macro-calibration
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Macro-calibrationMacro-calibrationKamin WhitehouseKamin Whitehouse
David CullerDavid Culler
WSNA, September 28 2002WSNA, September 28 2002
Macro-CalibrationMacro-Calibration
Calibration problems in Sensor Networks Calibration problems in Sensor Networks Many, many devicesMany, many devices noisy devices and environmentsnoisy devices and environments Post-deployment calibrationPost-deployment calibration
Macro-calibrationMacro-calibration Calibrate the network, not the devicesCalibrate the network, not the devices Leverage redundancy to reduce noiseLeverage redundancy to reduce noise Use the network to calibrate itselfUse the network to calibrate itself
Talk OutlineTalk OutlineExample application: distance estimationExample application: distance estimation
Traditional calibrationTraditional calibration Iterative calibrationIterative calibration
Macro-calibrationMacro-calibration Joint calibrationJoint calibration Auto-calibrationAuto-calibration
Calamari OverviewCalamari Overview
Simultaneously send sound and RF signalSimultaneously send sound and RF signal
Time stamp both upon arrivalTime stamp both upon arrival
SubtractSubtract
Multiply by speed of soundMultiply by speed of sound
No Calibration: 74.6% ErrorNo Calibration: 74.6% Error
Sources of Noise in CalamariSources of Noise in Calamari
Bias – startup time for mic/sounder Bias – startup time for mic/sounder oscillationoscillation
Gain – Volume and sensitivity affect PLLGain – Volume and sensitivity affect PLL
Frequency -- |FFrequency -- |FTT-F-FRR| affects volume| affects volume
Orientation – |OOrientation – |OTT-O-ORR|| affects volumeaffects volume
The calibration problem in CalamariThe calibration problem in Calamari
Chicken or egg?Chicken or egg? Need sounder to calibrate microphonesNeed sounder to calibrate microphones Need microphone to calibrate soundersNeed microphone to calibrate sounders
Note that all calibration problems are really Note that all calibration problems are really sensor/actuator problems.sensor/actuator problems.
Traditional CalibrationTraditional Calibration
Iterative CalibrationIterative Calibration Designate one ‘reference’ nodeDesignate one ‘reference’ node Calibrate all others against itCalibrate all others against it
De facto standard for relative calibration:De facto standard for relative calibration: The ‘standard meter’ approachThe ‘standard meter’ approach Hightower ’00 used it for localization Hightower ’00 used it for localization
Traditional Calibration: 19.7%Traditional Calibration: 19.7%
Naive Calibration: 21% ErrorNaive Calibration: 21% Error
Traditional CalibrationTraditional Calibration
WeaknessesWeaknesses Noise propagationNoise propagation Unobserved parametersUnobserved parameters
Macro: Joint CalibrationMacro: Joint Calibration
Collect distance estimates for all pairsCollect distance estimates for all pairs
Create system of equationsCreate system of equations
rrii* = G* = Gttrrii + G + Grrrrii + B + Btt + B + Brr
Choose device parameters that optimize Choose device parameters that optimize overall systemoverall system
Joint Calibration: 10.1%Joint Calibration: 10.1%
Macro: Joint CalibrationMacro: Joint Calibration
StrengthsStrengths Exploits redundancy to reduce noiseExploits redundancy to reduce noise
WeaknessesWeaknesses Centralized computationCentralized computation Cannot handle non-linear parametersCannot handle non-linear parameters
Macro: Auto-CalibrationMacro: Auto-Calibration
All transmitter/receiver pairs are also All transmitter/receiver pairs are also receiver/transmitter pairsreceiver/transmitter pairs
These symmetric edges should be equalThese symmetric edges should be equal
Let Let ddTRTR = = BBTT + B + BRR + G + GTT*r + G*r + GRR*r *r
For all transmitter/receiver pairs For all transmitter/receiver pairs i, k:i, k:
ddik = ik = ddkiki
Macro: Auto-CalibrationMacro: Auto-Calibration
All distances in the network must follow All distances in the network must follow the triangle inequalitythe triangle inequality
Let Let ddTRTR = = BBTT + B + BRR + G + GTT*r + G*r + GRR*r *r
For all connected nodes For all connected nodes h, i, k:h, i, k:
ddih + ih + ddikik - d - dhkhk >=0 >=0
Consistency/constraint-basedConsistency/constraint-based
Choose parameters that maximize Choose parameters that maximize consistency while satisfying all constraintsconsistency while satisfying all constraints
A quadratic program arisesA quadratic program arises
Minimize: Minimize: ΣΣikik (d(dik ik –– ddkiki))2 + 2 + ΣΣTT(G(GTT–– 11))2 + 2 + ΣΣRR(G(GRR–– 11))22
Subject to: dSubject to: dih + ih + ddjjkk - d - dhkhk >=0 for all triangle >=0 for all trianglehikhik
Future WorkFuture Work
Non-gaussian variations of the above Non-gaussian variations of the above algorithmsalgorithms
Non-linear parameter estimationNon-linear parameter estimation Expectation\maximizationExpectation\maximization MCMCMCMC
ConclusionsConclusions
Macro-calibration Macro-calibration Easier and fasterEasier and faster Allows global optimizationAllows global optimization
Leverages redundancy Leverages redundancy
Dependencies between sensorsDependencies between sensors
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