Th ree 2dim ensiona l se lf2loca liza tion schem e fo r w ire le ss sen so r ne two rks

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1 Journal of Beijing University of Aeronautics and A stronautics June 2008 Vol. 34 No16 (, ) : AP IT23D (App roximate Point2In2Tetrahedron),,,., AP IT23D 40% AP IT23D,, : ; ; : TP 393 : A : (2008) Th ree 2dim ensiona l se lf2loca liza tion schem e fo r w ire le ss sen so r ne two rks L iu Yuheng Pu Juhua He Yang Xiong Zhang ( School of Computer Science and Technology, Beijing University of Aeronautics and A stronautics, Beijing , China) Ab s tra c t: A novel three2dimensional ( 3D ) self2localization scheme AP IT23D ( app roxim ate point2in2te2 trahedron) was p resented for w ireless sensor networks (W SN s). The target sensor perform ed AP IT23D test to judge whether it resided inside or outside of tetrahedrons, which narrowed down the possible location areas ( PLA ). Then, AP IT23D averaged the centers of gravity ( COG) of the intersection of PLA as the unknown sensorπs estim ated location. Simulation results indicate that, as a range2free scheme, AP IT23D can achieve lo2 cation accuracy w ithin 40% of radio range, while the comm unication cost remains reasonable comparing w ith its 2D counterpart. Since AP IT23D depends on no ranging measures or global infrastructure, it p resents a low2 cost solution for self2localization of densely dep loyed and large scale W SN s in 3D spaces. Ke y wo rd s: w ireless sensor networks; self2localization schemes; three2dim ensional space,, [ 1 ] ;, [ 2 ].,,,,,. ( GPS, Global Positioning System ),,,, Cricket [ 3 ], AHLos (Ad2Hoc Localization System) [ 4 ] AOA APS (Adhoc Positioning System based on : : (05E551010) ; (XK ) : ( ),,,, hengly@cse. buaa. edu. cn.

2 Angle Of A rrival) [ 5 ].,., AP IT(App roximate Point2In2Triangle) [ 6 ],,,,,,, AP IT, AP IT23D,, 1 AP IT23D,. (Anchor Nodes),., AP IT2 3D : 4, ( PLA, Pos2 sible Location A rea)., PLA,,., P IT23D ( Point2 In2Tetrahedron) 1. 1 P IT23D, : 4 : A ( a x, a y, a z ), B ( b x, b y, b z ), C ( c x, c y, c z ) D ( d x, d y, d z ) M AB CD ( )., 2 : 1 M AB CD, M, A, B, C D ( 1a ). 2 M AB CD,, M, 4 A, B, C D ( 1b ). a 1 b 2 1 P IT23D 1 : M M 4 A, B, C D 1a, M AB CD, X, 2 : 1) X AM, BM, CM DM., X AM, Y,, A Y < AM, M A,. 2) X MAB C, MB CD, MACD MABD, X MAB C. M AB C ( ), Z. Z AB C,,. 2 : X M Z, R. ZR < ZM,, B R < BM, B,. X MAB Z, MB CZ MACZ,, X MB CZ, S, S B CZ, T, T B CZ. B CZ, : B T B Z CT CZ. B ZC B TZ + CTZ >,,,, B T < B Z CT < CZ, B T < B Z. ST < M Z,, B S < BM,

3 6 : 649 B,. AX, BX, CX DX, M X A, B, C D, M M 2 : 1b, AB CD M, 4 M, AB C, M D M, Y. M X,, AX < AM, B X < BM, CX < CM DX < DM, 4 A, B, C D; M, M Z, 4 A, B, C D. 2, P IT23D :, M M AB CD 4 A, B, C D, M ABCD, M AB CD. P IT23D, P IT23D, 2 : 1) ; 2)., 2, PIT23D ) (RSS, Received Signal Strength) :,,.,,, 2, [ 7 ]. [8 ] (DO I, Degree of Irregularity) : RSS real = Random [ (1 - DO I) RSS, (1 + DO I) RSS] (1), RSS real, RSS, Ran2 dom ( a, b), [ a, b ], DO I [ 0, 1 ]. RSS AP IT23D 2,, 2, P IT23D ( AP IT23D, App roxim ate Point2In2 Tetrahedron) : M M AB CD 4 A, B, C D, M AB CD ( 2a) ;, M AB CD ( 2b)., P IT23D. a b 2 A PIT23D 1. 3 A P IT23D AP IT23D, AP IT2 3D.,, ID.,.,,

4 ,., PLA., PLA,. AP IT23D : Receive location beacons { ( x i, y i, z i ) } from N an2 chors. Exchange N anchors RSS and Location information w ith neighboring sensor nodes. PLASet = / / the set of tetrahedrons in which I re2 side, also denoted as Possible Location A rea For ( each tetrahedron T i N 4 If (AP IT23D ( T i ) = = TRUE) PLASet = PLASet { T i } If ( Tested Num ( PLASet) } tetrahedrons) { = = MAX) break; / 3 Center of gravity (COG ) calculation 3 / Estimated Position = (COG PLASet) ; AP IT23D,, AP IT23D., AP IT23D,,, 3 (ND = 30, DO I = 0. 1), AH., PLA,,, ANR, AP IT23D, ANR,,,. AH 40, 0. 4R (R ), [ 6 ] ND.,, AP IT23D,, AP IT2 3D Matlab AP IT23D. : 1) (ND, Node Density) : ; 2) (AH, Anchor Heard) : ; 3 ) (ANR, Anchor to Node Range Ratio) ; 4) DO I AH. 4 (AH = 32, DO I = 0. 1) DO I., DO I, AP IT23D, AP IT, DO I AP IT23D, AP IT23D

5 6 : (AH = 32, ND = 30), AP IT AP IT23D. 1 B 1, ANR, 1 B ANR 2., B ( ), S ( ), C AP IT = ANR 4 AH AD B ( ) + ND S ( ) (2), 1, AP IT23D C AP IT23D = ANR 4 AH ND [B ( ) + 1 ] + ND [S ( ) + 1 ] (3) (2) ( 3), AP IT23D AP IT : C = ANR 4 AH ND + ND (4) (4), ANR ND,,., 6 2 (4). 6 (ND = 30, ANR = 4) 3 P IT23D, AP IT23D,, AP IT23D,, AP IT2 3D., ( References) [ 1 ] D ragos N. Positioning in ad hoc sensor networks[ J ]. IEEE Net2 work, 2004, 18 (4) : [ 2 ] Rao A, Ratnasamy S, Papadim itriou C, et al. Geographic rou2 ting without location information [ C ] / /MobiCom. San D iego: ACM Press, 2003: [ 3 ] Priyantha N B, Chakraborty Anit, Balakrishnan H. The cricket location2support system [ C ] / /MobiCom. New York: ACM Press, 2000: [ 4 ] Savvides A, Han C C, Strivastava M B. Dynamic fine2grained localization in ad2hoc networks of sensors [ C ] / /MobiCom. Rome: ACM Press, 2001: [ 5 ] N iculescu D, Nath B. Ad hoc positioning system (APS) using AOA [ C ] / / InfoCom, IEEE. San Francisco: IEEE Press, 2003: [ 6 ] He Tian, Huang Chengdu, B lum B M, et al. Range2free locali2 zation schemes for large scale sensor networks[ C ] / /MobiCom. San D iego: ACM Press, 2003: [ 7 ] Zhou Gang, He Tian, Krishnamurthy S, et al. Impact of radio irregularity on wireless sensor networks[ C ] / /MobiSys. Boston: ACM Press, 2004: [ 8 ] Hu L ingxuan, Evans D. Localization for mobile sensor networks [ C ] / /MobiCom. Philadelphia: ACM Press, 2004: ( : )