Macro-calibration Kamin Whitehouse David Culler WSNA, September

Macro-Calibration Calibration problems in Sensor Networks Many, many devices Many, many devices noisy devices and environments noisy devices and environments Post-deployment calibration Post-deployment calibrationMacro-calibration Calibrate the network, not the devices Calibrate the network, not the devices Leverage redundancy to reduce noise Leverage redundancy to reduce noise Use the network to calibrate itself Use the network to calibrate itself

Talk Outline Example application: distance estimation Traditional calibration Iterative calibration Iterative calibrationMacro-calibration Joint calibration Joint calibration Auto-calibration Auto-calibration

Calamari Overview Simultaneously send sound and RF signal Time stamp both upon arrival Subtract Multiply by speed of sound

No Calibration: 74.6% Error

Sources of Noise in Calamari Bias – startup time for mic/sounder oscillation Gain – Volume and sensitivity affect PLL Frequency -- |F T -F R | affects volume Orientation – |O T -O R | affects volume

The calibration problem in Calamari Chicken or egg? Need sounder to calibrate microphones Need sounder to calibrate microphones Need microphone to calibrate sounders Need microphone to calibrate sounders Note that all calibration problems are really sensor/actuator problems.

Traditional Calibration Iterative Calibration Designate one ‘reference’ node Designate one ‘reference’ node Calibrate all others against it Calibrate all others against it De facto standard for relative calibration: The ‘standard meter’ approach The ‘standard meter’ approach Hightower ’00 used it for localization Hightower ’00 used it for localization

Traditional Calibration: 19.7%

Naive Calibration: 21% Error

Traditional Calibration Weaknesses Noise propagation Noise propagation Unobserved parameters Unobserved parameters

Macro: Joint Calibration Collect distance estimates for all pairs Create system of equations r i * = G t r i + G r r i + B t + B r Choose device parameters that optimize overall system

Joint Calibration: 10.1%

Macro: Joint Calibration Strengths Exploits redundancy to reduce noise Exploits redundancy to reduce noiseWeaknesses Centralized computation Centralized computation Cannot handle non-linear parameters Cannot handle non-linear parameters

Macro: Auto-Calibration All transmitter/receiver pairs are also receiver/transmitter pairs These symmetric edges should be equal Let d TR = B T + B R + G T *r + G R *r For all transmitter/receiver pairs i, k: d ik = d ki

Macro: Auto-Calibration All distances in the network must follow the triangle inequality Let d TR = B T + B R + G T *r + G R *r For all connected nodes h, i, k: d ih + d ik - d hk >=0

Consistency/constraint-based Choose parameters that maximize consistency while satisfying all constraints A quadratic program arises Minimize: Σ ik (d ik – d ki ) 2 + Σ T (G T – 1) 2 + Σ R (G R – 1) 2 Subject to: d ih + d j k - d hk >=0 for all triangle hik

Future Work Non-gaussian variations of the above algorithms Non-linear parameter estimation Expectation\maximization Expectation\maximization MCMC MCMC

Conclusions Macro-calibration Easier and faster Easier and faster Allows global optimization Allows global optimization Leverages redundancy Dependencies between sensors