OPTIMAL QUANTIZERS FOR DISTRIBUTED BAYESIAN ESTIMATION

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1、OPTIMALQUANTIZERSFORDISTRIBUTEDBAYESIANESTIMATIONAdityaVempatyBiaoChenPramodK.VarshneyDepartmentofEECS,SyracuseUniversity,NY,13244USAemail:favempaty,bichen,varshneyg@syr.eduABSTRACTparameterhasapriorprobabilitydensityfunction(pdf)p()where2.ThereareatotalofN+1sens

2、orsS0;S1;


;SNinthenet-Inthispaper,weconsidertheproblemofquantizerdesignfordis-workandsensorS0playstheroleofFCwhereastheotherNsensorstributedestimationundertheBayesiancriterion.Wederivegeneralareperipheralsensors.EachsensorSi,fori=0;1;


;Nreceivesoptimalityconditio

3、nsundertheassumptionofconditionallyinde-alocalobservationYiwhichisanoisyrealizationoftheparameterpendentobservationsatthelocalsensorsandshowthatforacondi-andtakesvaluesinasetYi.WeassumethroughoutthispaperthattionallyunbiasedandefficientestimatorattheFusionCenter,iden

4、-Yi’sareconditionallyindependentandidenticallydistributed,henceQticalquantizersareoptimalwhenlocalobservationshaveidenticalNtheoveralllikelihoodfunctionisp(yj)=p(yij).Thislike-distributions.ThisresultsinanN-foldreductionincomplexityi=0lihoodfunctionisknownattheFC.w

5、hereNisthenumberofsensors.WeillustrateourapproachbyEachsensorSi,i6=0,quantizesitsobservationyi,whichisaapplyingittothelocationparameterestimationproblem.realizationoftherandomvariableYi,usingalocalquantizeri(
).IndexTerms—DistributedEstimation,QuantizerDesign,Pos-The

6、quantizeroutputui=i(yi)21;


;DistransmittedtotheteriorCramerRaoLowerBound(PCRLB)´FCerrorfree.TheFCusesu1;


;uNalongwithitsownobserva-tiony0(realizationofY0)andestimatestherandomparameteras^=N!1.INTRODUCTION0(y0;u1;


;uN)2.Here0:Y0f1;


;Dgisafunctionthatwillb

7、ereferredtoastheestimator.Fori=Distributedparameterestimationfromquantizeddatahasbeenan1;2;


;N,weuseitodenotethesetofallpossiblequantizersofactiveareaofresearch[1–5].IdenticalquantizersatthesensorssensorSi.Thecollection=(1; 2;


; N)ofquantizerswillhavetraditional

8、lybeenusedbyresearchersasitsimplifiesthede-bereferredtoasastrategy.Theestimatorisassumedtobegivensignproblem[3][6].However,relativel