We analyze the performance of a distributed Kalman filter proposed in recent work on distributed dynamical systems. This approach to distributed estimation is novel in that it admits a systematic analysis of its performance as various network quantities su

H bound: λ = 2

10

10

10

|Hey|10

10

10

10

ω (normalized)

Fig.10.Theboundontheerrortransferfunctionforthenet-workwith“diagonal”connections.Weseethesamequali-tativedependenceonthenumberofmessageexchanges,butthisnetworkhassigni cantlylargerλ2.Thisisveri edbyimprovedperformanceinthesimulationresults,asshowninFigure8

work,andthissuggeststhattheproposedKalman ltercanbetranslatedtoapracticalimplementation.

Ourperformanceanalysisshowsasimpleboundfortheerrortransferfunctionwhichincorporatesthenetworktopol-ogy,connectiondensity,andcommunicationbandwidth.Wehaveshownsimulationsdemonstratingthisdependence,along-sidetheboundsforthiserrortransferfunction.Thisis,webelieve,anovelcontributiontodistributedestimation,whichtypicallydoesnotallowsystematicanalysisofper-formanceundernon-idealizednetworkconditions.

Thesimulationresultsdonotspeaktothefullpowerofthisapproach,inthatthisdistributed lteringmecha-nismisnaturallyandsimplyscalabletoarbitrarilylargenetworks,whilemaintaininganalyticalperformanceboundsthataredirectlyrelatedtotheunderlyingsensornetwork.Ofcourse,boundsontheerrortransferfunctionarenotnec-essarilyappropriateforallapplicationsofdistributedesti-mation,butitislikelythatthiswillbeusefulfordistributedcontrolapplicationswherequantitativeperformancemea-suresareessential.Nonetheless,itremainstobeseenwhetherapracticalversionofthisdesigncancompetewithmorees-tablishedapproachestodistributedestimation.

8.REFERENCES

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