of the WSN, multple-target localzaton s one of the most challengng and Artcle number P_1482 183
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 mportant ssues, because the locaton nformaton s typcally useful for coverage, deployment, routng, locaton servce, target trackng, and rescue operatons n WSN. In the development of ocean resource, utlzng WSN together wth engneerng boat, ocean drllng platform and underwater robot to collaboratvely determne the target locaton, can mprove the precson of underwater ppelne layng, olfeld mnng and waterway dredgng [2]. In salvagng the crash shp and arcraft, usng the WSN and the engneerng boat to collaboratvely determne the poston of black box for shp and/or arcraft, can mprove the precson and effcency of underwater salvage. In enforcng oceanc law, usng WSN postonng technology can mprove the tmelness and accuracy of sea polce deployment. As for space envronment montorng, maneuverng status of flyng vehcles (FVs) may be descrbed n detaled through cooperatve postonng among the S 2 WSN and the FVs. As such, they have superor postonng precse and relablty durng trackng the FVs n the bad ocean envronment because they can automatcally deploy nodes and deal wth the communcaton malfuncton among the nodes when some network nodes fal or new nodes become a member of the network. he remander of ths paper s organzed as follows. Secton 2 ntroduces the relevant work about relatve postonng method for multple targets based on WSN. In Secton 3, we descrbe the basc prncple of relatve postonng on basc of the sparse dstrbuted WSN (SWSN). Secton 4 deduces the mathematcal model of constrant poston for the SWSN. Secton 5 presents smulaton results to verfy the effectveness of the proposed algorthm. Fnally, Secton 6 summarzes the contrbutons and concludes the paper. 2. Relevant Work As to the features of modern WSN wth large node number and huge network scale, the postonng algorthms proposed currently for multple targets have many superor performances, such as low energy consumpton, low dependence, strong robustness and hgh adaptablty. ng and Jan consdered cooperatve postonng usng acoustc range measurements for underwater sensor networks, ncludng networks formed by autonomous unmanned underwater vehcles. Severe multpath scatterng from the seabed and sea surface can result n naccurate range measurements. In an nhomogeneous medum, such as sea water, the drect path was not necessarly the strongest path or the frst arrval. hen, the range measurements based on the frst or strongest arrval could be sgnfcantly based. ng and Jan ntroduce heren a centralzed cooperatve postonng algorthm for underwater multple targets, referred to as the weghted Gerchberg-Saxton algorthm (WGSA). he proposed algorthm assumed that for each acoustc rangng channel, multple range measurements correspondng to several propagaton paths, one of whch was the drect path, were avalable for cooperatve postonng. he WGSA can be used to automatcally dentfy the drect path [3]. He et al. presented multple target localzaton va compressed sensng n the WSN. he multple target localzaton ssue was transformed nto compressed sensng ssue by desgnng teraton backtrackng algorthm usng mult-resoluton analyss dea. he achevement of ths algorthm was to save the energy of WSN nodes, by mnmzng nter-node communcaton, n the result of whch the lfetme of the WSN was prolonged, at the cost of ncreasng the computaton complexty n the fuson center nstead. However, the tme complexty of the algorthm was ncreased [4]. An ultra-wdeband 3-D postonng technque was descrbed for locatng wreless sensor nodes n extreme multpath envronments [5]. hey typcally constructed part of a network of sensors used to montor salent parameters such as temperature and humdty n large ndustral storage vessels. he novelty of ths approach was twofold. Frst, a leadng ultra-wdeband pulse edge detecton method was combned wth a seres of spatally dverse measurements to solate the lne-of-sght (LOS) component from the unwanted multpath nterference from the vessel walls. Second, a new locaton algorthm based on the statstcal analyss of sphercal functon ntersecton ponts was appled to the receved tme-doman data to mprove the estmaton of the tme of flght at each measurement locaton. hese two features combned to facltate both precson postonng and cumulatve error source estmaton and yelded resolutons approachng 2 cm n rch scatterng envronments. Lterature [6] descrbed moble anchor postonng, a range-free postonng method, whch made use of the beacon packets of moble anchor and the locaton packets of neghbor nodes to calculate the locaton of the nodes. he anchor node, whch was equpped wth global postonng system, e.g., GPS, broadcasts ts coordnates to the sensor nodes as t moved through the network. As the sensor nodes collect enough beacons, they were able to calculate ther locatons locally. But for sea-surface wreless sensor networks, the network connectvty and sngle-hop dstance was low because of ocean dynamc envronment, sea clutter, and other nfluences. herefore, to solve ths problem, we need to mprove ther network densty or ncrease the antenna heght, etc. As to the WSN constructed by flyng vehcles, the hgh-densty network n the ar can t be random deployed on account of ground control, arcraft loadng, cost and other factors. Meanwhle, caused by antenna scope, transmsson meda, costs and other nfluence, ths type of sensor was dffcult to mplement through mult-hop mesh to mprove connectvty and relable relatve postonng. 184
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 Generally, through the deployment of a lmted number of nodes accordng to a certan spatal confguraton to accomplsh specfc tasks, ths WSN s named as a sparse dstrbuted WSN (SWSN) n ths paper. Based on the dstrbuton characterstcs of the SWSN, we propose a relatve postonng algorthm for multple targets based on spatal constrants, whch s named as RPSC. In benchmark dened sea areas and unavalable solvng locaton parameters of the target nodes, the SWSN network relablty and precson of relatve postonng may be mproved by ntroducng spatal constrants and spatal correlaton condtons of the SWSN. Furthermore, the effectveness of the algorthm s testfed by Monte Carlo smulaton. 3. he Basc Prncple of Relatve Postonng for Multple argets Wthout loss of generalty, takng a sea-surface SWSN wth four sensors, namely, four nodes or targets, as an example for collaboratve task, the state equaton of the SWSN can be expressed as F U W, (1) k+ 1 = k+ 1/ k k + k + k 1 2 3 4, and denote the state vectors of four sea-surface sensors,.e., [ ] = x x x y y y z z z, ( x, yz, ) are the poston components of the surface sensor, whle x, yz, x, yz, are where = [ ] ( ) are the velocty components and ( ) the acceleraton components. F s the state transton matrx. Whle, U s the nput matrx and W s the system process nose, whch s assumed to be a zeromean Gaussan whte nose. It s worth notng that lterature gves ts adaptve varance Q as follows [7]. 2 Qk = 2ασaQ (2) where α s the recprocal of the maneuver (acceleraton) tme constant and Q s an ntal value of adaptve varance Q k. For example, α 1/6 for a lazy turn, α 1/2 for an evasve maneuver, and α 1for atmospherc turbulence. he localzaton protocols are classfed nto two categores: range-based protocol and range-free protocol. he range-based protocols employ dstance or angle estmaton technques to acheve fne accuracy, whch requre the use of expensve hardware. On the other hand, the range-free technques depend on the contents of receved messages to support coarse accuracy. Currently, avalable observaton nformaton for postonng SWSN has tme of arrval (OA), tme dfference of arrval (DOA), receved sgnal strength ndcator (RSSI), frequency dfference of arrval (FDOA) and other forms [8-9], commonly usng DOA. herefore, takng a SWSN based on OA among the target nodes as an example for followng dscussons, the relatve dstance measurements among the nodes are 2 2 2 1/2 rj = [( x xj) + ( y yj) + ( z zj) ] + vj (3) where (,, ) x yz ( j j and, j = 1, 2,..., 4) are the coordnates of the SWSN. hen, the nonlnear observng equaton s wrtten as ( ) zk = f k + vk where [ ] (4) z k = r12 r13 r14 r43, whch s the measurement vector, and v k s the measurement nose, whch s assumed to be a zero mean whte Gaussan nose vector wth covarance matrx R ( k). Convertng equaton (4) nto lnear format, t yelds the error equaton as follows: V = Aˆ L (5) where A s measurement equaton f ( k ) x k + 1/ k 4. he Mathematcal Model of Constrant Poston for SWSN Usng relatve dstance observatons r j among sensors for ndependent relatve postonng, f the rangng lnks of the sensor were unnterrupted, we may attan 12 range measurements. Fortunately, ths number s equal to the number of unknown coordnates of the four sensors, whle meets the requrements of the necessary number of observatons [1]. he transmsson lnks between the target nodes are easly unlocked, furthermore, reducng the connectvty on account of transmsson meda, node atttude, atmosphere, oceans envronment, and other nfluences. At ths moment, wthout loss of generalty, settng u as the number of the coordnates parameters for the whole SWSN nodes whle t as the necessary number of observatons n solvng equaton (5), the rank of the measurement matrx A s rank( A ) = t < u, and the number of rank defcency d = u t. Accordng to the prncple of least squares V PV = mn, where P s nonsngular empowerng matrx,the norm equaton s wrtten as where W= A PL, and N = W, (6) rank( ) = rank( ) = t < u N A PA. he normal equaton has many nfnte solutons whle N s sngular.. 185
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 In order to acheve the only soluton of the unknown parameters, the constrant condton of the gven datum S s S P ˆ =, (7) where rank( S ) = d, and AS =. Left multplyng AS by where AP, we can attan ( ) = = APAS NS, S s row full rank. P s named as the datum weght,and the dfferent P reflects the dfferences n datum constrants [1-11]. Generally, when SWSN conducts collaboratve detecton msson, e.g., underwater survellance, they must mantan a requred geometry confguraton by some control methods. In other words, the SWSN topology s correlated n adjacent moments. Accordng to the above-mentoned assumpton, two categores of spatal benchmark condtons are defned. a) Absolute dsplacement benchmark. As shown n Fg. 1, the sold lnes denote the poston lnes of the sensors before adjustment, whle the dashed lnes after adjustment. Pont O s the vrtual centrod. where ( x ˆ, y ˆ, z ˆ ) are the dsplacement values of poston adjustments. b) Drecton rotaton benchmark condton. As shown n Fg. 2, θ ( = 1, 2,..., 4) are the relatve rotaton angles centerng at vrtual centrod after poston adjustment. Fg. 2. Drecton rotaton benchmark of the SWSN. he drecton benchmark means that the sums of drecton rotaton angles before and after adjustment are equal to zeros n the respectve coordnate plane. hat s ( z y y z) ( x z z x ˆ ) ( y x x y) 4 ˆ ˆ = = 1 4 ˆ =, = 1 4 ˆ ˆ = = 1 (9) Fg. 1. Absolute dsplacement benchmark of the SWSN. where ( x, y, z ) denote the approxmate coordnates,.e., the system output at moment k 1. It follows that equaton (8) and equaton (9) can be unformly represented as hen, the absolute dsplacement datum condton means that the sums of dsplacement values before and after adjustment are equal to zeros n the respectve axs. hat s represented as 4 xˆ = = 1 4 yˆ = = 1 4 zˆ = = 1 (8) S ˆ =, (1) where = [ xˆ yˆ zˆ xˆ yˆ zˆ zˆ ]. 1 1 1 2 2 2 4 Accordng to the aforementoned sx benchmark condtons, the coeffcent matrx S s gven by 1 1 1 1 1 1 1 1 1 1 1 1 S = (11) z1 y1 z2 -y2 z3 y3 z4 y4 -z1 x1 -z2 x2 -z3 x3 -z4 x4 y1 -x1 y2 -x2 y3 -x3 y4 -x4 186
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 Accordng to the dfferent measurements and the confguratons of the SWSN, able 1 lsts the general expresson of the correspondng constrant benchmark S. Accordng to the above constrant datum S and the prncple of least squares, settng the functon ϕ as ϕ = V PV + 2 K ( S P ˆ ) = mn, we can acheve the followng equatons [11]. Nˆ + P SK = W, (12) ˆ S P = where K s the coeffcent matrx. Left multplyng the frst equaton n equaton (12) by S, and consderng AS = and NS =, we can attan S P SK (13) = able 1. he constrant benchmark S for the dfferent confguratons Confguraton Horzontal dstrbuton network Spatal dstrbuton network Measurement Datum Number Datum Parameter Range and angle d=2 2 dsplacements Range or range and angle d=3 Angle d=3 Range or range and angle Range d=6 Angle d=6 2 dsplacements and 1 drecton 2 dsplacements and 1drecton d=3 3 dsplacements 3 dsplacements and 3 drecton 3 dsplacements and 3drecton Dsplacement Benchmark 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 z y z y Drecton Benchmark y x y x z x z x y x y x For the quadratc form S P S can t be equal to zero, the matrx K= n equaton (13). Obvously, ϕ = V PV =mn. It s concluded that the solvng nature of the relatve postonng of the SWSN s unrelated wth the addtonal constrant datum S of the unknown parameters, namely, V PV s an nvarant, and the correcton value V obtaned from solvng sn t changed wth the dfferent constrant benchmark. In other words, under the condton wthout changng the fnal arguments precson, through ntroducng the spatal constrant benchmark, the numerous solutons problem of the measurement equaton s overcome due to lack of benchmark, namely, solvng ambguty. Left multplyng the second equaton n equaton (12) by P S, then addng the frst equaton of equaton (12), consderng K=, we can attan N + P SS P ˆ = W (14) ( ) At ths moment, coeffcent matrx ( N + P SS P ) s full rank. Settng matrx Q P as 1 QP = ( N + PSS P ), the fnal estmates of node localzaton parameters s 5. Smulaton and Analyss ˆ = QW (15) o valdate the effectveness of the proposed postonng algorthm wth benchmark constrant, we set a Monte Carlo smulaton wth 5 tmes. he four target nodes are deployed to a rectangle. he smulaton lasts for 225 s wth a 1-s samplng nterval. Durng 1 8 and 1743 225 s, the SWSN maneuver n a straght lne at constant velocty. Durng 81 1742 s, the SWSN maneuver n a semcrcle wth a rotatng speed of.19 deg/s. he ntal poston of node No. 1 s (1,, ) km, wth an ntal velocty of ( 15,, ) m/s. he precson of P 187
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 the two-way rangng s 1. m whle the precson of the velocty measurng s.2 m/s. he nfluence of the ocean current or ar turbulence s.5 m. able 2 lsts the statstc value of the nodes trackng error respondng to the envronmental nfluence by the proposed algorthm compared wth the conventonal Kalman flterng (KF). Fg. 3 shows the trackng error of the vrtual centrod as to the dfferent postonng algorthms. able 2. he statstcal value of trackng error for the vrtual centrod wth dfferent postonng algorthms. he error unt s meter. Maneuverng Mode Mnmum Value Maxmum Value Mean Value RMSE KF RPSC KF RPSC KF RPSC KF RPSC Straght lne maneuverng.1.76 4.35 2.61 1.69 1.47.82.74 Semcrcle maneuverng 2.14 1.35 7.19 3.17 4.28 2.13 1.58 1.6 From Fg. 3, t s shown that the RPSC algorthm has smlar trackng performance to that of the conventonal KF method when the SWSN maneuver n a straght lne wth constant velocty. Durng 1 8 s, the two methods have approxmately equal root-mean-square errors (RMSE) for trackng. However, when maneuverng n a semcrcle, the KF method has an obvously sudden change compared wth the RPSC algorthm, partcularly at the startng pont of semcrcular moton, e.g., at 81 s. However, at ths moment the RPSC algorthm uses spatal constrant benchmarks and the vrtual centrod O'of the SWSN tracks the sudden maneuverng tmely. node,.e., No. 1. he smulaton lasts for 2 s wth a 1-s samplng nterval. he SWSN maneuvers wth a constant velocty of 2 m/s, and other smulaton parameters are not changed. Durng 7 12 s, an external nterference s added to node No. 1, and the rangng sgnal s unlocked n the network consequently. Fg. 4 shows the trackng error of the four target nodes. Fg. 4 shows that, when node No. 1 loses synchronzaton at 7 s due to communcaton falure, ts postonng error s suddenly deterorated to a scale of [9.2~12.8] m. Other nodes affected by the nter-rangng error have a about 5-m postonng precson. After about 6 s, by recevng a sgnal-tonose rato (SNR), the RPSC algorthm determnes communcaton falure, deletes the wrong nformaton of the node No. 1. hen, the algorthm contnuously locates the rest nodes whle ncreasng the postonng precson. At 12 s, after reparng the rangng equpment of the node No. 1, the RPSC algorthm tmely utlzes the relatve measurements among the four nodes to accomplsh postonng msson and the postonng precsons of the four nodes are all recovered to the scale before communcaton falure. If by flterng technology to calculate the nodes postons, we may judge the sudden changes of the SWSN nodes wth the sensor fault detecton algorthm accordng to the flterng gan [12]. Fg. 3. rackng error of vrtual centrod wth dfferent postonng algorthms. As shown n able 2 and Fg. 3, at 81s, the trackng error of RPSC s 2.37 m. he trackng accuracy of the RPSC algorthm ncreases by 32.9 % compared to the KF method wth a 1.58 m precson. In order to verfy the processng performance of the RPSC algorthm to deal wth communcaton falure, a communcaton falure s assumed n a 6. Conclusons o mprove the precson and relablty of relatve postonng for the multple targets based on the SWSN, ths paper proposes a relatve postonng method on basc of space constrants by ntroducng a spatal constrant condton to solve ambguty of the relatve postonng due to mssng benchmark. Compared wth the common methods, e.g., Kalman flterng, the proposed RPSC algorthm, whch utlzes graphcal topologcal condtons among target 188
Sensors & ransducers, Vol. 158, Issue 11, November 213, pp. 183-189 nodes by ntroducng a spatal constrant benchmarks, can acheve a contnuous trackng of nodes whle SWSN network responds to envronmental sudden change. he relatve postonng accuracy s around 32.9 % and relatve poston devaton s less than 3 m. Fg. 4. rackng error of the four nodes when a communcaton falure happened to No. 1. he RPSC algorthm can respond tmely to communcaton lnk falure. When a node s destroyed, t s able to remove the node, whch ensures the relablty of relatve postonng for the multple targets. It s to note partcularly that we only consder how to mprove the locatng performance from the spatal constrants n ths paper, actually, SWSN also has some statstcal correlaton n the tme doman when the multple targets maneuverng. In the future, we may ntegrate the spatal-doman benchmark wth the tme-doman constrant to enhance the postonng performance for the targets accordng to a pror movement statstcs nformaton. Acknowledgements hs work was supported by the Natonal Scence Foundaton under Grant 61716, by the Natonal Scence Foundaton for Post-doctoral Scentsts of Chna (Grant No. 22125871,21149189), by Open Fund of State Key Laboratory of Informaton Engneerng n Surveyng, Mappng and Remote Sensng under Grant 1P3, and by the Start Fund of Laonng Provnce Doctor under Grant 21113. References [1]. Y. Jennfer, M. Bswanath, G. Dpak, Wreless sensor network survey, Computer Network, Vol. 52, Issue 12, 28, pp. 2292-233. [2]. S. D. Moreno, A. M. Pascoal, J. Aranda, Optmal sensor placement for underwater postonng wth uncertanty n the target locaton, n Proceedng of the IEEE Internatonal Conference on Robotcs and Automaton, Shangha, Chna, 9-13 May 211, pp. 238-234. [3].. ng, L. Jan, Cooperatve postonng n underwater sensor networks, IEEE ransactons on Sgnal Processng, Vol. 58, Issue 11, 21, pp. 586-5871. [4]. F. H. He, Z. J. Yu, H.. Lu, Multple target localzaton va compressed sensng n wreless sensor networks, Journal of Electroncs & Informaton echnology, Vol. 34, Issue 3, 212, pp. 716-721. [5]. G. D. John, S. Robn, J. P. Anthony, A threedmensonal postonng algorthm for networked wreless sensors, IEEE ransactons on Instrumentaton and Measurement, Vol. 6, Issue 6, 211, pp. 1423-1432. [6]. W. H. Lao, Y. C. Lee, S. P. Keda, Moble anchor postonng for wreless sensor networks, IE Communcatons, Vol. 5, Issue 7, 211, pp. 914 921. [7]. R. A. Snger, Estmatng optmal trackng flter performance for manned maneuverng targets, IEEE ransactons on Aerospace and Electronc Systems, Vol. 6, Issue 4, 197, pp. 473-483. [8]. M. Sun, K. C. Ho, An asymptotcally effcent estmator for DOA and FDOA postonng of multple dsjont sources n the presence of sensor locaton uncertantes, IEEE ransactons on Sgnal Processng, Vol. 59, Issue 7, 211, pp. 3434-344. [9]. L. Bn, Z. G. Zhang, S. C. Chan, DOA estmaton and trackng of ULAS wth mutual couplng, IEEE ransactons on Aerospace and Electronc Systems, Vol. 48, Issue 1, 212, pp. 895-91. [1]. W. M. u, L. L. Kuang, J. H. Lu, Postonng algorthm wth jont space-tme constrants for unmanned network-flyng vehcles, IEEE ransactons on Geoscence and Remote Sensng, Vol. 47, Issue 8, 29, pp. 2694-274. [11].. Z. Cu, Z. C. Yu, B. Z. ao, Generalzed surveyng adjustment, 1 st edton, Wuhan Surveyng & Mappng Unversty Press, Wuhan, 21. [12]. C. M. Hajyev, F. Calskan, Fault detecton n flght control systems based on the generalzed varance of the Kalman flter nnovaton sequence, n Proceedng of the Amercan Control Conference, San Dego, Calforna, USA, 2-4 June 1999, pp. 19-113. 213 Copyrght, Internatonal Frequency Sensor Assocaton (IFSA). All rghts reserved. (http://www.sensorsportal.com) 189