Hybrid TOA/AOA-based Mobile Localization With and Without Tracking in CDMA Cellular Networks

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1 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs Hbrd OA/AOA-bsed oble Loclzton Wth nd Wthout rcng n CDA Cellulr Networs Vctor Yng hng, Albert K-sun Wong, Km m Woo nd Robn Wento Oung Deprtment of Electronc nd Computer Engneerng he Hong Kong Unverst of Scence nd echnolog Cler Wter B, Hong Kong vctor@usth, eelbert@usth, eetm@usth, owtece@usth Abstrct-hs pper proposes hbrd OA/AOA (me of Arrvl/Angle of Arrvl)-bsed loclzton lgorthm for Code Dvson ultple Access (CDA) networs he lgorthm etends the lor Seres Lest Squre (S-LS) method orgnll developed for OA-bsed sstems to ncorporte AOA mesurements In ddton, trcng lgorthms utlzng veloct nd ccelerton mesurements re nvestgted Smulton results llustrte tht the proposed OA/AOA S-LS cn provde better performnce thn conventonl schemes n loclzton ccurc nd n reduced lelhood of encounterng nonconvergence problem compred wth OA S-LS rcng lgorthms usng the Etended nd Unscented Klmn Flter ( nd ) cn trc the objects reltvel well, further decresng the postonng error s found to provde closer trcng of the trjector thn, for t trul cptures the sttstcl men nd vrnce of the noses Kewords-Etended Klmn Flter (); Postonng; lor Seres Lest Squre (S-LS); rcng; Unscented Klmn Flter () I INRODUCION Accurte locton fndng technques for people nd termnls hve receved consderble ttenton over the pst decde, especll snce the loclzton ccurc becomes mndtor n the Enhnced-9 (E-9) servces b Federl Communcton Commsson (FCC) [] Undoubtedl, the Globl Postonng Sstem (GPS) s the most well nown locton technolog n use tod Incresngl populr mong moble termnls s the use of Asssted-GPS (AGPS), whch gretl reduces the GPS tme-to-frst-f In [], we descrbed complete AGPS-bsed trcng sstem for elderl ndvduls he sstem hs been shown to wor qute well n the outdoor envronment, wth contnuous termnl btter operton of no less thn 7- ds f poston fes re performed nfrequentl Even for n AGPS-enbled sstem, t remns ttrctve tht the wdel deploed Code Dvson ultple Access (CDA) cellulr networs cn be used to perform networ-bsed loclzton Power consumpton for AGPS fes s much lower thn for GPS, but stll ech AGPS f consumes severl mnutes of stndb current hs mens tht fes cnnot be performed too frequentl, often resultng n nsuffcent dt to provde n ccurte pcture of the user moblt pttern Networ-bsed loclzton b the cellulr networ llevtes the termnl of ntensve processng nd thus reduces the power consumpton It cn ether be used b tself or n conjuncton wth AGPS to fll the vod of GPS dened cses nd tme gp between nfrequent AGPS fes n loclzton lgorthms for cellulr networs hve been proposed ost of them re mnl bsed on dfferent mesurement nformton ncludng me of Arrvl (OA) [3], [4], me Dfference of Arrvl (DOA) [5], Angle of Arrvl (AOA) [4], [6], Receved Sgnl Strength (RSS), nd n vrous combntons [7], [8] Both tme-bsed (e, OA nd DOA) nd ngle-bsed (e, AOA) schemes hve ther own dvntges nd lmttons For emple, OA/DOA methods requre t lest three non-collnerl locted Bse Sttons (BSs) to produce two-dmensonl (-D) f, whle AOA schemes need onl mnmum of two BSs On the other hnd, OA/DOA schemes generll hve better ccurc whle AOA schemes re hghl rnge dependent - when the oble Stton (S) s fr w from the BS, smll AOA mesurement error wll result n lrge loclzton error In [7], hbrd DOA/AOA loclzton lgorthm for CDA cellulr sstems s proposed whch tes dvntge of both DOA nd AOA to cheve hgh locton ccurc On the other hnd, loclzng the S usng trcng mode s beleved to provde hgher ccurc thn memor-less pproches (e, estmte the locton wth onl the current observton), becuse trcng eplores the reltonshp nd/or the phscl constrnts between the successve postons of the S rcng hs lso been etensvel nvestgted [9]- [] In [], the Klmn Flter (KF) s ppled n moble locton trcng nd moble veloct estmton In [], both the Unscented nd Etended Klmn Flters ( nd ) re proposed for nonlner ndoor trcng usng dstnce mesurements In [], novel pproch to dentf the sptl locton nd trjector of movng object from successve smples b sngle movng sensor s descrbed As OA nd AOA schemes cn be hghl complementr, nd trcng cn eld more ccurte results, n ths pper, we frst propose hbrd OA/AOA loclzton lgorthm n CDA cellulr sstems, whch etends the lor Seres Lest Squre (S-LS) pproch [3] orgnll developed for OA to ncorporte AOA mesurements, nd then propose the trcng lgorthms usng nd Smulton results revel tht the proposed OA/AOA scheme provdes better //$6 IEEE

2 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs performnce compred to other schemes, nd the trcng lgorthms cn trc the objects reltvel well he rest of the pper s orgnzed s follows Secton II ntroduces the sstem model Secton III ntroduces two conventonl hbrd OA/AOA loclzton lgorthms, followed b the proposed OA/AOA S-LS lgorthm Secton IV descrbes the trcng lgorthms usng nd Numercl results re gven n secton V Secton VI provdes the conclusons II SYSE ODEL We consder mcrocell CDA cellulr networ n ths pper he locton estmtes re determned through recepton of sgnls trnsmtted b the S to set of BSs he sgnls contn the current observed veloct nd ccelerton of the S whch we ssume cn be mesured b velocmeters nd ccelerometers respectvel he home BS performs OA nd AOA mesurement upon recevng the sgnl, whle the neghborng BSs onl mesure the OA Our lgorthm s relevnt to CDA networs becuse AOA mesurements requre the use of ntenn rrs or spce-tme sgnl processng t the BS, both re epected to be common n 3G CDA networs AOA cn be mesured b the Locton esurement Unt (LU) nstlled t the BSs Our lgorthm s relevnt mostl for the mcrocell scenro becuse for mcrocell, the BS s usull locted t hgh elevton wthout surroundng objects, thus llows the BS to receve sgnls from the S wth smll ngle spred [4] Smulton results for outdoor multpth envronments ndcte tht AOA cn be mesured wth ccurc of four degrees or less [3] In our model, nd ccordng to [7], AOA s mesured onl t the home BS for the followng resons: ) sgnls receved b neghborng BSs hve poor qult becuse of the ner-fr effect, resultng n poor AOA mesurement ccurc; ) s the S s reltvel close to ts home BS, the rnge-dependent AOA loclzton error cn then be reduced For OA mesurements n spred-spectrum communcton sstems, corse tmng cn be cqured wth sldng correltor or mtched flter nd fne tmng cn be cqured wth delloced loop (DLL) [4] As common prctce [3], [8], AOA nd OA mesurement errors re modeled s ndependent zero-men Gussns wth nown vrnces III HYBRID OA/AOA LOCALIAION ALGORIHS In ths secton, we frst ntroduce two conventonl hbrd OA/AOA loclzton schemes: wth sngle BS (home BS) onl nd wth multple BSs We then present the proposed hbrd OA/AOA S-LS postonng lgorthm Here, we onl consder the -D cse for smplct; however, the lgorthm cn be esl etended to the 3-D cse Denote (, ), (, ) s the poston of the S nd the th BS respectvel We ssume tht BSs n totl re nvolved n the locton estmton, nd tht the frst BS s the home BS s the AOA mesurement t the home BS, nd t s the OA mesurement t the th BS he rnge mesurement between the S nd the th BS cn then be nferred b r ct, c s the speed of lght A Loclzton Wth Sngle BS (Home BS) Wth OA nd AOA mesurements from the home BS, we cn locte n S As shown n Fg, the locton of the S cn be esl determned b the followng equtons: + r cos, + r sn () hs pproch s of low computtonl complet, but s ver senstve to the AOA mesurement error, especll when the S s fr from the home BS B Loclzton Wth ultple BSs Usng Lest Squre (LS) When mesurements from multple BSs (e, > ) re vlble, we wll hve set of overdetermned nonlner equtons, whch cn be reformulted nto lner ones nd cn be solved usng LS pproch he dstnce r between the S nd the th BS cn be epressed s r ( ) + ( ),,,, () From (), subtrctng the frst equton ( ) from ll the others, nd denotng + K, we obtn ( ) + ( ) K K + r r,,, (3) he AOA mesurement cn be epressed s sn tn (4) cos Combnng (3), (4), nd rewrtng n the mtr form, we hve Fg Loclzton usng the home BS onl DP C, (5) P [ ], Fg Lner ppromton of the AOA ( ) ( ) K K + r r D, (6) C ( ) ( ) K K + r r sn cos sn cos he locton of the S cn then be determned b solvng (5) usng LS method,

3 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs P ( D D) D C (7) In the bove pproch, f the mesurement for r hppens to be too nos, then ll the other rnge mesurements wll be contmnted, resultng n poor loclzton ccurc C Proposed Loclzton Algorthm Wth ultple BSs Usng lor Seres Lest Squre (S-LS) Denote the nose free vlue of {*} s {*}, the rnge mesurement r cn be modeled s r r + n ( ) + ( ) + n,,, (8) n s the mesurement error whch s modeled s zeromen Gussn vrble, e, n ~N(,σ n ) Epndng (8), nd ntroducng new vrble R +, we obtn r + n n r R + K,,,, (9) We then use the sme pproch to del wth the AOA s descrbed n [7] As shown n Fg, we hve the followng geometrcl reltonshp, r sn n ( )sn ( )cos () n s the AOA mesurement error whch s modeled s zero-men Gussn vrble, e, n ~ N( (,σ ) Usng the fct tht sn n n when n <<, we hve r sn + cos + sn cos () n Let [ ] form, we hve R, nd rewrtng (3), () n the mtr ϕ h G, () ( r K ) / h, (3) G ( r K ) / sn + cos sn cos Note from (8) tht r r + n, φ s found to be dg { r BE 5E E ϕ r n, r,, r }, B [ n n ] n (4) E (5) he smbol represents the Schur product (element-belement product) he covrnce mtr ψ s evluted s 4σ n I ψ E[ ϕϕ ] B' 4 4 σ n I + σ n ' + B σ (6) I nd re the dentt mtr nd ll-one mtr respectvel, nd B ' dg{ r, r,, r, r } Assumng the ndependence of, nd R, the mum Lelhood (L) estmtor of s gven b [5] rg mn{( h G ) ψ ( h G ( G ψ G ) G ψ h, (7) whch s lso the Weghted Lest Squre (WLS) estmte of ψ s not nown n prctce, snce t contns the true dstnces between the S nd BSs herefore, we cn frst use the mesured rnge to get n ntl estmte b (7), then use ths ntl soluton to derve the correspondng ψ, nd fterwrds reclculte to get more ccurte result usng the newl derved ψ Durng the dervton bove, we regrd, nd R s ndependent In ctult, the re relted b (8) herefore, we refne the soluton s follows Denotng the obtned ntl vlue of (, ) s ( ˆ, ˆ ), we hve ˆ + Δ, ˆ + Δ (8) Δ nd Δ re the estmton errors to be determned B epndng (8) nto lor Seres nd retnng the frst order terms, we obtn ˆ ˆ r + Δ + Δ, (9) ( ˆ ) + ( ˆ ) Substtutng (8) nto (), we obtn r n ˆ )sn ( ˆ ) cos + Δ sn Δ cos ( Defnng [ ] ' Δ Δ mtr form, we hve h )} (), nd epressng (9), () n the ϕ ' h ' G ' ', () ϕ' [ n n n ( r n ) n ], [ r r ( ˆ )sn ( ˆ )cos ], ' ˆ ˆ G ' ˆ ˆ sn cos () he covrnce mtr ψ E [ ϕ' ϕ' ] cn be esl evluted he WLS estmton of () s then gven b ' ( G ' ψ ' G ') G ' ψ ' h', (3) nd the covrnce mtr of ' s vr( ') ( G ' ψ ' G ') (4)

4 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs he locton estmte cn then be updted usng (5) ˆ ˆ + Δ, ˆ ˆ + Δ (5) We terte ()-(5) untl both Δ nd Δ rech below predefned threshold he resultng ( ˆ, ˆ ) s regrded s the locton estmte whch s then fed nto the trcng lgorthm to further mprove the loclzton ccurc Note tht f there s too lrge n error n the ntl locton estmte, nonconvergence m be encountered [3] We refer to the bove lgorthm s OA/AOA S-LS IV RACKING ALGORIH In ths secton, we descrbe the nd nonlner flterng lgorthms for trjector trcng of the S nd to further mprove the loclzton ccurc Defne the stte vector s X [ v ] v,,, v, v,, re the poston, veloct, nd ccelerton of the S on nd s respectvel he dnmc stte model cn be esl derved s A X AX + GW, 5 5, (6) 5 G, W [ n n ] 5 (7) s the observton tme nde, s the smplng ntervl, W s the sstem nose vector whch s ssumed to be zero-men Gussn wth n, n beng the rndom ccelerton nose on, s respectvel he covrnce of GW s gven b Q GQ, (8) G W Q s the covrnce mtr of the rndom W ccelerton nose W durng one tme perod Defne the observton vector s [ v ], the mesurement nose vector s V [ n n n nv n ], v nd re the veloct nd ccelerton of the S, nd n, n, n v, n re the observton noses for the S, locton, veloct, nd ccelerton, respectvel he observton noses re modeled s Gussn vrbles wth men zero he observton model s then gven b (9) whch s nonlner H X ) + V, (9) ( ABLE I [ H( ) 3 v + v + ], H ( X) X H( X) 3 rctn( ),, rctn( ) + π, rctn( ) + π, otherwse he covrnce mtr for the mesurement error s PARAEERS SEING IN HE SIULAION Stndrd Sstem odel Observton odel Devton σ (m/s ) (m/s ( ) o ) v (m/s) (m/s ) Vlue 3 (3) vr( ' ) R, R ' dg{ σ, σ v, σ } (3) R ' σ v nd σ re the vrnces of the veloct nd ccelerton mesurement errors respectvel s vrnt of the stndrd KF lnerzes the nonlner observton model b the frst-order lor Seres epnson, nd resorts to the Jcobn mtr for estmton he mn de of s to ppromte probblt dstrbuton b mnml set of determnstc smple ponts nsted of ppromtng set of nonlner functons b clcultng dervtves hese smple ponts re then propgted through the true nonlner observton functon to cpture the sttstcl men nd vrnce heoretcll, hs comprble computtonl complet whle producng more ccurte estmtes thn he detled stndrd recursve lgorthms for nd cn be found n [5] nd [6] respectvel nd re omtted here V NUERICAL RESULS Smultons re conducted to evlute the performnce of the proposed loclzton lgorthms A Smulton Results for OA/AOA S-LS We frst compre the performnce of the OA/AOA S-LS wth the other three conventonl lgorthms: OA S-LS s descrbed n [3], OA/AOA postonng wth sngle BS, nd multple BSs usng LS s descrbed n Secton IIIA nd IIIB We ssume hegonl lout whch s tpcll used n cellulr networs hree BSs re deploed t (m,m), ( 3m, m) nd ( 3m,m) he S s rndoml plced wthn 3 m 4 m rectngle enclosng the three BSs he stndrd devton of the OA mesurement error σ n s set to m, nd the other prmeters used n the smulton re specfed n ble I, unless otherwse stted he performnce crteron of the lgorthm s chosen s the

5 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs RSE (m) OA S-LS OA/AOA LS OA/AOA Sngle BS OA/AOA S-LS ABLE II NUBER OF NON-CONVERGENCE FOR DIFFEREN SCENARIOS o () σ,, runs for ech scenro σ n (m) OA S-LS OA/AOA S-LS (b) σ n m,, runs for ech scenro Stndrd Devton of OA esurement Error σ n (m) Fg 3 RSE versus stndrd devton of OA mesurement error σ ( o ) OA S-LS OA/AOA S-LS OA S-LS OA/AOA LS OA/AOA Sngle BS OA/AOA S-LS OA S-LS OA/AOA LS OA/AOA Sngle BS OA/AOA S-LS RSE (m) 6 4 RSE (m) Stndrd Devton of AOA esurement Error σ ( o ) Fg 4 RSE versus stndrd devton of AOA mesurement error Number of Herble BSs Fg 5 RSE versus number of herble BSs Root en Squre Error (RSE) defned n (3), nd s computed over, ndependent runs N RSE [ ( ˆ ) + ( ˆ ) ] (3) N Fg 3 depcts the RSE of the four lgorthms versus dfferent σ n, the stndrd devton of OA mesurement error It cn be seen tht OA/AOA S-LS hs the hghest ccurc, followed b OA/AOA wth sngle BS, OA S-LS nd then OA/AOA LS As σ n gets lrger, the RSEs of ll the four lgorthms ncrese lnerl Fg 4 shows the RSE for dfferent σ, the stndrd devton of AOA mesurement error OA/AOA S-LS gn performs the best for ll σ from to degrees As σ ncreses, the performnce of OA/AOA wth sngle BS nd OA/AOA S-LS gets worse OA S- LS does not utlze the AOA mesurement, nd thus t s not ffected b chnges n σ heoretcll, the performnce of OA/AOA LS should be ffected b σ But ths s not demonstrted b the smulton result, probbl due to the fct tht the ngle mesurement contrbutes reltvel lttle to the estmton n ths lgorthm It cn lso be observed tht the ccurc of OA/AOA wth sngle BS s qute senstve to σ, nd degrdes drmtcll s σ ncreses OA/AOA S-LS demonstrtes ts dvntge over OA S-LS snce t leverges the dvntge of both OA nd AOA lgorthms We lso nvestgte the non-convergence problem for OA S-LS nd OA/AOA S-LS We record the number of tmes ech of the two lgorthms encounters non-convergence when tertng ()-(5) As shown n ble II, both OA S-LS nd OA/AOA S-LS m suffer from non-convergence f the ntl estmte (from (7) for OA/AOA S-LS) devtes too much from the true poston; however, OA/AOA S-LS encounters non-convergence wth much lower probblt he mpct of the number of herble BSs on the loclzton ccurc s then nvestgted Assume tht the BSs re evenl locted on crcle centered t (, )m wth rdus rd m, the locton of the jth BS s π ( j ) j + rd cos, π ( j ) j + rd sn (33) he RSE of the four lgorthms versus number of herble BSs s depcted n Fg 5 As more BSs re nvolved, the estmton ccurc of OA/AOA wth sngle BS sts stble, whle tht of the other three ncreses drmtcll hs dues to the fct tht OA/AOA wth sngle BS onl utlzes the mesurements from the Home BS, nd thus hs no gns s the number of neghborng BSs ncreses Agn, the proposed OA/AOA S-LS performs the best n ll cses B Smulton Results for rcng Algorthms In ths subsecton, we emne the performnce of the trcng lgorthm usng nd

6 hs full tet pper ws peer revewed t the drecton of IEEE Communctons Socet subject mtter eperts for publcton n the WCNC proceedngs (m) rue rjector rue rjector (m) Fg 6 Smple source trjector nd trcng usng the nd Absolute Loclzton Error (m) OA/AOA S-LS OA/AOA S-LS me Inde Fg 7 Absolute loclzton error for OA/AOA S-LS, nd Smulton prmeters remn the sme s prevous, nd the smplng ntervl s set to 5s he S s sttonr t (45, -85) ntll, nd strts off wth ccelerton of 7m/s nd 7m/s on nd s respectvel If the OA/AOA S-LS encounters non-convergence, then we estmte the poston from the prevous estmton usng the stte model (6), gnorng noses Fg 6 shows smple trjector of the moton model nd the outputs from both the nd lgorthms Fg 7 depcts the correspondng Absolute Loclzton Error (ALE), ( ˆ ) ( ˆ + ), t ech tme nstnce It cn be seen tht both lgorthms cn trc reltvel well, nd the estmted route from sts closer to the true trjector thn tht from We cn lso observe tht the ALE of OA/AOA S-LS chnges more volentl thn tht of nd Smultons usng dfferent vlues of nd/or dfferent S routes produce smlr results Addtonl results re not shown here due to spce lmtton VI CONCLUSION In ths pper, hbrd OA/AOA loclzton lgorthm for CDA cellulr networs s proposed It etends the S-LS pproch orgnll developed for OA to ncorporte AOA mesurements Wth the ssumpton tht veloct nd ccelerton mesurements of the S re vlble, trcng lgorthms usng nd re ppled Numercl results revel tht the proposed OA/AOA S-LS outperforms the other conventonl lgorthms n loclzton ccurc, nd hs reduced lelhood of encounterng non-convergence problem compred wth OA S-LS OA/AOA S-LS ehbts ts dvntge over OA S-LS snce t utlzes the dvntge of both OA nd AOA schemes Use of trcng lgorthm cn further mprove the loclzton ccurc, wth demonstrtng ts dvntge over, s trul cptures the sttstcl men nd vrnce of the noses REFERENCES [] Fed Communcton Commsson (FCC) ech Rep R-843 Revson of the commssons rules on nsure comptblt wth enhnced 9 emergenc cllng sstems996 [] A K Wong, et l, "An AGPS-Bsed Elderl rcng Sstem," st Internntonl Conference on Ubqutous nd Future Networs, IEEE ICUFN, June 9 [3] K Yu nd Y J Guo, "NLOS error mtgton for moble locton estmton n wreless networs," n Vehculr echnolog Conference, 7 VC7-Sprng IEEE 65th, 7, pp 7-75 [4] J Cffer Jr nd G L Stuber, "Subscrber locton n CDA cellulr networs," Vehculr echnolog, IEEE rnsctons on, vol 47, pp 46-46, 998 [5] Y Chn nd K C Ho, "A smple nd effcent estmtor for hperbolc locton," Sgnl Processng, IEEE rnsctons on, vol 4, pp 95-95, 994 [6] S Sgm, S Aom, K Kubo, S Shrot nd A Aem, "Vehcle poston estmtes b multbem ntenns n multpth envronments," Vehculr echnolog, IEEE rnsctons on, vol 4, pp 63-68, 99 [7] L Cong nd W hung, "Hbrd DOA/AOA moble user locton for wdebnd CDA cellulr sstems," Wreless Communctons, IEEE rnsctons on, vol, pp , [8] V Y hng nd A K Wong, "Combned AOA nd OA NLOS Loclzton Wth Nonlner Progrmmng n Severe ultpth Envronments," Wreless Communctons nd Networng Conference, 9 WCNC 9 IEEE, pp -6, 9 [9] Wng Lu-j, Wng Jn-un, W Yun nd L Xo, "Locton estmton of moble user n wreless sensor networ bsed on unscented lmn flter," n crowve nd llmeter Wve echnolog, 8 IC 8 Interntonl Conference on, 8, pp [] Chn-Der Wnn, Y-ng Chen nd ng-shung Lee, "oble locton trcng wth NLOS error mtgton," n Globl elecommunctons Conference, GLOBECO ' IEEE,, pp vol [] H Qsem nd L Rendl, "Unscented nd etended lmn estmtors for non lner ndoor trcng usng dstnce mesurements," n Postonng, Nvgton nd Communcton, 7 WPNC '7 4th Worshop on, 7, pp 77-8 [] X Chen, D Schonfeld nd A Khohr, "Loclzton nd trjector estmton of moble objects wth sngle sensor," n Sttstcl Sgnl Processng, 7 /SP 4th Worshop on, 7, pp [3] R Klus nd Fttouche, Lne-of-sght ngle of rrvl estmton n the outdoor multpth envronment, IEEE rns Veh echnol, vol47, pp 34 35, Feb 998 [4] R emer nd R Peterson, Dgtl Communctons nd Spred Spectrum Sstems New Yor: cmlln, 985 [5] S K, Fundmentls of Sttstcl Sgnl Processng-Estmton heor Englewood Clffs, NJ: Prenctce-Hll, 993 [6] E A Wn nd R Vn Der erwe, "he unscented lmn flter for nonlner estmton," n Adptve Sstems for Sgnl Processng, Communctons, nd Control Smposum AS-SPCC the IEEE,, pp 53-58