06 6 th Internatona Conference on Informaton echnoogy for Manufacturng Systems (IMS 06 ISB: 978--60595-353-3 LS-SVM Based WS Locaton Agorthm n LOS Envronments Hongyan Zhang, Zheng Lu, Bwen Wang Unversty of Eectronc Scence and echnoogy of Chna (UESC, Chengdu, Chna Peng Lu Space Star echnoogy Co., Ltd. and State Key Laboratory of Space-Ground Integrated Informaton echnoogy, BeJn, Chna Jyan Huang Insttute of Eectronc and Informaton Engneer n Dongguan Uestc, Dongguan, Chna huangyan@uestc.edu.cn Daoxn L orth Engneerng Co., LD of the Eectrfcaton Bureau Group, Crcc, ayuan, Chna ABSRAC: Locaton methods based on earnng theory perform we n wreess ceuar networks. hese methods may be further mproved snce range measurements among a nodes are not taken nto consderaton, whe these range measurements n the WS ocaton system are generay avaabe. In ths paper, we propose an mproved LS-SVM based ocaton agorthm to sove mobe ocaton probem n a LOS envronment. We extend LS-SVM method from wreess ceuar networks to WS ocaton system. Compared wth LS- SVM n wreess ceuar networks ony usng the range measurements between anchor nodes and bnd nodes, the proposed method can mprove the postonng accuracy by usng a the range measurements among the nodes. Moreover, steepest descent method s used n the proposed method to teratve search the optma poston estmaton of bnd nodes. he smuatons resuts n dfferent cases ustrate that the proposed agorthm outperforms the kerne method and LS-SVM method on ocaton accuracy. KEYWORDS: Mobe ocaton; Wreess Sensor etworks (WS; Least Squares Support Vector Machne (LS-SVM; Steepest Descent Method IRODUCIO Aong wth the quck deveopment of sensor technoogy and wreess communcaton technque, wreess sensor networks (WS have emerged as the tmes requre. A WS usuay conssts of tens or hundreds of wreessy connected sensors and the dfferent nodes n network share the resources wth each other. At present, WS have been wdey used for montorng and contro n mtary, envronmenta, heath and commerca systems []- [5]. However, there s a very mportant premse for reazaton of these appcatons, sensng nodes must be aware of ther own poston. Many methods have been proposed to estmate nodes poston. here are range-based ocazaton agorthms and range-free ocazaton agorthms for sensor network ocazaton. Exampes of the rangefree ocazaton agorthms can ncude centrod agorthm [6], Dv-Hop agorthm [7], API agorthm [8]. he range-free ocazaton agorthm does not need addtona hardware, thus, t s a costeffectve approach for the WS ocazaton probem. However, the range-free ocazaton agorthm can ony gve rse to a round estmate. he range-based ocazaton agorthms estmate the postons of nodes accordng to the dstance and drectona anges nformaton among nodes. he measurement technoogy of the range-based ocazaton agorthms are many wth the tme-ofarrva (OA, the tme-dfference-of-arrva (DOA, the ange-of-arrva (AOA, the sgna strength (SS based methods or hybrd ocaton methods. At present, non-ne-of-sght (LOS s the maor factor that affected WS ocaton precson. For LOS stuaton, the propagatng sgna between bnd nodes and anchor nodes goes through refectons and refractons off many obects n ts path. hs causes the sgna to arrve the recever 44
from a dfferent ange than the drect path between bnd nodes and anchor nodes, and for rangng measurements (or equvaenty, tme of arrva, t w add a arge postve error n addton to standard measurement error [9]-[0]. Athough many ocaton methods such as LOS dentfcaton agorthm [], nequaty constrant [] and scatter nformaton [3] were addressed to suppress LOS errors, ther performance mprovement s not sgnfcant snce a of these methods don t consder the pror nformaton on sampe ponts. Based on the pror nformaton of sampe ponts, severa earnng ocaton methods have been proposed to estmate the poston of bnd nodes [4]-[6] and obtan the hgher postonng accuracy. he method n [4] frst generates a LOS correcton map based on Krgng method, and then uses the correcton map to rectfy the dstorted bnd nodes ocaton. he method presented n [5] ntroduces the use of nonparametrc kerne-based estmators for ocaton of the bnd nodes usng measurements of propagaton deays. Furthermore, a LS-SVM based ocaton method n [6] s proposed to earn the reatonshp between the OA measurements and the bnd nodes ocaton. A of these methods mentoned n [4]-[6] perform we n wreess ceuar networks. hese methods may be further mproved snce range measurements among a nodes are not taken nto consderaton, whe these range measurements n the WS ocaton system are generay avaabe. hus, n ths paper, we propose an mproved LS-SVM based ocaton agorthm to sove mobe ocaton probem n a LOS envronment. We extend LS-SVM method from wreess ceuar networks to WS ocaton system. Compared wth LS-SVM n wreess ceuar networks ony usng the range measurements between anchor nodes and bnd nodes. he proposed method can mprove the postonng accuracy by usng a the range measurements among the nodes. Moreover, steepest descent method s used n the proposed method to teratve search the optma poston estmaton of bnd nodes. he smuaton resuts verfes the proposed method. he rest of ths etter s organzed as foows. Secton presents the proposed agorthm, and Secton 3 presents the smuaton resuts. Fnay, concuson s gven n secton 4. PROPOSED MEHOD In ths secton, we extend LS-SVM method from wreess ceuar networks to WS ocaton system. Compared wth LS-SVM n wreess ceuar networks ony usng the range measurements between anchor nodes and bnd nodes, the proposed method can mprove the postonng accuracy by usng a the range measurements among the nodes. 45 In genera, earnng agorthms consst of two phases: tranng and postonng. Durng the tranng phase, parameters of earnng agorthms are estmated usng measurements of tranng ponts. Durng the postonng phase the measurement of bnd nodes s performed, and then the poston of bnd nodes can be computed usng the parameters estmated n the tranng phase. For smpfcaton, we consder a OA based WS ocaton system. Assumng that devces ( x, y,,..., M s the poston of the th anchor node wth the known coordnates and devces x, y,,..., s the poston of the th ( tranng pont and r s the correspondng range measurement to the th anchor node. Gven a tranng data set of ponts: D {( R, v, L, } ( Wth nput data R r L r M R and output data R. In LS-SVM method, optma v probems can be descrbed as [6]-[7]: mn J ( w, e w w + γ e ( Subect to: v w ϕ( R + b + e (3 h Where ϕ( : R R s a nonnear mappng h n kerne space, weght vector w R, error varabe e [ e L e ], and b s a bas. J s a oss functon and γ s an adustabe constant. Accordng to optma functon ( and (3, we defne the Lagrange functon as: L( w, b, e, a w w + γ e a { w ϕ( R + b + e v } (4 Where a are Lagrange mutpers, as support vectors ( a R. he condtons for optmaty are gven by: L 0 w a ( ϕ R w L 0 a 0 b L 0 a γ e e L 0 ϕ( + b + e v 0 w R a (5 From (5, and emnaton of w and e, we get the foowng matrx equatons:
0 M b 0 M Ω + I a v γ Where [ ] k,,...,, [ ] (6 L, Ω ϕ( R ϕ( R, a a L a, k k v [ v L v ]. Accordng to Mercer s condton, there s mappng ϕ ( and kerne functon: K( R k, R ϕ( Rk ϕ( R (7 Assumng that ( x, y s the poston estmaton of the th bnd node, ( x, y s the true poston of th bnd node, r s the range measurement to the th anchor node. R [ r L rm ] s the correspondng vector of range measurements. Durng the poston phase, the ocaton of bnd nodes can be obtaned: v( R a K( R, R + b (8 Where the parameters a and b can be obtaned by sovng (6. Kerne functon has dfferent types, such as poy-nomna, MLP, spnes, RBF and so on. We w focus on RBF kerne whch corresponds to [5] [6]: k K( Rk, R exp( R R (9 σ he poston estmaton of bnd nodes by (8 may be further mproved snce range measurements among a nodes are not taken nto consderaton, whe these range measurements n the WS ocaton system are generay avaabe. hus, n order to mprove the ocazaton accuracy of bnd nodes n the WS ocaton system, we can use the range measurements between anchor nodes and bnd nodes and steepest descent method to teratve search the optma poston estmaton of bnd nodes. Cacuate the dstance among the poston estmaton of bnd nodes. r (x x + (y y Where ( x, y (0 s the poston estmaton of the th bnd node. he foowng crteron s used to determne the ne-of-sght (LOS path: r r ξ* σ ( r 46 Where r + s the (x x (y y + n correspondng range measurement between the th bnd node and the th bnd node, n s the standard range measurement nose and s subect to Gaussan dstrbuton wth zero-mean and varance σ, ξ s the dscrmnant coeffcent. When ( r hods, the r w be added to LOS range measurement set L. he sze of LOS range measurement set L s affected byξ, because the vaue of ξ determne r whether or not add to LOS range measurement set L. ormay dstrbuted data assumes that about 99% of the vaues n the sampe are wthn.58 standard devaton of the mean. We assume that the more bnd nodes n the LOS path, so n our smuaton, we choose: ξ.58 ( Accordng to formua (0 and (, we can defne the cost functon of dstance vector: K K ( (3 > J r r Where r L, and K s the number of eements for LOS range measurement set L. J Substtutng (3 nto x J and y, gves: K J x x ( r r x r (4 K J y y ( r r y r From (4, the steepest descent method s used to teratvey search the optma poston estmaton of the th bnd node: J J x y m m x y m u m (5 x y m m Where u s the step sze, m s the number of teratons. o sum up, here are the steps: ( Gven tranng data D {( R, v, L, }, cacuate [ ] a a a L and b from (6. ( Caucate the poston estmaton of bnd nodes from (8. (3 From(0, cacuate the dstance among the poston estmaton of bnd nodes.
(4 Determne the LOS path from (. 3 SIMULAIO RESULS Assumng n a Manhattan-ke urban envronment, the geometry of anchor nodes wth the known coordnates confguraton s shown n Fg.. he square regons of dmensons represent budngs, and the other regons represent streets. hs confguraton s used snce smar confguratons have been used to evauate other bnd nodes ocaton schemes [0] [4]-[5]. he coordnates of Anchor nodes are m, m, m. he tranng ponts are unformy dstrbuted n the street, and the postons of ten bnd nodes are randomy depoyed. he standard range measurement error of OA, brought by the measurement equpment, coud be modeed as a Gaussan random varabe wth zeromean. Fgure. Performance comparson wth dfferent number of tranng ponts. 3. Performance comparson wth dfferent standard range measurement error In ths smuaton, for a practca system t s nterestng to study the mpacts of the standard devatons of range measurements. Fg3, shows the MLE versus standard devatons of range measurements when the number of tranng ponts s 50. he standard devatons of range measurements are vared from 0m to 30m. It can be observed from fgure that the mean ocaton error ncreases wth the standard devatons of range measurements and the proposed method outperforms the kerne method and LS-SVM method. As the range nose becomes sma, the postonng accuracy of the proposed method ncreases. Fgure. Manhattan-ke urban envronment. In ths secton smuaton, to compare wth the proposed methods, kerne method [5] and LS-SVM method [6] are seected here due to them wde appcaton n the WS ocaton system. he poston error of bnd nodes s obtaned from the average of 500 ndependent runs, and shown as: MLE E x x + y y [ ( ( ] 3. Performance comparson wth dfferent number of tranng ponts (6 Fgure 3. Performance comparson wth dfferent standard range measurement error. 4 COCLUSIOS In ths smuaton, Fg. s performed to study the effects of the number of tranng ponts on the WS ocaton system. he number of tranng ponts s Athough ocaton methods based on earnng theory vared from 0 to 80, and the standard range perform we n LOS envronments wreess measurement error s 30m. It can be seen from fgure ceuar networks, these methods may be further that the mean ocaton error decreases wth the mproved snce range measurements among a number of tranng ponts and the proposed method nodes are not taken nto consderaton, whe these provdes much better performance than the kerne range measurements n the WS ocaton system are method and LS-SVM method. generay avaabe. In order to overcome ths shortcomng, we propose an mproved LS-SVM 47
based ocaton agorthm n ths paper to sove mobe ocaton probem n a LOS envronment. A comparson s performed between the proposed method and two other earnng methods (kerne method and LS-SVM method. he smuatons resuts n dfferent cases ustrate that the proposed agorthm outperforms the kerne method and LS- SVM method. As a resut, the proposed agorthm can enhance the postonng accuracy and obtan reabe postonng nformaton. ACKOWLEDGEMES hs work was supported by the Open Research Fund of State Key Laboratory of Space-Ground Integrated Informaton echnoogy under grant o.04_cxjj-dh_09, the atona atura Scence Foundaton of Chna (6075, the Fundamenta Research Funds for the Centra Unverstes (ZYGX03J06, the Guangdong Provnca atura Scence Foundaton of chna (05A030338. REFERECES [] Akydz, I. F., Su, W., Sankarasubramanam, Y., & Cayrc, E. (00. A survey on sensor networks. Communcatons magazne, IEEE, 40(8:0-4. [] Patwar,., Ash, J.., Kyperountas, S., Hero III, A. O., Moses, R. L., & Correa,. S. (005. Locatng the nodes: cooperatve ocazaton n wreess sensor networks. Sgna Processng Magazne, IEEE, (4:54-69. [3] Chu, W. Y., Chen, B. S., & Yang, C. Y. (0. Robust reatve ocaton estmaton n wreess sensor networks wth nexact poston probems. Mobe Computng, IEEE ransactons on, (6:935-946. [4] J, X., & Zha, H. (004, March. Sensor postonng n wreess ad-hoc sensor networks usng mutdmensona scang. In IFOCOM 004. wenty-thrd AnnuaJont Conference of the IEEE Computer and Communcatons Socetes (Vo. 4, pp. 65-66. IEEE. [5] Huang, J., Wang, P., & Wan, Q. (0. CRLBs for WSs ocazaton n LOS envronment. EURASIP Journa on Wreess Communcatons and etworkng, 0(, -4. [6] Su, X., & Le, Z. (0, October. Improved centrod agorthm ocazaton for WS based on Partce Swarm Optmzaton. In Computatona Integence and Desgn (ISCID, 0 Fourth Internatona Symposum on (Vo., pp. 39-4. IEEE. [7] L, Y. (0. Improved DV-HOP Locaton Agorthm based on Loca Estmatng and Dynamc Correcton n Locaton for Wreess Sensor etworks. Internatona Journa of Dgta Content echnoogy and ts Appcatons, 5(8. [8] Meng, F., L, X., & Zhou, Y. (0. he Improved Locaton Agorthm of Apt Based on Mdne Segmentaton for Wreess Sensor etwork. In Advances n Computer Scence and Engneerng (pp. 4-48. Sprnger Bern Hedeberg. [9] Caffery Jr, L. J., & Stüber, G. L. (998. Overvew of radoocaton n CDMA ceuar systems. Communcatons Magazne, IEEE, 36(4:38-45. [0] Huang, J. Y., Wang, P., Wan, Q., Chang, L. P., & Choo, F. H. (009, December. Robust east squares support vector machne agorthm for mobe ocaton. In Wreess Mobe and Computng (CCWMC 009, IE Internatona Communcaton Conference on(pp. 5-8. IE. [] Ma, L. C., Hwang, J. H., Cho,. H., & Km, J. M. (008. Adaptve Moduaton Method usng on-lne-of- Sght Identfcaton Agorthm n LDR-UWB Systems. he Journa of Korean Insttute of Communcatons and Informaton Scences, 33(A:77-84. [] Venkatraman, S., Caffery Jr, J., & You, H. R. (004. A nove OA ocaton agorthm usng LOS range estmaton for LOS envronments. Vehcuar echnoogy, IEEE ransactons on, 53(5:55-54. [3] Yang,., Yu, C., Wang,., & Jn, L. (0. A snge observer ocaton method under the scatter sgnas poston dsturbance stuaton: the constrant tota east square method. Scence Chna Informaton Scences, 54(:46-5. [4] L, B., Rzos, C., & Lee, H. K. (005. Utzng krgng to generate a LOS error correcton map for network based mobe postonng. Postonng, (09. [5] McGure, M., Patanots, K.., & Venetsanopouos, A.. (003. Locaton of mobe termnas usng tme measurements and survey ponts. Vehcuar echnoogy, IEEE ransactons on, 5(4:999-0. [6] Sun, G., & Guo, W. (005. Robust mobe geo-ocaton agorthm based on LS-SVM. Vehcuar echnoogy, IEEE ransactons on, 54(3:037-04. [7] Van Geste,., De Brabanter, J., De Moor, B., Vandewae, J., Suykens, J. A. K., & Van Geste,. (00. Least squares support vector machnes (Vo. 4. Sngapore: Word Scentfc. 48