of Computer Science and Engineering National Institute of Technology Tiruchirapalli Dept of Electronics and Communication Engineering National Institute of Technology Tiruchirapalli Dept of Computer Science and Engineering Recon64257gurable and Inte ID: 12629
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HCIprovidesaninterfacetoaccessthebasebandcontrollerandlinkmanager.ReceivedSignalStrengthIndicator(RSSI)isaparametergeneratedbythebluetoothradio.Itisanindicationofthepowerlevelofthereceivedsignal.GoldenReceiverPowerRange(GRPR)isapowerlevelrangedenedbytwothresholdlevels(upperandlower).BluetoothimplementsAdaptivePowerControli.e.thetransmittedpowerisautomaticallyincreasedordecreasedifitdifferstoomuchfromidealcharacteristics,denedbytheGRPR.BasedonwhethertheRSSIisgreaterorlesserthantheGRPR,thetransmissionpowerleveliseitherdecreasedorincreased.TheexactboundsofGRPRarenotclearlydenedandaremanufacturer-dependenttominimizeBit-ErrorRate([3]triedtoguesstheGRPR).PowercontrolimplementationisoptionalforClass-2andClass-3devicesandmandatoryforClass-1devices.Manyworkslike[9]usedtheHCIcommandhci read rssiwhichrequiresaconnectionbetweenthedevices.Itisdifculttoestablishandmaintainmultipleconnectionswithabluetoothdevice[2].Moreover,hci get rssidoesnotreturntheRSSIvalueitselfbutthedifferenceofRSSIandthelimitsofGRPR[8].TheabovementionedAdaptivePowerControltakesplaceonlyafteraconnectionisestablished.RSSIobtainedusingthismethodwillvaryovertimeduetoadaptation,henceisnotveryinformative.AnotherHCIcommand,Inquiry with RSSIexists,thatreturnstheactualRSSIvalue,atthetimeofinquiryi.e.withoutmakinganyconnections.[6]mentionedthisbutdidnotuseitastheirhardwaredidnotsupportit.Sincepowercontroldoesnottakeplace,theuseofInquiry with RSSIwithInquiry modesetto0x01,makesRSSImorereliableandinformative.Bluetoothdeviceshavealimitonthenumberofconnectionsthatcanbemaintainedatagiventime(usually7).Sincenoconnectionsaremadeinourmethod,thisdrawbackiseliminated.TherequiredcommandsweresenttothecontrollerusingBlueZ/Candtheeventsandfunctionsdenedtherein.Itinvolvedthefollowingsteps:1.SetInquirymodeto0x01.2.CongureparametersforInquiry with rssiviz.Durationofinquiry,numberofresponses,discoverymodeofde-vicestodiscover(GIACorLIAC).3.Sendthecommandinquiry with rssitothecontroller.4.Waitforeventin-quiry result with rssitooccur.5.ExtractRSSIvaluesfromthepacketreturned.6.Repeattilleventinquiry completeoccurs.Atimeoutof3swasused.B.VariationofRSSIwithdistanceAsdistancebetweentwobluetoothdevicesincreases,theRSSIvalueisexpectedtofall.TheaimistoobtainamappingfromRSSItodistance.However,duetoeffectsofinterferenceandmultipathing,aone-to-onemappingisnotpossible.[1]notesthatRSSIvariesevenforastationaryobject(Fig.1and2).[10]citesthreemethodstoobtainthismapping.Inthiswork,interpolationalongwithmotionisusedtoobtainthemapping.Therobotexecutesstraight-linemotioninsteps,stoppingaftereverysteptoperformaninquiry.ThevariationofRSSIastherobotmovesawayfromabeaconisshownbelow(Fig.3).ThismethodofmappingRSSItodistancerequiressignicantlylessermem-oryandtrainingtimeascomparedtongerprinting.Duringlocalization,anobservedRSSIvectorfrom3beacons,say(r1;r2;r3)correspondstomanydistancetriplets(d1;d2;d3),eachofwhichisconsideredbythetrilaterationalgorithmandthenbytheparticlelter. Fig.1:VariationofRSSIv/sTimeataxeddistanceof3m Fig.2:HistogramofthegraphshowninFig.1 Fig.3:ObservedRSSIvariationastherobotmovesawayfromthebeaconataconstantvelocity outputasdescribedintheprevioussectionsviz.[xy]T.Sinceoff-the-shelfbluetoothdonglesdonotpossessdirectionalantennae,theangledoesnotappearinthemeasurementvectorandinthemeasurementmodel.Theproblemoflocalizationcanbestatedascomputingtheposteriordensityp(xkjz1:k).p(x0)isassumedasininitialdistribution,inthiscaseauniformdistributionoverallpossiblelocations[xy]T.B.BayesianFilteringIntheory,theposteriordensitycanbecomputedre-cursivelyintwostages:predictandupdate.Supposethatp(xk�1jz1:k�1)isavailableasapriorPDFofxk�1,pre-dictionobtainsthepriorPDFofxkviatheChapman-Kolmogorovequationp(xkjz1:k�1)=Zp(xkjxk�1;z1:k�1)p(xk�1jz1:k�1)dxk�1IfweassumeaMarkovprocessoforderone,p(xkjxk�1;z1:k�1)=p(xkjxk�1),whichisthestatetransitionprobability.Intheupdatestage,zkisusedtoupdatethepredictedpriorviaBayesrulep(xkjz1:k)=1 p(zkjxk)p(xkjz1:k�1)wherethenormalizingconstant=p(zkjz1:k�1)=Zp(zkjxk)p(xkjz1:k�1)dependsonthelikelihoodp(zkjxk)denedbythemeasure-mentmodel.Bayesianlteringisoptimalinthesensethatitcomputestheposteriorbyusingalltheavailableinformation.KalmanFilterbasedapproachescanbeusedaswell.However,byusingaMonte-Carlosampling-basedapproachtolocaliza-tion,thefollowingadvantagesareachieved[13]:1.Itcanrepresentmulti-modaldistributionsincontrasttotheKalmanlter.2.ItdrasticallyreducesthememoryrequirementascomparedtoGridBasedapproaches.3.ItismoreaccuratethanMarkovLocalizationwithaxedcellsize,sincethediscretizationerrorisavoided.4.Itiseasytoimplement.C.MonteCarloLocalizationInMonte-CarloLocalization(MCL)basedapproaches,therequiredposteriorp(xkjz1:k)attimekisrepresentedbyasetofweightedsamplesSk=fxi;wig;i=0;1;2:::Npeachcontainingaweightwi,alsocalledimportancefac-tor.TheweightsarenormalizedaftereachupdatesothatPNpi=1wi=1.ToavoidintractableintegrationintheBayesianstatistics,theposteriordensityisrepresentedbyaweightedsumoftheseNpsamples.p(xkjzk)1 NpX(xk�xki)whereistheDiracdeltafunction.ForsufcientlylargeNp,thesummationapproximatesthetrueposteriordensity.IntheparticlelterimplementationofMCL,thesetofNpparticlesisrecursivelylteredintwostages:predictandupdate.1)Prediction:Inthisstep,theposteriorp(xkjxk�1;uk�1)attimekispredictedfromthebeliefstatep(xk�1jz1:k�1)andacontrolvectoruk�1.ThesetofparticlesSk�1cor-respondstothestatexk�1.Thecontrolactionuk�1hastobeappliedtoeachparticleinSk�1takingintoaccountthemotionmodeloftherobot.ThisgivesasamplesetS0k=x0i;w0i;i=0;1;:::Np.Notethatw0i=wi2)Update:Inthisstep,themeasurementmodelistakenintoaccount.Namely,eachparticleofS0kisweightedbythelikelihoodp(zkjxki);i=0;1;::Np.NowwehavethenewparticlesetSk.3)Degeneracy:Acommonproblemwithparticleltersisdegeneracy.Afterafewiterations,mostoftheparticleshavenegligibleweightandonlyfewofNpparticlescontributesignicantlytotheposterior.Thishappensbecausemostparticleshavedriftedfarawayfromtheactualpositionandhencetheirweights(whichisproportionaltothelikelihoodofmeasurement)isnegligible.Manyresamplingtechniqueshavebeensuggested.Inthiswork,thelineartimeresamplingtechniquein[14],[15]hasbeenused.Toavoidtheover-headofresamplingateveryiteration,theeffectivesamplesize(ESS)iscomputed.OnlyiftheESSdropsbelowacertainthreshold,resamplingisperformed.Resamplingdiscardsparticleswithnegligibleweightandduplicatestheparticleswithconsiderableweight.ESSiscomputedasfollows:cvt2=var(wti) E2(wti)=1 NpNpXi=1(Npwi�1)2ESSt=Np (1+cvt2)D.MotionModelThisinvolvespredictingthestateoftheparticle,givenitsinitialstateandacontrolvectoru.Thestateoftherobotisrepresentedbythevector[xy]T.Acontrolvectorisrepresentedby[d12]T.Thatis,therobotexecutes1unitsofrotationfollowedbydunitsoftranslationandthen2unitsofrotation.Noiseintranslationandrotation,anddriftingareconsidered.Themeanandvarianceoferrorintranslation,rotationsanddriftoftherobotwerecalculatedexperimentally.ThiserrorwasmodeledasaGaussianfunc-tion.Arandomsamplefromthisfunctionisaddedasnoisetothenewpredictedstate.LetN(;;x)denotethenormalfunctionwithmeanandvariance.ForthePresentstate-X=[xy]TandControlvector-u=[1d2]T,thecontrolvectorwithsomeaddednoiseu0isgivenbyu0=[01d002]T01=1+N(rot;rot;RANDOM)02=2+N(rot;rot;RANDOM)d0=d+N(trans;trans;RANDOM) RunNo. NI k "f Comments 1 9 15.45 0.20 Nofurniture 2 17 59.06 0.78 Amidstfurniture 3 12 13.83 0.30 Centreof2beacons 4 23 11.22 0.63 Nearbeacon 5 18 12.60 0.15 Centreof3beacons 6 14 21.35 0.50 Farthestfrombeacons TABLEII:Thistableshowstheresultsoftheexperiment:NI-No.ofiterations,k-Avg.No.oftrilaterations,"f-nalerror(m),Comments-aboutthestartinglocation.Thenumberofiterationsaredifferentforeachtrialsimplybecausetherobothadreachedtheboundaryofthearenadueitspurelyrandommotion.clutteredareas.InmostotherRFbasedmethodspositioningerrorsincreasedramaticallyinclutteredindoorenvironments,butouralgorithmstillperformsreasonably.Thelocationsofthebeaconswereknownbeforeeachtrial.Itwasobservedthatwhentherobotstartsfromormovesintoanunfavorablelocation,thenumberofdistancemappingsandtheaveragenumberoftrilaterationsincrease.AnunfavorablepositionisoneinwhichthethemeasuredRSSIisanoutlier.Motionplanningtechniquessuchas,movingtowardsthecentroidofthebeacons(say),canbeexplored.Itwouldreducetheerroraswellasthenumberofiterations.Thisbecomescrucialwhentheenvironmenthasalotofobstacles.VI.CONCLUSIONSANDFUTUREWORKInthispaperweshowthatbluetoothcanbeusedforrobotlocalizationinindoorenvironmentswithanaccuracyof1musingacomputationallyinexpensivemethod.InspiteoftheGaussianassumptionsandlackofodometry,weachievedanaccuracyof0.4270.229m.Exceptthelocationsofthebeacons,anextensiveknowledgeoftheenvironmentisnotrequired.Limitationsascitedbypreviousworkshavebeenovercome.Thetimeforeachiterationisdominatedbythetimerequiredtoperforminquiry.ThiscanbeimprovedbytheuseofInterlacedinquiry.Presenceofobstaclesintheenvironmentaffectstheperformanceofoursystem.Itcanbeseenthatsomelocationsarefavorableandplanningthemotionaccordinglywouldresultinbetterresults.Wealsoplantoexploretheuseofauxiliaryparticleltersandclass1donglestoobtainbetterperformance.AlthoughwechoseBluetooth,thissystemcanbeimplementedanywirelesstechnologythatprovidesanRSSIvalue.VII.ACKNOWLEDGMENTSWeacknowledgeBalajiLakshmananfromtheRISElab,IndianInstituteofTechnology,Madrasfordevelopingthe'MoBo'mobilerobotplatformthatwasusedintheexperiments.REFERENCES[1]J.Hallberg,M.Nilsson,andK.Synnes.Positioningwithbluetooth.InICT2003:10thInternationalConferenceonTelecommunications,volume2,pages954-958vol.2,Feb-March2003.[2]A.MadhavapeddyandA.Tse,AStudyofBluetoothPropagationUsingAccurateIndoorLocationMapping,2005,vol.3660.[Online].Avail-able:http://www.metapress.com/content/2FGWHFACYGC011HY[3]TimothyM.Bielawa,PositionLocationofRemoteBluetoothDevices,MSThesis,VirginiaPolytechnicInstituteandStateUniversity,2005[4]KotanenA.,HannikainenM.,LeppakoskiH.andHamalainenT.D,ExperimentsonlocalpositioningwithBluetooth.InITCC2003:InternationalConferenceonInformationTechnology:CodingandComputing[ComputersandCommunications],2003.Proceedings,pages297-303,28-30April2003.[5]SilkeFeldmann,KyandoghereKyamakya,AnaZapater,andZighuoLue.Anindoorbluetooth-basedpositioningsystem:Concept,imple-mentationandexperimentalevaluation.InInternationalConferenceonWirelessNetworks,pages109-113,2003.[6]VarunAlmaulaandDavidCheng,BluetoothTriangulator,FinalProject,DepartmentofComputerScienceandEngineering,UniversityofCalifornia,SanDiego,2006[7]ShengZhouandJ.K.Pollard.Positionmeasurementusingbluetooth,IEEETransactionsonConsumerElectronics,52(2):555-558,May2006.[8]SpecicationoftheBluetoothSystem,Version2.0+EDR,BluetoothSIG,2004[9]AlbertHuangandLarryRudolph,APrivacyConsciousBluetoothInfrastructureforLocationAwareComputing,MassachusettsInstituteofTechnology2004.[10]Bing-FeiWu,Cheng-LungJen,andKuei-ChungChang.NeuralfuzzybasedindoorlocalizationbyKalmanlteringwithpropagationchannelmodeling.InIEEEInternationalConferenceonSystems,ManandCybernetics,2007,pages812-817,Oct.2007.[11]Erin-Ee-LinLauandWan-YoungChung.EnhancedRSSI-basedreal-timeuserlocationtrackingsystemforindoorandoutdoorenviron-ments.InICCIT07:Proceedingsofthe2007InternationalConferenceonConvergenceInformationTechnology,pages1213-1218,Washing-ton,DC,USA,2007.IEEEComputerSociety.[12]SebastianThrun,WolframBurgardandDieterFox,ProbabilisticRobotics,September2005[13]ZheChen,Bayesianltering:FromKalmanlterstoparticlelters,andbeyond,Technicalreport,McMasterUniversity,2003.[14]IoannisM.Rekleitis,Aparticleltertutorialformobilerobotlocaliza-tion,TechnicalReportTR-CIM-04-02,CentreforIntelligentMachines,McGillUniversity,3480UniversitySt.,Montreal,Quebec,CanadaH3A2A7,2004.[15]J.Carpenter,P.Clifford,andP.Fernhead,Animprovedparticlelterfornon-linearproblems,tech.rep.,DepartmentofStatistics,UniversityofOxford,1997.