BAYESIAN MOBILE LOCATION IN CELLULAR NETWORKS

Transcription

1 BAYESIAN MOBILE LOCATION IN CELLULAR NETWORKS Mhamed Khalaf-Allah Iniue f Cmmunicain Engineering, Univeriy f Hannver Appelrae 9A, D-3067, Hannver, Germany phne: , fax: , khalaf@ik.uni-hannver.de eb:.ik.uni-hannver.de Kyandghere Kyamakya Deparmen f Infrmaic Syem, Univeriy f Klagenfur Univeriäraße 65-67, A-9020, Klagenfur, Auria phne: , fax: , kyamakya@iy.uni-klu.ac.a eb:.iy.uni-klu.ac.a ABSTRACT Deermining he lcain f mbile ain culd be achieved by cllecing ignal rengh meauremen and crrelaing hem pre-calculaed ignal rengh value a reference lcain. Thi mehd i advanageu, becaue n LOS cndiin are needed, i can rk even ih ne bae ain BSnd i implemenain c are prey l. Hever, he crrelain prce need an apprpriae likelihd funcin uch a ha prvided by Bayeian aiical eimain apprache. They ue all available infrmain urrunding candidae hyphee deermine heir likelihd. In hi paper, e preen a Bayeian mbile lcain algrihmnd h i perfrmance by field meauremen in a rking GSM nerk.. INTRODUCTION The key driver fr develping mbile ain MS lcain echnlgie in he USA a E-9. In he EU, i a cmmercial ervice in he fir placend laer E-2 ha uilize he ame echnique. Emergency call lcain ha becme a requiremen in fixed and cellular nerk in he USA in 996 [] and in he EU in 2003 [2]. Piining f a MS i cnidered mre criical becaue MS uer and hence MS riginaed emergency call are cninually increaing. I i eimaed ha abu 50% f all emergency call in he EU are MS riginaednd he expeced endency i riing [2]. While emergency call lcain culd be cnidered he m impran f lcain-baed ervice LBS due i urgency fr life and prpery afey, cmmercial LBS are believed make increaing revenue fr nerk perar h culd prvide cumer ih aracive and ailred ervice [3]. The MS lcain i uually achieved uing aellie-baed r cellular yem baed mehd [4], [5]. Thee mehd differ in erm f accuracy, cverage, c, per cnumpin and yem impac. Saellie-baed echnlgie cme in flavur: and-alne GPS r Aied-GPS A-GPS. Main draback are per cnumpin, need f clear vie a lea fur aellie fr and-alne GPS and he c f inegraing GPS receiver in he mbile erminal. Furhermre, A-GPS luin require he addiinal inallain f reference GPS receiver. Cellular yem baed echnique include: cell-id CI, ime f arrival TOA / uplink ime difference f arrival U- TDOA, enhanced berved ime difference E-OTD and angle f arrival AOA. There are many varieie f he cellid mehd [6], [7], namely CI, CI+TA iming advance f erving cell, CI+TA f everal adjacen cell hi i uually n he cae in GSM nerknd CI+TA+ received ignal level. Here, he meauremen can be inpu an empirical frmula r cmpared ih he enrie f a lk-up able in rder eimae diance bae ain r yield a lcain eimae f he MS repecively. The laer handling i knn a daabae crrelain mehd DCM [8] []. The lcain ervice i divided in hree level [7] accrding he accuracy requiremen f he differen applicain. The le accurae i he baic ervice level, hich uilize CI mehd. Technique ued fr he enhanced ervice level are E-OTD, TOA/U-TDOA, r AOA. A-GPS i uually emplyed fr he exended ervice level, hich i he m accurae lcain ervice. Cell-id mehd are he imple implemen becaue hey uilize nly nerk available infrmain. Thu, hey are advanageu in erm f c, cveragend yem impac. TOA/U-TDOA and E-OTD baed echnique need muual ynchrnizain f a lea hree bae ain BS hich i difficul achieve. Inallain f pecial anenna a BS i a mu fr he implemenain f AOA mehd. Lcain accuracy f TOA/U-TDOA, E-OTD and AOA apprache are everely influenced by mulipah prpagain hich i he dminan prpagain cndiin in buil-up envirnmen.

2 Baic ervice level lcain mehd ill ill be needed al hen mre accurae echnlgie are fully available. They ill achieve piining fr applicain ih l accuracy requiremen; hey ill be deplyed in area f he nerk here mre accurae mehd are n uppred; and finally, hey ill rk a backup in cae he accurae echnique fail fr any rean. Unlike he US mandae, he EU lcain requiremen d n pecify accuracy r andard. Thi a anher rean ha puhed ard he implemenain f CI mehd by EU nerk perar. Hever, lcain accuracy i in he range f hundred meer up everal kilmere depending largely n he envirnmen characeriic, nerk layu and prpagain cndiin. Therefre, imprving piining accuracy f CI echnique i an acive reearch pic. In hi paper, e preen a daabae crrelain mehd DCM ihin a Bayeian aiical framerk fr mbile lcain in GSM nerk. The prped lcain algrihm i a generic ne ha culd al be applied her cellular yem and irele nerk. The mahemaical derivain and he pracical implemenain f he prped Bayeian filering algrihm are prvided in he nex ecin. In ecin 3, e dicu he mdel f he irele envirnmen. Experimenal reul are given in ecin 4. Secin 5 ummarize he paper. 2. THE BAYESIAN LOCATION ALGORITHM 2. Mahemaical Derivain f he Baye Filer Baye Filer BF [3], [4] i a prbabiliic framerk fr ae eimain ha uilize he Markv aumpin i.e. pa and fuure meauremen are cndiinally independen if he curren ae i knn. In he cae f mbile lcain, BF eimae he perir belief diribuin f he MS piin given i prir belief erie f meauremen, and a mdel f i rld envirnmen. The prir belief i a prbabiliy diribuin ver all lcain f he given cell cmbined ih he TA meauremen befre aking he MS acin and meauremen in accun. The perir belief i he cndiinal diribuin f hee lcain given he MS acin and meauremen. The rld mdel i a daabae ha cnain prediced a he candidae lcain. The perir belief diribuin i expreed a = 0 : 0 : Where i he perir belief ver he ae piin f MS a ime, i he ae a ime re he 0: 0 a 0: meauremen daa frm ime up ime re he acin perfrmed by he MS frm ime 0 up ime nd m i he rld mdel. Applying Baye rule equain e ge =, 0: 0: P 0: 0: 0: 0: Herecin and meauremen are aumed ccur in an alernaive equencelhugh in realiy hey ake place cncurrenly. They are eparaed nly fr cnvenience and clariy f he mahemaical reamen. Emplying Markv aumpin he fir erm in he nminar, and ning ha he denminar i a cnan prbabiliy denedη relaive, equain 2 i rerien a Bel =η, 3 0: 0: m Wih he help fη, hich i al called nrmalizain facr, he reuling prduc ill alay inegrae. Thu, Bel repreen a valid prbabiliy diribuin. Expanding he righ m erm in 3 uing he Therem f al prbabiliy ill reul in = η, 0:, a0: 0:, a0: d 2 Applying Markv aumpin he fir erm in he inegrain and ning ha he ecnd erm i imply e bain = η d Exprein 5 i a recurive equain ha i uually cmpued in ep called predicin and updae [3], [4]. Predicin ep: Bel 6 Where = d Bel a 4 5 i he perir belief ju afer execuing he acin and befre incrpraing he meauremen, and, a i he MS min mdel, i.e. he raniin prbabiliy ha ell u h he ae evlve ver ime a a funcin f he MS mvemen. Thee mvemen are undeerminable ihu an exra meauremen urce, i.e. inerial meauremen. Updae ep =η Bel 7

3 Where i he meauremen mdel ha pecifie he prbabiliic la accrding hich meauremen are generaed frm he ae, i.e. meauremen are imply niy prjecin f he ae [4]. Bh min and meauremen mdel decribe he dynamical chaic yem f he MS and i envirnmen. The ae a ime i chaically dependen n he ae a a ime and he acin. The meauremen depend chaically n he ae a ime. Such a empral mdel i al knn a hidden Markv mdel HMM r dynamic Baye nerk DBN [4]. 2.2 Pracical Implemenain The Baye Filer BF algrihm derived in he previu ecin cann be direcly implemened n a digial cmpuer. Hever, nnparameric filer [4] prvide implemenable algrihm fr he BF. Nnparameric filer NPF apprximae perir by a finie number f parameer, each crrepnding a regin in he ae pace, i.e. hey d n rely n a fixed funcinal frm f he perir. Mrever, he number f he parameer ued apprximae he perir can be varied. The qualiy f apprximain depend n he number f hee parameer. A he number f parameer apprache infiniy, NPF end cnverge unifrmly he crrec perir under pecific mhne aumpin [4]. The NPF apprach dicued here apprximae perir ver finie pace by decmping he ae pace in finiely many regin and repreen he cumulaive perir fr each regin by a ingle prbabiliy value. Such an apprach i knn a dicree Baye Filer DBF [4]. The DBF i al referred a he frard pa f a hidden Markv mdel. The DBF apprximae he belief f n eighed lcain candidae a Bel : {, } n a any ime by a e Where i he i-h MS lcain candidae and i a prbabiliy value al called eigh ha deermine he imprance f. The um f all eigh equal ha repreen a valid prbabiliy diribuin. A any ime, he eigh f a lcain candidae i calculaed a = + + MM MM Where nd are he eigh accrding he meauremen mdel, neighburhd degreend rnge neighbur repecively. They are calculaed a ime a MM = p j DB M j 2 2σ = e j= σ 2π 0 Where M i he number f berved BS main and neighburing, i.e. M max = 7, σ i he andard deviain f he meaured, j frm he j-h berved BSnd i he meaured DB j i he daabae predicin value f he j-h berved BS a = l α. Wherel i he number f berved neighbur BS ha cin- he li f he prediced ix rnge neighbur BS cide ih a nd α i a cnan bnu value, i.e. l max = 6. Where α = α 2 i a cnan bnu valuend i aigned if he The final lcain eimae ŝ i calculaed frm he be- lief a rnge berved neighbur BS cincide ih he prediced fir r ecnd rnge neighbur BS a. Oher- ie, = 0. k ˆ = 3 k Where k < n nd i red accrding. Thu, ŝ i he average f a cerain number k f he be eighed lcain candidae. Exprein 3 i al knn a rimmed average eimae TAE. prir TABLE I depic he implemenain f he prped Baye- ian mbile lcain algrihm hen run a ime. Ne ha n min mdel i inegraed, becaue nerk meauremen are he nly urce f infrmain. The prir Belief a ime dened Bel i iniialized ver he hle ae pace f he MS candidae lcain uing he CI and TA a im e ih iniial eigh i =, i.e. he prir n belief i a unifrm diribuin ver he deermined ae pace. 3. ENVIRONMENT MODEL The uilized daab ae ha been cnruced uing a 3D de- number, cell idenifier, erminiic radi prpagain predicin mdel, decribed in [2], ih a reluin f 5 m. Thi daabae i a by-prduc f he nerk planning age and cnain lcain dependen parameer value e.g. ignal rengh in GSM nerk a reference lcain. The prvided cell infrmain in he inere area include anenna gegraphical lcainnenna heighzimuh and il, effecive irpic radiaed per, channel ec.

4 The MS acquire infrmain abu i envirnmen r rld hrugh he nerk meauremen. Hever, he MS envirnmen i a chaic yem. Therefre, he nerk meauremen are fen niy and deviae frm he predicin value, hich are in urn n precie. In rder enhance he prir belief f he dicree Baye filer much infrmain a pible culd be exraced frm he predicin daabae. Thi uld enhance he crrelain prce f meauremen ih knledge abu he MS rld. Achieving hi need rerganizain, pariining, and cluering f he iniial predicin daabae. Every cell anenna f he e area ha acquired a eparae daabae, called he cell daabae CDB, hich cnain nly he lcain erved by i. Each daabae enry cni f lcain ID, lcain crdinae, predicin frm erving cell, predicin value and ID f he rnge neighbur cellnd diance he erving cell anenna. Furhermre, every CDB ha been divided in ub-daabae accrding all pible TA value ih an aumed errr f ± 0. 5 bi; each called cell TA daabae CTADB and labelled ih a amp indicaing i TA value. The lcain algrihm ill prce nly he CTADB maching he TA meauremen, hu, reducing he nline cmpuainal burden a minimum. Anher inereing apec can be explained by he help f Figure, hich illurae he lcain f a ecr cell an- d alng ih heir erving CI and he her enna black d, lcain erved by he cell anenna frta = 0 red pnd he ecr bundary uing he azimuh and crdinae f he cell anenna depiced in blackl ata = 0. The hie area inide he bundary are lcain erved by her cell anenna. Such lcain culd be deermine infrmain a abve a all pible TA value fr every cell, and hen red in eparae daabae, each called uider lcain daabae OLDB. f he MS i mehere in he hie area a explained abve a lea in he fir perid f ime afer iching. Thi i very advanageu fr he dicree Baye filer, in hich he ae pace i mre pecified by he cncenrain f he prir belief n lcain f mre likelihd. Inpu: Bel : prir = {, } n : j = M Bel = 0 // Iniialize perir belief η = 0 // Iniialize nrmalizain facr ˆ = 0 // Iniialize lcain eimae fr i = : n d // Cmpue eigh + + endfr i i = MM // Iner in perir belief i Bel = {, // Updae nrmalizain facr value η =η + // Nrmalize eigh f r i = : n d = endfr /η // Sr perir belief accrding eigh in decend- rder ing Bel = r } // Eimae he lcain uing TAE f r i = : k d ˆ = ˆ + endfr ˆ = ˆ / k reurn ŝ TABLE I Implemenain f he dicree Baye filer Figure Definiin f uider lcain When he acual nerk meauremen repr a iching a ne erving cell, i i m prbably ha he rue lcain 4. EXPERIMENTS Field meauremen hav e been clleced in a rking GSM- 800 nerk by pederian alking alng a rue f abu 2400 m uing a nebk cnneced a GSM mdem and a GPS receiver ha prvided rue piin reference. The e

5 field i a 9 km 2 uburban area in Hannver, Germany, ih 8 and 4 ecr and indr cell repecively. The clleced meauremen have been prceed ffline uing he prped Bayeian lcain algrihm. We inveigaed he perfrmance by running he algrihm nce ih nly he CTADB and anher nce ih bh CTADB and OLDB a explained in he previu ecin. Uing nly he CTADB, he achieved lcain accuracy a a hn in TABLE II. Errr percenile 67% 95% mean Lcain errr 240 m 49 m 26 m TABLE III depic he enhancemen f he perfrmance achen incrpraing OLDB in he lcain alg- curacy rihm. The imprvemen f he 67 and 95 percenilend mean errr i 2%, 9%nd % repecively. The uilizain f OLDB ha enhanced prir belief hen erving cell changedccrdingly he Bayeian filering prce culd perfrm beer ih mre ueful infrmain. TABLE II Lcain accuracy uing nly CTADB Errr percenile 67% 95% mean Lcain errr 2 m 382 m 9 m TABLE III Lcain accuracy uing CTADB and OLDB Lcain accuracy depend rngly n he cell ize. The perfrmance f ur algrihm i ill mre accurae han he preened in, e.g. [0], [], fr imilar cell ize al uing daabae crrelain mehd. 5. CONCLUSION The Baye filer BF algrihm calculae he perir ver he ae cndii ned n he meauremen daa. I i elluied repreen cmplex mulimdal belief a i he cae in he prblem f MS piining in irele nerk. BF aume ha he rld i Markvian. Thi aumpin culd be cnidered meh evere, becaue i i already vilaed in building he rld mdel and during real meauremen due he fac ha unmdeled dynamic e.g. peple and car are n included in calculain depie heir influence n, e.g. mulipahnd hence n he reulan value a differen lcain. Hever, he prped apprach i rbu in he face f uch aumpin, niy meauremen, and her inaccuracie in he envirnmen mdel. They are handled a cle--randm effec. Anher limiain i he apprximain f perir diribuin in cninuu envirnmen. Thi i, hever, unavidable in rder make he lcain algrihm cmpuainally feaible. Field experimenal reul hed gd perfrmance accuracie f he implemened algrihm in a uburban envirnmen ih l BS deniy. REFERENCES [] Federal Cmmunicain Cmmiin FCC Fac Shee, FCC Wirele 9 Requiremen, 200. [2] EU Iniuin Pre Releae, Cmmiin Puhe fr Rapid Deplymen f Lcain Enhanced 2 Emergency Service, DN: IP/03/22, Bruel, July [3] T. M Ranalainen, M. A. Spirind V. Ruuu, Evluin f lcain ervice in GSM and UMTS nerk, in Prc. The 3rd In. Symp. n Wirele Pernal Mulimedia Cmmunicain WPMC 2000, Bangkk, Thailand, Nv. 2000, pp [4] H. Laiinen edir, Cellular Lcain Technlgy, Public deliverable f IST/CELLO prjec, 200. [5] T. S. Rappapr, J. H. Reed, D. Werner, Piin lcain uing irele cmmunicain n highay f he fuure, IEEE Cmmunicain Mag., vl. 34, pp. 33-4, Oc 996. [6] M. Schreiner, M. Tangemannnd D. Niklai, A ne nerk-baed piining mehd fr lcain ervice in 2G and 3G mbile cmmunicain, in Prc. 5h Eurpean Pernal Mbile Cmmunicain Cnference Cnf. Publ. N. 492, April 2003, pp [7] M. Weckröm, M. Spirind V. Ruuu, Mbile Sain Lcain, ch. 4 in GSM, GPRSnd edge perfrmance: evluin ard 3G/UMTS, T. Halnen ed., 2nd ed., Chicheer, Wiley, [8] H. Laiinen, J. Läheenmäki, T. Nrdröm, Daabae Crrelain Mehd fr GSM Lcain, preened a IEEE Vehicular Technlgy Cnference VTC200-Spring, Rhde, Greece, May 200. [9] F. Erba, K. Kyamakya, K. Jbmann, On he uer prfile and he predicin f uer mvemen in irele nerk, preened a IEEE Inernainal Sympium n Pernal, Indr and Mbile Radi Cmmunicain PIMRC 02, Libn, Prugal, [0] H. Schmiz, M. Kuiper, K. Majeki, P. Sadelmeyer, A ne mehd fr piining f mbile uer by cmparing a ime erie f meaured recepin per level ih predicin, preened a IEEE Vehicular Technlgy Cnference VTC2003-Spring, Jeju, Suh Krea, May [] D. Zimmermann, J. Baumann, M. Layh, F.M. Landrfer, R. Hppe, G. Wölfle, Daabae Crrelain fr Piining f Mbile Terminal in Cellular Nerk uing Wave Prpagain Mdel, preened a IEEE Vehicular Technlgy Cnference VTC2004-Fall, L Angele, USA, Sep [2] T. Kürner, A. Meier, Predicin f udr and udr--indr cverage in urban area a.8 GHz, IEEE Jurnal n Seleced Area n Cmmunicain, Vl. 20, N.3, pp , April [3] D. Fx, J. Higher, L. Lia, D. Schulznd G. Brriell, Bayeian Filer fr Lcain Eimain, IEEE Pervaive Cmpuing, vl. 2, n. 3, [4] S. Thrun, W. Burgardnd D. Fx, Prbabiliic rbic. Cambridge, Ma.: MIT Pre, 2005.