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Macro-calibration

Macro-calibration. Kamin Whitehouse David Culler WSNA, September 28 2002. Macro-Calibration. Calibration problems in Sensor Networks Many, many devices noisy devices and environments Post-deployment calibration Macro-calibration Calibrate the network, not the devices

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Macro-calibration

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  1. Macro-calibration Kamin Whitehouse David Culler WSNA, September 28 2002

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

  3. Talk Outline • Example application: distance estimation • Traditional calibration • Iterative calibration • Macro-calibration • Joint calibration • Auto-calibration

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

  5. No Calibration: 74.6% Error

  6. Sources of Noise in Calamari • Bias – startup time for mic/sounder oscillation • Gain – Volume and sensitivity affect PLL • Frequency -- |FT-FR| affects volume • Orientation – |OT-OR|affects volume

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

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

  9. Traditional Calibration: 19.7%

  10. Naive Calibration: 21% Error

  11. Traditional Calibration • Weaknesses • Noise propagation • Unobserved parameters

  12. Macro: Joint Calibration • Collect distance estimates for all pairs • Create system of equations ri* = Gtri + Grri + Bt + Br • Choose device parameters that optimize overall system

  13. Joint Calibration: 10.1%

  14. Macro: Joint Calibration • Strengths • Exploits redundancy to reduce noise • Weaknesses • Centralized computation • Cannot handle non-linear parameters

  15. Macro: Auto-Calibration • All transmitter/receiver pairs are also receiver/transmitter pairs • These symmetric edges should be equal • Let dTR =BT + BR + GT*r + GR*r For all transmitter/receiver pairs i, k: dik = dki

  16. Macro: Auto-Calibration • All distances in the network must follow the triangle inequality • Let dTR =BT + BR + GT*r + GR*r For all connected nodes h, i, k: dih + dik - dhk >=0

  17. Consistency/constraint-based • Choose parameters that maximize consistency while satisfying all constraints • A quadratic program arises Minimize: Σik(dik –dki)2 + ΣT(GT–1)2 + ΣR(GR–1)2 Subject to: dih + djk - dhk >=0 for all trianglehik

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

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

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