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