Macrocalibration Kamin Whitehouse David Culler WSNA September 28
Macro-calibration Kamin Whitehouse David Culler WSNA, September 28 2002
Macro-Calibration problems in Sensor Networks n n n Many, many devices noisy devices and environments Post-deployment calibration Macro-calibration n Calibrate the network, not the devices Leverage redundancy to reduce noise Use the network to calibrate itself
Talk Outline Example application: distance estimation Traditional calibration n Iterative calibration Macro-calibration n n Joint 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 -- |FT-FR| affects volume Orientation – |OT-OR| affects volume
The calibration problem in Calamari Chicken or egg? n n Need sounder to calibrate microphones Need microphone to calibrate sounders Note that all calibration problems are really sensor/actuator problems.
Traditional Calibration Iterative Calibration n n Designate one ‘reference’ node Calibrate all others against it De facto standard for relative calibration: n n The ‘standard meter’ approach Hightower ’ 00 used it for localization
Traditional Calibration: 19. 7%
Naive Calibration: 21% Error
Traditional Calibration Weaknesses n n Noise propagation Unobserved parameters
Macro: Joint Calibration Collect distance estimates for all pairs Create system of equations r i * = G t r i + G rr i + B t + B r Choose device parameters that optimize overall system
Joint Calibration: 10. 1%
Macro: Joint Calibration Strengths n Exploits redundancy to reduce noise Weaknesses n n Centralized computation 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 = BT + BR + GT*r + GR*r For all transmitter/receiver pairs i, k: dik = dki
Macro: Auto-Calibration All distances in the network must follow the triangle inequality Let d. TR = BT + BR + GT*r + GR*r For all connected nodes h, i, k: dih + dik - dhk >=0
Consistency/constraint-based Choose parameters that maximize consistency while satisfying all constraints A quadratic program arises Minimize: Subject to: Σik (dik – dki)2 + ΣT(GT– 1)2 + ΣR(GR– 1)2 dih + djk - dhk >=0 for all trianglehik
Future Work Non-gaussian variations of the above algorithms Non-linear parameter estimation n n Expectationmaximization MCMC
Conclusions Macro-calibration n n Easier and faster Allows global optimization Leverages redundancy Dependencies between sensors
- Slides: 19
