Macrocalibration

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
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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
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Traditional Calibration

• Weaknesses
• Noise propagation
• Unobserved parameters

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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

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Joint Calibration 10.1
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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 GTr GRr For all
  transmitter/receiver pairs i, k
• dik dki

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Macro Auto-Calibration

• All distances in the network must follow the
  triangle inequality
• Let dTR BT BR GTr GRr For all
  connected nodes h, i, k
• dih dik - dhk gt0

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Consistency/constraint-based

• Choose parameters that maximize consistency while
  satisfying all constraints
• A quadratic program arises
• Minimize Sik (dik dki)2 ST(GT 1)2
  SR(GR 1)2
• Subject to dih djk - dhk gt0 for
  all trianglehik

18
Future Work

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

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Conclusions

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