Localization Algorithm for Sparse-Anchored WSN in Agriculture

Transcription

1 A Localzaton Algorthm for Sparse-Anchored WSN n Agrculture Chunjang Zhao 1,Shufeng Wang 1, Kay Wang 1, Zhongqang Lu 1, Feng Yang 1, Xand Zhang 1 1 Bejng Research Center for Informaton Technology n Agrculture, Bejng, Chna, { Zhaocj,Wangsf,Wangy,Luzq,Yangf,Zhangd}@nercta.org.cn Abstract. The locaton nformaton s very crucal for the sensng data n modern agrculture. However, postonng errors and sparse anchors are two ey problems that should frst be solved for the localzaton of the sensor nodes. We proposed a novel algorthm to tacle wth these challenges. When the system of adjacent anchor dstance equatons s ll, a mnmzed-stress search algorthm (MSS) can decrease postonng error greatly. A collaboratve sparse-anchored scheme (CSA) has an ecellent postonng effect on low densty of anchor, specfcally on margnal sensor nodes. Our epermental result verfed valdty and accuracy of the algorthm. It mproved feasblty and cost of WSN postonng technque, sgnfcantly. Keywords: WSN, localzaton, Sparse anchors, Mult-hop cooperaton. 1 Introducton Recent advances n mcro-electro-mechancal systems (MEMS) technology, wreless communcatons, and dgtal electroncs have enabled the development of low-cost, low-power, multfunctonal sensor nodes that are small n sze and communcate n short dstances [1]. These sensor nodes wth sensng, data processng, and wreless communcatng capabltes can be self-organzed together n ad-hoc mode and be deployed n pre-determned or random fashon n naccessble terrans or dsaster relef operatons. Therefore there are a wde range of applcatons for wreless sensor networs (WSN): mltary, nfrastructure securty, envronment and habtat montorng, ndustral sensng, traffc control, etc []. Especally,WSN are appled to vared felds n agrculture to mprove the agrcultural nformatzaton n recent years [3]. In the last decade, WSN have been ncreasngly appled n modern agrculture [4].Sensor nodes can be used for montorng a wde varety of agrcultural parameters that nclude the followng phenomena: temperature, humdty, mosture, lghtnng condton, sol maeup, lvestoc ID, and so on [5]. However, the sensng data s not meanngful wthout the company of the sensng locaton. Naturally, the localzaton of WSN nodes s very crucal for sensng data usage. Furthermore,

2 accurate locaton mght also be useful for routng and coordnaton purposes n large scale WSN. The Global Postonng System (GPS) s the most well nown locaton servce n use nowadays. The approach taen by GPS, however, s unsutable for the low-cost, low -power large scale sensor networs nodes n agrculture because of the followng reasons: cost, power consumpton, naccessblty, mprecson, sze [6]. It s necessary to develop an alternatve nepensve, more applcable localzaton approach. Ths paper wll present the novel localzaton algorthm n sparse-anchored WSN. The rest of the paper s organzed as follows: The net secton gves a bref eplanaton of theoretcal bacground. Secton 3 s our proposed algorthm of localzaton system. Secton 4 descrbes the resoluton of the sparse-anchored problem. Secton 5 s epermental results and analyss. Fnally, secton 6 concludes the paper. Theoretcal bacground Trangulaton, scene analyss, and promty are the three prncpal technques for locaton sensng [7]. Typcally, lateraton s the most popular locaton method that employs trangulaton technque. Lateraton computes the poston of an unnown node by measurng ts dstance from multple reference postons. Calculatng an object's poston n two dmensons requres dstance measurements from 3 non-collnear anchors as shown n Fgure 1. In 3 dmensons, dstance measurements from 4 noncoplanar anchors are requred. But, these crcles can not ntersect at the same pont sometme for the error of dstance measurng. Fgure 1. Lateraton localzaton scheme. The most classc dstrbuted lateraton algorthm s AH-Los algorthm proposed by Andreas Savvdes, et al. Ths algorthm defned three operatonal prmtves: atomc multlateraton, collaboratve multlateraton and teratve multlateraton. If an unnown node have three or more neghborng anchors and have measured the dstance to neghborng anchors, atomc multlateraton can be deployed to determne the poston of unnown node. Fgure (a) llustrates a topology for whch atomc multlateraton can be appled.

3 Fgure. Multlateraton eamples The error of estmated poston can be epressed as the dfference between the measured dstance d and the estmated Eucldean dstance (Equaton 1). The and y are the estmated coordnates for the unnown node. Accordng to the mnmal mean square estmate (MMSE) [8],.e. Equaton, the optmal soluton of and y can be obtaned. f (, y) d ( ) (y y ) (1) n 1 mn(f (, y)) mn f (, y) () If a node has three or more neghborng anchors, an over-determned system wth a unque soluton for the poston of unnown node can be yelded. By settng f (,y)=0,squarng and rearrangng terms, equaton 1 became equaton 3. y y y d ( y ) (3) If unnown node has neghborng anchors, equatons le equaton 3 can be acheved. Then, we can elmnate the y terms by subtractng the th equaton from the rest, depcted as equaton 4. ( - ) (y - y )y d - d ( y ) ( y ) (4) Ths system of equatons has the form of AX = b and can be solved usng the matr soluton for MMSE. Collaboratve multlateraton can be deployed n the stuaton where the number of 1-hop neghborng anchors s less than 3, but mult-hop anchors can provde adequate nformaton to locate the poston of the unnown node. Fgure (b) llustrates a basc eample. The unnown node 1 has two 1-hop anchors and two -hop anchors through the unnown node. We can buld the system of lnear equatons le equaton 4 and then obtan the soluton of equatons usng MMSE. When an unnown node acheved ts poston usng atomc multlateraton or collaboratve multlateraton, t can nform ts neghborng unnown nodes that t has become an anchor. If the nformed unnown node satsfes the condtons of atomc

4 multlateraton or collaboratve multlateraton, t can estmate tself poston. Ths process can be teratve untl the postons of all the nodes that can have three or more anchors are estmated eventually. Ths s teratve multlateraton prncple. In ths paper, we proposed novel algorthms to mprove poston error and poston rato under sparse-anchored condton. 3 Localzaton algorthm AH-Los algorthm elmnates the y term n equaton 3 by subtractng the th equaton from the rest. Essentally, the soluton of system s the ntersecton of common chord equatons between th crcle and th crcle. As depcted n fgure 3, equatons 5 represent 3 crcles wth each anchor poston as center and the dstance from the unnown to the anchor as radus. The frst equaton subtracted from the second equaton gves common chord lne L1 and The frst equaton subtracted from the thrd equaton gves common chord lne L. The ntersecton of lne L1 and the lne L s the estmated poston of the unnown node. y y y d ( y y yy d ( y) (5) y 3 y3y d3 ( 3 y3 ) ) Fgure 3. The ntesecton of L1 and L s the estmated poston. When ths common chord lnes s parallel to each other, only small error of estmated anchor poston can mae a very large error of the ntersecton poston. As demonstrated n fgure 4, three anchors upsde are close to each other and a anchor downsde s far from the other anchors, the soluton of equatons has hgher error. Let dfferent anchor equaton as the subtrahend, the soluton have dfferent error. The red crcle represents the real poston of the unnown node. Four red asterss denote four

5 neghborng anchors of the unnown node. Four blue trangles denote the estmated poston wth dfferent anchor as the subtrahend. Fgure 4. Let dfferent th as the subtrahend,have dfferent error Our algorthm does not elmnate y term n equaton 3. Settng z y, we can get the system of equatons as follows: z 1 y1y d1 (1 y z y y d ( y z The system of equatons has the form of AX =b where The soluton can be solved by X (A A) T 1 T A b. At the same tme, usng delta z - y as judge condton, we can judge f the system of equatons s ll. When the condton number of the equatons s very large, the delta s also very large. Ths means the poston error s too large to locate the node. We proposed the mnmzed-stress search localzaton algorthm (MSS) to tacle wth ths stuaton. Before presentng the algorthm, we frst mae some defntons. Defnton 1. The dstance between the current poston of the unnown (,y) and ) 1 ) (6) yy d ( y ) and 1, 1, y1 1,, y... 1,, y A X z,, y T d 1 1 y1 d y b.... d y

6 the th neghborng anchor (,y ) s d cur and the measured dstance to th neghborng anchor s d.the stress from th anchor s F where As d cur,> d, the drecton of F s ponted to the th anchor from current poston, vce versa. Defnton. The resultant stress of the unnown, F component stress F., s composed of every The process of the MSS algorthm s descrbed as follows: Step 1: when the system of equatons 6 s ll, we frst select two anchors whch the dstance between them s the farthest and then compute the ntersecton of two anchor crcles whch radus s the measured dstance from anchor to unnown node. Step : We select each of ntersecton as search orgnal poston and compute the each component stress F and then composed the resultant stress F by equaton 7 and equaton 8, respectvely. Step 3: Pulled by the resultant stress F, each estmated poston move to new poston ( n,y n). Net, we judge f the new poston have less dstance error than the old poston As shown by equaton 9, F, F y,lstep denotes as component, y as component and the steplength for movng, respectvely. Step 4: If F ((1 d / d cur ) * ( y F 1 F... F n n F (8) y Xgma L L 1 Xgma now Xgma, old 0 n, y0 y n ), (1 0 0 d step step (d, Otherwse steplength steplength / and repeat step for several tmes. Step 5: when estmated poston cannot move on, we turn F 90 degrees clocwse or 90 degrees counter clocwse to test a new marchng drecton. If we fnd a new drecton, step s repeated agan. Otherwse the process s termnated. So we estmated two possble fnal postons. Step 6: We compare the two fnal dstance resduals and then select the fnal poston wth the smallest resdual as the poston of the unnown node. The MSS algorthm have overcome the defect of hgher poston error when the equatons s ll-condtoned and conquered the drawbac of one startng pont that s ease to get n the local mnmum. A sample process of MSS algorthm s demonstrated n the fgure 5. * F * F cur / d y cur d ) ) * (y y)) (7) (9)

7 Fgure 5. The eample of MSS algorthm process 4 Sparse-anchored localzaton algorthm After teratve multlateraton localzaton s repeated, The poston of the unnown nodes that only have two anchors or one anchor eventually can not be determned We proposed to utlze the collaboraton of ts one or two anchors to locate the poston of the unnown. Under the condton of only two adjacent anchors, the unnown can estmate tself poston U or U, as shown n fgure 6. Rma Rma A3 A4 U A1 A U Unnown node Anchor Fgure 6. Localzaton algorthm wth only two -hop anchors The unnown sent the two possble postons, U and U to ts 1-hop anchors,.e. A 1 and A, and then the one-hop anchors pass the possble postons to the -hop anchors,.e. A 3.and A 4.The two-hop anchors wll judge f U or U s n ts mamum sensng range, R ma. Once ether of the two possble postons belongs to the mamum sensng range of A 3 or A 4 by computng dstance, the unnown node s nformed that ths poston s ecluded from the estmated poston because A 3 or A 4 have not been ts 1-hop anchor. When each of U and U can not be ecluded, ther mdpont s taen as the estmated poston. Ths method can be deployed n the larger

8 scale, such as 3-hop scale or mult-hop scale. Another case s where the unnown node only has a 1-hop anchor. The prevous algorthm wll be helpless. We wll resort to another method to locate the poston appromately. I4 Rma I3 I5 I d I1 I6 Unnown node Anchor Intersecton pont Estmated poston Fgure 7. The Localzaton algorthm wth only one 1-hop anchor As shown n fgure 7, the unnown node has one 1-hop anchor and three -hop anchors. The crcle wth the dstance d as radus has s ntersecton ponts wth the mamum sensng range of three -hop anchors,.e. I 1, I, I 3, I 4, I 5 and I 6,. We can compute the dstances from the ntersecton ponts to three -hop anchors, respectvely. Once the dstance for the ntersecton pont s less than R ma (the largest sensng range), the ntersecton pont s ecluded. Fnally, the ntersecton ponts, I 1 and I 6, are left. So the estmated poston s on the pn arc from I 1 to I 6. We can tae the mdpont of the arc or the mdpont of the lne from I 1 to I 6 as the estmated poston. As ths scheme has a larger error, the estmated poston should not be taen as anchor n the teratve process. 5 Epermental results To verfy our proposed localzaton algorthm, we randomly generate a scenaro wth 00 nodes wthn a square feld (100100) n Matlab. These nodes are deployed randomly n the feld and can measure the dstances to the adjacent nodes n the sensng range R by RSSI or other ranged methods. The anchor rato to all nodes s A rato. To smulate real ranged error, the true dstances (d) are blurred wth Gaussan nose, e r. So the measured dstance have the dstrbuton, d*(1+n(0, e r )). When the transmsson range of the nodes(r), the range error(e r ) and anchor rato (Arato) s set to 15, 5% and 10%, respectvely, the topology s shown n fgure 8. The blue trangles represent the anchors, the red crcles represent the unnown nodes, and the azury lnes represent the wreless connectons between the nodes.

9 Fgure 8. The topology wth R=15, e r =5% and A rato =10%. Fgure 9 shows the postonng result of our MSS and CSA algorthms. The startng pont of the blue arrows represents the estmated poston and the end pont of the blue arrows represents the real poston. The longer the blue arrow s, the larger the postonng error s. when there are appromate 9 connectvty degree and 10 percent anchor rato, AH- Los algorthm can acheve 90 percent poston rato and 6-7% poston error (about 0 cm) [9,10]. But under sparse-anchored condtons, there are hgher poston error and lower poston rato. Fgure 9. Fnal poston estmaton result. Under the same stuaton, our algorthms have a hgher postonng rato of 100% and lower average postonng error of.45%.

10 Anchor densty has a sgnfcant effect on the postonng rato and error. Contrast to the AH-Los algorthm, the postonng rato was shown wth varous anchor densty n fgure 10. As shown, when the percentage of anchors s low, our MS-CSAL algorthm substantally ncreased the postonng rato. These algorthms can not only effectvely decrease the number of anchors to lower the cost of WSN, but also mprove the localzng of the unnown node on the edge of the networs. AH-Los algorthm our SM-CSAL algorthm Postonng Rato Anchor Percentage Fgure 10. Effect contrast between AH-Los and MSS-CSPL 6. Concluson We have proposed a novel MSS-CSA algorthm for WSN postonng n agrculture. The mnmzed-stress algorthm mproved the postonng precson greatly when the system of mult-anchors postonng equatons s ll. The collaboratve sparse-anchored localzaton algorthm has solved the postonng problem of anchor defcency, specal for the unnown node on the edge of WSN n agrcultural postonng. Our smulaton eperments have verfed the effect of the algorthm n terms of postonng rato and postonng errors. Our future wor wll be concentrated on the Zgbee-based mplementaton and analyss of error propagaton n agrcultural postonng. Acnowledgments. Ths wor s supported by Natonal 11th Fve-year Plan for Scence & Technology of Chna under Grant no. 009BADB6B0. References 1. Hautefeulle, Matheu; O'Mahony, Conor; O'Flynn, Brendan; Khalf, Krmo; Peters, Fran. A MEMS-based wreless multsensor module for envronmental montorng. Mcroelectroncs Relablty, v 48, n 6, p , June 008.

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