Approximate distributed Kalman filtering in sensor networks(6)

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

Typical Measurement History

432

t

ne1merus0aeM 1dna n 2oitisoP 3 4 5

6

01002003004005006007008009001000

Time Index

Fig.6.Ameasurementhistoryusedinoursimulation.Themeasurementnoiseisdeliberatelysetveryhigh,withvari-ance vetimestheamplitudeofthesignal.

True Positions and Centralized Kalman Filter1

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etam0.5itsE dna0 snoitiso 0.5P 1

0200

4006008001000

Time Index

Fig.7.ThesimulationresultsfromthetopologyshowninFigure5.Thetrajectoryshownistheworstamongallsen-sors,inthemean-squareerrorsense.Evenwithrelativelyfewmessagesperunittime,thedistributedestimatesdifferfromthecentralizedestimatebytento ftypercent,despitetheextremelynoisymeasurements(comparethescalesoftheseplotstothescaleofFigure6).Asthenumberofmes-sagesperunittimeincreases,theperformanceofthedis-tributedestimatorimprovesdramatically.

True Positions and Centralized Kalman Filter1

s

etam0.5itsE dna0 snoitiso 0.5P 1

0200

4006008001000

Time Index

Fig.8.ThesimulationresultsfromthetopologyshowninFigure5withall“diagonal”connectionsadded.Notethattheimprovedcommunicationtopologyhassigni cantlyimprovedtheperformanceofthedistributedestimationscheme.

H bound: λ = 1

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|Hey|

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ω (normalized)

Fig.9.Theboundontheerrortransferfunctionforthenet-workdepictedinFigure5,inlogarithmicscale.Notethedrasticimprovementintrackinglow-frequencysignalsasnincreases.