distributed estimation and quantization

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1、IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.39,NO.4,PP.1456{1459,JULY1993DistributedEstimationandQuantizationJohnA.Gubner,Member,IEEEAbstract

2、AnalgorithmisdevelopedforthedesignofaconsiderationsareimportantiftheestimateofXmustnonlinear,n-sensor,distributedestimationsystemsubjecttobecomputedinrealtime.By

3、usingasuboptimales-communicationandcomputationconstraints.ThealgorithmtimatorofXforwhichsomeoftheprocessingcanbeusesonlybivariateprobabilitydistributionsandyieldslocallydonelocallyatthesensorplatforms,itmaybepossi-optimalestimatorsthatsatisfytherequiredsystemconstraints.bletodesignanacceptableestim

4、atorthatcanoperateItisshownthatthealgorithmisageneralizationoftheclassicalinrealtime.Lloyd{Maxresults.3)AsindicatedinFig.1,thesensorplatformstransmitIndexTerms

5、Nonlinearestimation,distributedestima-theirdatatothefusioncenter.However,usinganytion,sensorfusion,Lloyd{Maxalgorithm.physicalcommunication

6、system,itisnotpossibletotransmitreal-valuedquantitieswithoutdistortion.InI.Introductionthissituation,theconditionalexpectation,oreventhebestlinearestimate,isgenerallyaphysicallyunreal-ONSIDERthedistributedestimationsystemshowninizablesolution.CFig.1.Thesystemconsistsofnsensorplatformswhoserespectiv

7、emeasurements,Y;:::;Y,arerelatedtosome1nInthispaperwedevelopanalgorithmtodesignsolutionsunobservablequantity,sayX.Eachsensorplatformpro-tothedistributedestimationproblemthatdonotsuercessesitsrespectivemeasurementandtransmitstheresultfromthesediculties.overacommunicationchanneltoacommonfusioncen-t

8、er.Thesensorsdonotcommunicatewitheachother,andYY1nthereisnofeedbackfromthefusioncentertothesensorplatforms.Thetaskofthefusioncenteristoestimatethe^unobservedquantityX.WedenotethisestimatebyX.??^Clearly,XisafunctionofY;:::;Y,andwecanwrite1nSensorSensor...^Platform1PlatformnX=f(Y;:::;Y)forsomefunctio

9、nf.Theproblemthen1n^istochoosethefunctionfsothatXisclosetoXinsome@?sense.Forexample,itiswellknownthatintheappropriate@?@?probabilisticsetting,theminimum-mean-square-erroresti-@?mateofXgivenY;:::;Yisthecondi