ateareferencesignalstrengthmapSS-MAP.TheproposedsystemusesfiveAPsdeployedinabuildingof65×48meter.Tolo-cateamobileuser,twodifferentlocalizationmethod(LMSEandprioritizedmaximumpower)areevaluatedandcompared.There-sultsshowthattheLMSEmethodprovidesbetterestimationper-formanceforuserswithinthebuilding.However,prioritizedmaxi-mumpowerislesssusceptibletoreferencegridresolutionandcanachievebetterestimateswhenmobileuserresideswithinthevicin-ityareaoutsideofthebuilding.TheresultsfromHatami(Figure3in[19])showarelationof10meterscomplementarycumula-tivepositioningerrorwith54%probabilityforprioritizedmaxi-mumpowermethod.TheresearchbyHatami[19]mainlyfocusedonlocalizationalgorithmstargetedatintruderdetection.ItusesraytracingsoftwaretoconstructsignalstrengthmapSS-MAPwithoutintroducingtheindoorradiopropagationmodel.
Differentfromthesesystems,thispaperintroducesARIADNE,anewindoorlocalizationsystem.Itcontainstwomodules,thefirstmoduleismapgeneration,anditincludesanewindoorradiopropa-gationmodel.Thesecondmoduleissearchmodule,anditpresentsaclustering-basedlocalizationalgorithmthatworksonimpreciseradiopropagationmaptables.Theradiopropagationmodeliseval-uatedbycomparingestimatesagainstactualsignalstrengthmea-surements.ThispaperreportsthelocalizationperformanceoftheARIADNEsystem,andfurthercomparestheproposedlocalizationalgorithmwithotherexistingalgorithms.
Figure3:Radiopropagationwithraytracing
3.1.2Raytracing
ARIADNEconsistsoftwomodulesasillustratedinFigure2-namelymapgenerationandsearch-thataredevelopedinSec-tion3.1andSection3.2,respectively.
3.1MapGenerationModule
Mapgenerationincludesmultiplesteps:Subsection3.1.1devel-opsthefirststepthatconsistsofcapturingthecharacteristicsofthefloorplanandproducea3-Dmodelnecessaryforraytracing.Sub-section3.1.2explainshowraytracingisusedforthedeterminationoftheindividualraycontributiontothesignalstrengthonagridofpoints.Apropagationmodelisproposedinsubsection3.1.3,anditsparametersissolvedinSubsection3.1.4andSubsection3.1.5usingsimulatedannealing.
Raytracing(RT)approximatestheradiopropagationwithafi-nitenumberofisotropicraysemittedfromatransmittingantenna[23].Foranomnidirectionalantenna,eachrayisassumedtotrans-mitwiththesameamountofenergyatthetransmitter,andtheen-ergyoftherayswillbeattenuatedatwallsorfloorsduetoreflec-tionsandtransmissions.Raytracingtechniquehasbeenwidelyusedtosimulatetheindoorradiopropagationcharacteristicsandtopredictthesite-specificfeaturesoftheindoorradiochannels[22,24,25].
Rayimagingtechniquesareusedtorecordeachrayfromthetransmittertothereceiver.Intherayimagingtechnique,thetrans-mitterisassumedtobereflectedateachsurfacearoundittopro-duceimagetransmitters,thereflectedraystothereceiverfromtherealtransmitterareconsideredasdirectpathsfromthemirrorim-agesofthetruetransmitter.Basedongeometricaloptics(GO),eachrayfromthetransmittertothereceivercanbeexactlydeter-mined.Thedetailedraytechniqueisomittedhereforlackofspace(agoodreferencecanbefoundin[24,26,27]),butinstead,severalkeypointsofARIADNEareemphasized.
oSimilartotheresearchbyHassan-AliandPahlavanin[12]andBertonietal.in[28],thediffractionandscatteringeffectareneglectedintheproposedpropagationmodelbecauseoftheminorcontributionoOnlyrayswithpoweraboveafixedthreshold[29]areconsid-eredbecausehighlyattenuatedraysdonotreachthereceiverinrealityeventhoughatransmissionpathexistsintheory.oSimilarto[12],themultipathpoweratreceiverisdeterminedasthesumofallindividualpowersregardlessofthephaseofeachpath.Figure3depictsasimplescenariowherethreeraysareshownfromthetransmitterTtothereceiverR.Eachrayriiscomposedbymultiplesegmentswheredistanceofthejthsegmentisdij.Di-rectpath(rayr1)isdenotedbyasolidline.Theothertwopaths(rayr2andr3)areindirectandcontainreflections.Thefaintdashedline(rayr2)hasonereflectionanddottedline(rayr3)hastwore-flections,respectively.Thedistancestraversedbyeachrayisalsodepictedinthefigure.
3.1.1Floorplaninterpretation
Themainpurposeofthefloorplaninterpretationistointegratethegeometryacquisitionprocessasanautomaticprocedure.ThemajortaskoftheinterpretationprocessistoextractthestructuralparametersfromconstructionCADfilesorfloorplanimagefiles.Structuralinformationisextractedfromthepictureusingbasicimageprocessingtechniques,inwhichapictureisdenotedasamatrix.Eachelementinthematrixhasavaluecorrespondingtothebrightnessofthepixelatthecorrespondingposition,whichisanintegerbetween0and255.The0correspondstoblackand255towhite.Ifthepixelvalueofthelinesinthepictureisdenotedby0,thenthegroupingofasetofconnected0valuepixels,verticallyorhorizontally,yieldsaline.
Thewallgeometryinformationisconstructedbyextendingthelinesverticallyin2Dimagewithbasecoordinatesandthefloorheight.Bystackingthewallinformationateachfloor,overallstruc-turalrepresentationofthebuildingisobtained.Similartomostpre-viousresearch[22],awall/floorismodelledasasingleplaneinthemiddle.Theoffsetbetweenrefractedandincidentraysis
3.1.3Radiopropagationmodel
AsexplainedinSection3.1.2,thesignalpoweratthereceiveristheaccumulatedmultipathpowerfromallindividualraysfromthesametransmitter.Foreachray,theattenuationpathlossincludesthreecomponents:
1.Thedistance-dependentpathloss,whichisassumedasfree
2.Theattenuationduetoreflections,whichistheproductofthereflectioncoefficientandthetotalnumberofreflectionsfromtran3.Theattenuationduetotransmission,whichistheproductofthetransmissioncoefficientandthetotalnumberoftransmis-sionwalls.Consequently,themodelisdefinedas:
somechangesthatincreaseit.Thus,SAmethodcanachieveglobaloptimizationwithoutgettingtrappedatalocalminima[32].
TheoriginalMetropolisscheme[30]indicatesthataninitialstateofathermodynamicsystemischosenatenergyEandadesiredtemperatureT.HoldingatthattemperatureT,theinitialconfigu-rationisperturbedandthechangeinenergydEiscomputed.Ap-plyingMonteCarlosamplingtechniques,thephysicalannealingprocessismodelledsuccessfullybycomputersimulationmethods.Aconvenientformulacanbeborrowedfromthermodynamics:
E?)P(E)=exp(-kT
(P0-20log10(di)-γ·Ni,ref-α·Ni,trans)(3)
wherePisthepower(indB)atreceiver,Nr,jisthetotalnum-berofraysreP0isthepower(indB)atadistanceof1di,Ni,ref,andNi,transrepresentthetotaltransmissiondistance,thetotalnumberofreflectionsandthetotalnumberof(wall)transmissionsoftheithray,respectively.γisthereflectioncoefficient,andαisthetransmissioncoefficient.
InFigure3,thetransmissiondistancesforthreerays(r1,r2,andr3)ared1,1,d2,1+d2,2,andd3,1+d3,2+d3,3,respectively.Rayr2hasonereflection,andrayr3hastworeflections.Allthreerayshavetwowalltransmissions.WhenstartingfromtransmitterT,allthreeraysareassumedtoholdthesameamountofpower.Withdifferenttransmissionconditions,thefinalsignalpowerofeachindividualrayobservedatthereceiverRaredifferent.AndtheoverallsignalpoweratthereceiverRisthesumofthepowersfromallreceivedrays.
Thesitespecificparameters(Nray,di,Ni,ref,andNi,trans)inEquation3canbeobtaineddirectlyfromraytracingasdescribedintheSection3.1.2.Theotherthreeparameters(P0,γ,andα),inothersimilarresearch,areusuallyderivedfromtediousmea-surements.ARIADNEdoesnotrequireextensiveonsitemeasure-ments.Instead,simulatedannealing(SA)techniqueisusedtode-termineoptimalvaluesforthethreeparametersoftheproposedmodel.ONEreferencemeasurementonlyisrequired.
?whichexpressestheannealingprobabilityP(E)ofachangeon
energyEattemperatureT,wherekisBoltzmann’sconstant.
Giveninitialvaluesofx=[P0γα]TatatemperatureT,thepowerofeachindividualraycanbecomputed(Equation3).(Theinitialvaluescanbeanypositivenumbers,however,bettervalueswillminimizethesearchtime.Generally,bettervaluescanbede-rivedfromliterature.)Neglectingthoserayswithpowerbelowthethreshold,andsummingthepowersofallothers,yieldthemulti-pathpoweratthereceiver.Theleastminimumsquarederror(Equa-tion2)allowsthecomparisonofthepowerestimatesfitnesswiththemeasurements,andhenceforththeadjustmentoftheparametersofxaccordingly.
Toadjusttheparameters,arandommovementisgeneratedbyaddingadeviatefromtheCauchydistributiontoeachparameterofx=[P0γα]T:
?),i=1,2,3xi+1=xi+T·tan(P
ThecoolingscheduleforthetemperatureTcanuseasimplemethod
similarto[31]:
Ti+1=a·Ti,a∈(0,1)
Consequently,theSimulatedannealingsearchalgorithmcanbede-tailedbelow:
1)Defineinitialvaluesforx=[P0γα]T.
2)Definethetemperature,TmaxforhighesttemperatureandTminfo3)CalculatetheannealingprobabilityfromEquation4;4)UpdatethedisplacementfortheparametersusingEquation5;5)Calculatethefitnessbetweentheestimatesandthemeasure-mentsusingequation2:ifabetteragreementisobtained,keepthedisplaceelse,keepthedisplacementwi6)UpdatethetemperatureTbyequation6,andrepeatsteps3,4,and5untilT&Tminorspecifiedminimumerrorsisachieved.Simulatedannealingmethodcaneffectivelyestimateparametertriplex=[P0γα]TwithonlyONEreferencemeasurement.
3.1.4ParametersEstimation
Toestimatetheradiopropagationparameters(referencepoweroftherayP0,reflectioncoefficientγ,andtransmissioncoefficientα),somemeasurementsatreferencepositionsinsidethebuildingareneeded.Ifamaximumofnreferencemeasurementsareavail-able,alinearsystemofAx=b(derivedfromequation3)canbeusedtodeterminethethreeunknownsx=[P0γα]T.
Tosolvethelinearequations,themethodofleastsquarescouldbeused.However,itisdifficult.Asstatedearlier,onlyrayswithpowerabovecertainthresholdareconsideredintheradiopropaga-tionmodel.Orinotherwords,fromraytracingsimulation,amax-imumnumberofNraysmayexist,theoretically,fromthetrans-mittertothereceiver.Inreality,onlyn(n&N)raysareactuallyreceivedbecauseofthedifferentattenuationalongeachindividualpath.Sincesomeraysaretooweaktocontributetheenergyatre-ceiver,theymustbeeliminatedfromthelinearsystem.Suchaneliminationprocessisverydifficultatthisstagebecauseofthelackoftheenergyinformation(again,theChickenandEggDilemma).Inthisresearch,weusesimulatedannealingalgorithmtosearchtheoptimalvalueofx=[P0,γ,α]T.
3.1.5SimulatedAnnealingSearchAlgorithm
Searchmodule:Clustering-basedSearchAlgorithm
SimulatedAnnealing(SA)[30,31]isamethodusedtosearchforaminimuminageneralsystem.Itisbasedontheprocessofthewayametalcoolsdowntotheoptimalstate(theannealingpro-cess).SA’smajoradvantageisanabilityofarandomsearchwhichnotonlyacceptschangesthatdecreaseobjectivefunction,butalso
Tolocateamobileuser,thecurrentuser’ssignalstrengthmea-surementtripletissearchedfromthesignalstrengthmapSS-MAPforamatch.Currently,mostsearchalgorithmsarebasedontheLMSEandselectasinglelocationastheestimate.ThismethodworksifadetailedandpreciseSS-MAPforthebuildingisavail-able.Asindicatedinmanypapers,thesignalstrengthisobserved
tobeverydynamicatdifferentmeasurementtimes,andtocollectafine-gridsignalstrengthmapistime-consumingforlargescalebuildingdeployments.Consequently,theLMSEmethodwillnotgenerateoptimalestimatesinmostcircumstances.Therefore,itisdifficulttomakeadecisionifthismethodistobeusedexclusively.ARIADNEproposesaclustering-basedsearchalgorithmfortheindoorlocalizationofamobileuserbasedonthefollowingfind-ings:
oARIADNEconstructsfine-gridsignalstrengthmapSS-MAPbasedontheradiopropagationmodelandthesite-specificgoTheSS-MAPfromthepropagationmodelprovidesreal-timeestimateswithoutfurtherhumanintervention.However,itisonlyaclosefittothemeasurements,orinotherwords,itisimpreciseandsmallestimationerrorsareexpeoConsequently,LMSEmayresultmultiplepossiblelocationsintheSS-MAPtable,ortheuniquelocationcorrespondingtotheLMSEisnotnecessaoIfasetofpositions(correspondingtolowmeansquareerrorwithrespecttoapredeterminedthreshold)isselected,thepositionscanbegroupedintoseveralclusters.Thelargestclusterwillgenerallyhavehigherprobabilitytocontainthetruepositionforthemobileuser.oThelocationestimateswiththeclustering-basedsearchmethodmayprovidelargererrorsforsomepositions,however,theoverallestimationerrorgetsloweredandtheconfidenceisimproved.Theclustering-basedsearchalgorithmisatwo-phasesearchal-gorithm.Thefirstphaseisnamedasdatacollectionandclusterpreparationphase,anditisintroducedinSubsection3.2.1,whereasetofcandidatelocationswithlowermeansquareerrorwithinthethresholdareselectedandpreprocessedwiththepurposetone-glectisolatedlocationsfromtheset.Thesecondphaseisclusteringphase,anditispresentedinSubsection3.2.2,wheretheremainingcandidatelocationsaregroupedintoseveralclustersandthecenterofthelargestclusterischosenasthefinalestimate.
Figure4:Positionisolationexample
clusterxihaslargerdistancedi,jtoeveryotherclusters,itmeansthatclusterxiisanisolatedcluster.Iffurtherthisclustercontainsmuchsmallerpopulations,itmaybeomittedfromthecandidatelocationset.
Figure4showsanexampleofasetofpositionsinspace.Inthefigure,position8isipositions5and7areclosetoeachotherandtheymaybetreatedasonegroupwhichisagainseparatedfromothers.Figure5givesthedistanceinfor-mationbetween(group)positionsforthedatasetinFigure4.Ifpositionsof{1,2,3,4,6}aregroupedintoonecluster,andpositions{5,7}formasecondcluster,thentheminimumdistancebetweenthesetwoclustersis0.3340.Ifpositionsof{1~7}aretobegroupedintoabiggercluster,andtheposition8isanothergroup,thentheminimumdistancebetweenthemis0.8311.Forthedatasetintheexample,positionsof{5,7,and8}maybeneglecteddur-ingthispreparationphase.
3.2.2ClusteringPhase
3.2.1DataCollectionandClusterPreparationPhase
IntheDataCollectionandClusterPreparationphase,thecurrentsignalstrengthmeasurementtripletM(SA,SB,SC)(L,Now)ofmobileMatsomelocationLiscomparedwithallrecordsfromtheestimatedSS-MAP.Insteadofselectingonlyasinglelocationforestimation,ARIADNEselectasetofcandidatelocationsaccordingtoapredeterminedmeansquareerror(MSE)threshold.
BecauseoftheimprecisenatureoftheestimatedSS-MAP,someoftheselectedcandidatelocationsmaybescatteredaroundthefloorplan.Inordertopreparethecandidatelocationsforclus-tering,thescatteredorisolated(unlikely)locationpointsmustbedetectedandomittedfromthesetofcandidatelocations.Theiso-latedpositionischaracterizedbyalargerdistancefromitslocationtoallothercandidatelocations.Forexample,iftherearetotalNcandidatelocationsinaselectedlocationset,letxiandxjbetwolocationclusterswithmandncandidatelocations,respectively,m,n∈[1,N],andm+n≤N;andletdi,jbetheminimumpairwisedistancefromanymemberinstancesofthesetwoclusters.
di,j=min(dist(xi,r,xj,t))
whererandtrepresentthepositioninstanceinclusterxiandxj,1≤r≤m,and1≤t≤n.Ifthecandidatelocation
Aftertheclusterpreparationphase,mostoftheremainingposi-tionshaveneighborsclosetothem.Consequently,themainpur-poseoftheclusteringphaseistodeterminetheintrinsicgroupingofthesetforthesepositions,andtoselecttherightclusterfortheestimates.
Togroupthesetofpointsinspace,twocommonmethodsareavailable.Thefirstoneisanhierarchicalclusteringmethod,andthesecondoneisK-clusteringmethod.
oThehierarchicalclusteringmethod[33]producesahierarchytreestructureoftheoriginaldataset.Theleavesareindivid-ualelementsandinternalnodesaresub-clusters.Eachlevelofthetreerepresentsapartitionoftheoriginaldatasetofseveralsub-clusters.Figure5isanexampleofthehierarchi-calclusteringmethod.oK-clusteringmethodsearchesthebestkclustercentroids,andpartitionthedatasetbyassigningeachpointtoitsnear-estcentroid.K-meansclustering[34]isoneofthemostcom-monK-clusteringalgorithm.Theclusteringprocedureismoreobservableifhierarchicalstruc-tureoftheoriginaldatasetisobtained(Figure5).Ifaminimumofthreeneighborsareselected({1,2,6}),ittranslatestotheclosenesseliminationschemeaddressedbyPrasithsangareein[17].Andifonlytwoneighborsarechosen({1,2}),itisthetwoclosestneigh-boringschemebyPandey[18].Howeveritisdifficulttodeterminetheexactnumberofneighboringpositionsthatshouldbeselectedin
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