Particle Filters for Positioning with focus on Wireless Networks

Transcription

1 conrol & Paricle Filers for Posiioning wih focus on Wireless Neworks Fredrik Gusafsson Prof. Communicaion Sysems De. of EE, Linköing Universiy Background Presenaion based on Work in comeence cener ISIS wih SAAB Aircraf: aircraf errain aided osiioning and navigaion SAAB Dynamics: missile racking and oredo osiioning NIRA Dynamics: Ma-Aided Posiioning MAP for cars Ericsson: wireless neworks conrol & F. Gusafsson, F. Gunnarsson, N. Bergman, U.Forssell, J. Jansson, R. Karlsson and P-J. Nordlund: Paricle filers for osiioning, navigaion and racking. IEEE Trans. On Signal Processing, P-J Nordlund, F. Gusafsson and F. Gunnarsson: Paricle filer for osiioning in wireless neworks. EUSIPCO F. Gusafsson and F. Gunnarsson: Posiioning using ime-difference of arrival measuremens. Submied o ICASSP 2003.

2 Ouline conrol & Wireless osiioning survey The aricle filer for osiioning Ma-based osiioning Aircraf, missiles and oredos Vehicles Framework for wireless osiioning TDOA based osiioning Posiioning mehods conrol & Cell-Idenifier CI Secor informaion or Angle of Arrival AOA requires adaive anennas Timing Advance TA d TA ½ 3.69µs symbol eriod 3e8 m/s 554m Enhancemen: usage of received signal levels RXLEV, see oeraor s ower aenuaion ma below. 2

3 Trilaeraion: ime differences in nework RTD conrol & GTD OTD RTD RTD : Real Time Difference OTD : Observed Time Difference GTD : Geomeric Time Difference OTD GTD 0 RTD0 in he CDMA sandard IS-95. Advanced Forward Link Trilaeraion A-FLT is sandardized. BTSs are no synchronized in GSM RTD 0, need Locaion Measuremen Unis. E-OTD is sandardized. Posiion calculaion via hyerbolic rilaeraion beween BTS airs Trilaeraion Locaion Measuremen Unis LMU Tye A, sand-alone Tye B, inegraed in he BTS LMU can be avoided by synchronizing BTSs wih GPS synchronizaion by ime-saming DL emissions TA circle Base Saion conrol & communicaion@liu Base Saion E-OTD/OTDOA hyerbolas Base Saion 3

4 Assised GPS conrol & Buil in GPS in Mobile Saion: Requires long ime o firs fi 60 s Energy consuming measuremens Comuaional eensive Assised GPS A-GPS Fied saions ransmi informaion of visible saellies and heir clock correcion and ehemeris orbial correcions, sreading codes, doler ec. MS finds he informaion in s Nework comues osiion Does no work indoor and in urban canyons Posiioning mehods: summary conrol & communicaion@liu Saellie osiioning GPS, Global Posiioning Sysem 0-30m DGPS, Differenial GPS -0m A-GPS, Assised-GPS -0m GSM R99 Cellular osiioning COO, Cell of origin 0.2-0km GSM R99 TA, Timing Advance 0.5 km AOA, Angle of arrival 0.-2km TOA, Time of arrival m GSM R99 E-OTD, Enhanced Observed Time Difference m GSM R99 In-door osiioning WLAN, Blueooh, GPS-seudolies 4

5 Eeced Revenues conrol & Localised Services Billing Informaion Roadside assisance Traffic & navigaion M-Commerce Adverising 2005 EU oeraor revenues Sraegies Grou ~$Bio 5.9 ~$Bio 3.5 ~$Bio.7 ~$Bio.6 ~$Bio 32.7 Ovum ~$Bio.9 ~$Bio. ~$Bio 2. ~$Bio 5 Y00-Y05 cumulaed revenues ~$Bio 8.9 ~$Bio Cerainly quie uncerain redicions! Models Model when velociy is measured: X, X, Y, Y X Y Ψ T X, X, Ψ Ψ TΨ y h X, Y e X Tv cos Ψ w Y Tv sin Ψ w 2 T 0 0 T / T 0 w T T 0 / 2 T y h X, Y e Y, X, conrol & communicaion@liu Model when velociy is no measured hen esimae i!: 5

6 6 conrol & Bayesian filering Sae sace model: Bayesian ime udae and measuremen udae e h y w f e w Y h y C Y y Y y Y d Y f d Y Y conrol & communicaion@liu PF Algorihm Generic Paricle Filer. Generae random saes 2. Comue likelihood 3. Resamling: 4. Predicion: 0 0 i i e i h y ω N i i i, ω ω w i i i i w w f, Eamle: Terrain navigaion in D Noe:. Cramer-Rao: osiion error > sqr aliude error * velociy error / errain variaion 2. The aricle filer normally aains his bound!

7 conrol & Digial Terrain Elevaion Daabase: grid oins 50 meer beween oins 2.5 meers uncerainy Ground Cover Daabase: 4 yes of vegeaion Obsacle Daabase: All man made obsacles above 40 m 2D Eamle conrol & communicaion@liu Animaion of errain navigaion in 2D using real GIS 7

8 Car osiioning conrol & Iniizalizaion using manual marking or GSM osiioning Paricles Posiion esimae True osiion Car osiioning conrol & Iniizalizaion using manual marking or GSM osiioning Afer sligh bend, four aricle clusers lef 8

9 Car osiioning conrol & Iniizalizaion using manual marking or GSM osiioning Afer sligh bend, four aricle clusers lef Convergence afer urn Car osiioning conrol & Iniizalizaion using manual marking or GSM osiioning Afer sligh bend, four aricle clusers lef Convergence afer urn Sread along he road 9

10 Car osiioning conrol & Paricle filer using sree ma and v, Ψ from car s ABS sensors. Green - rue osiion Blue esimae Red - aricles Paricle filer using sree ma and v, Ψ from car s ABS sensors and GSM cell ID and secor for iniializaion Purle: GPS Blue: aricles Car osiioning Ligh blue: esimae Phoo background conrol & communicaion@liu 0

11 Car osiioning Red GPS Ligh green: aricles Blue: esimae afer convergence Real-ime imlemenaion on Comac ipaq Works wihou or wih GPS Ma daabase background Comlee navigaor wih voice guidance! Ineger imlemenaion of he aricle filer ISIS rojec PF in simulaion mode off-road # aricles u o 5000 wihou GPS or as small as 50 wih GPS On-going R&D work a NIRA Dynamics AB and ISIS conrol & communicaion@liu Nework measuremens. Cell ID and Received signal srengh: Secor informaion usually 60 degrees One or more secors: Conneced anenna yellow ages service Power measuremens from 5 GSM or 6 WCDMA anennas Power aenuaion: Haa s formula or ma-based conrol & communicaion@liu

12 2. Time of arrival Nework measuremens Time of arrival TOA in ulink gives ime delay in ulink ransmission. Uncerain due o muliah. Time difference of arrival TDOA measures downlink ime differences. Enhanced observed ime difference E-OTD as TDOA bu for unsynchronized base saions. conrol & communicaion@liu Informaion sensor fusion conrol & communicaion@liu Posiioning of mobiles/cars using wo ou of hree of he following informaion sources:. Road ma vecorized enalizes osiions off-road 2. Velociy vecor: ABS sensor measuring wheel seed in cars gives v and Ψ 3. Wireless nework arameers and anenna osiions: TOA ime of arrival TDOA ime difference of arrival E-OTD enhanced ime difference of arrival AOA angle of arrival These can all be described by measuremen equaion y h X, Y e wih a cerain error disribuion 2

13 Reducing he comleiy conrol & Comleiy increases in sae dimension, bu no eonenially as for oin mass filer and oher numerical aroimaions. Sli sae vecor in osiion and oher saes. Marginalizaion imlies ha KF can be used for linear ar. Marginalizaion conrol & PF on all saes PF on osiion saes, KF on he oher ones Same Riccai equaion for all KF s v, a ˆ i, P v, a v, a v, a 3

14 D Eamle conrol & PF on he model: requires > aricles PF on he model: requires < 000 aricles TDOA esimaion roblems conrol & The mahemaical roblem seu Saic osiioning, using oimizaion Dynamic osiioning using dynamic moion model and filering 4

15 Mahemaical roblem conrol & Aligned anennas a -D/2,0 and D/2,0 giving GTDd gives nonlinear equaion for osiion d y D y D Corresonding equaion for hyerbola: 2 2 y d / 4 D / 4 d / 4 Transiion o global coordinae sysem gives for BTS air i,j: d h X, Y, X, Y, X, Y h P, P, P i, j i i j j i j Several GTD s rovide non-linear equaion sysem Measured ime has Rice/Rayleigh noise Covd non-diagonal 2 TDOA roblem seu n n BTS rovides hyerbolas 2 Each air of hyerbolas can have 0,,2,3 or 4 inersecions! Aroaches:. Solve hese non-linear equaions air-wise 2. Use he aricle filer for saic oimizaion 3. Solve a non-linear leas squares roblem numerically ˆ T n n P arg min P h P,{ Pi } i R h P,{ Pi } i Only 2 can be generalized o dynamic models conrol & communicaion@liu 5

16 TDOA saic osiioning conrol & The leas squares error is for his configuraion a unimodal funcion. Seees descen algorihms work for all iniializaions TDOA saic osiioning conrol & communicaion@liu Paricle filer wih decaying roughening noise 6

17 Simulaions Simulaion seu Arificial sree ma Known velociy Power measuremen sd 6 db and TOA disance measuremen sd 3dB wih random walk biases Bias are eiher esimaed or no The no bias case invesigaed for comarison 2000 aricles, 50 Mone Carlo runs conrol & communicaion@liu Simulaions conrol & communicaion@liu Resuls: Uer lo shows RMSE when bias esimaed solid and no esimaed dashed. Doed line is for simulaions wihou bias. Lower lo shows bias esimae. 7

18 Conclusions conrol & Posiioning of cellular hones using nework measuremens Focus on dynamic esimaion and auomoive alicaion Fleible framework configurable wih an asynchronous miure of informaion sources:. Ma: sree, aliude, aenuaion 2. Angle and range o fi-oin: AOA, TOA, TDOA, GPS 3. Velociy and urn rae: v, Ψ Paricle filer suiable because of is abiliy o include:. Non-linear consrains ma 2. Non-Gaussian noise Rice and Rayleigh fading, oeraor s ower aenuaion ma, ec. 8