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

2. Introduction r* = f(r, ß) Light Sensor Response Stimulus Observed
Desired
Light Sensor

3. Introduction

4. Introduction Macro-Calibration Calibrate the network, not the devices
Exploit sensor redundancy
Global optimization

5. Talk Outline Distance estimation Traditional (micro-)calibration
Iterative calibration
Macro-calibration
Joint calibration

6. Calamari Overview
Antenna
Speaker
Tone Detector
Microphone

7. Acoustic Time of Flight
Calamari Overview
Transmit Time
Receive Time
Acoustic Time of Flight

8. Experimental Setup

9. No Calibration: 74.6% Error

10. Traditional Calibration
Time
Adjust transmitter
and receiver to
minimize error
Observed
Desired
Distance

11. Chicken or Egg?
TOF
Transmit
Receive
Tns
Receive
TOF
Transmit
Rcv
TOF

12. Iterative Calibration
Tref T T R R

13. Iterative Calibration: 19.7%

14. Naive Calibration: 21% Error

15. Calibration as Parameter Estimation
Stimulus
Response
Observed
r* = f(r, ß)
Desired

16. Parameter Estimation r*1 = ß1 + ß2r1 + ß3r21 r*2 = ß1 + ß2r2 + ß3r22
Stimulus
Response
r* = f(r, ß)
r*1 = ß1 + ß2r1 + ß3r21 r5
r*2 = ß1 + ß2r2 + ß3r22
r*6 r4
r*3 = ß1 + ß2r3 + ß3r23
r*5 r3
r*4
r*4 = ß1 + ß2r4 + ß3r24 r2
r*3 r1
r*5 = ß1 + ß2r5 + ß3r25
r*2
r*1

17. Joint Calibration
Tk, Rk
Ti, Ri
dik = f(tik, Ti, Rk)

18. Joint Calibration

19. Joint Parameter Estimation
d12 = f(t12, T1, R2)
d13 = f(t13, T1, R3)
2n parameters
d14 = f(t14, T1, R4)
n2 equations …
d21 = f(t21, T2, R1)
d23 = f(t23, T1, R2)

20. Joint Calibration: 10.1%

21. Conclusions Iterative Joint Calibration Micro-calibration
One-by-one
Observed each device
Macro-calibration
All-at-once
Observed system
Single Reference
Propogates Noise
Exploits Redundancy
Cancels Noise
Greedy
Optimizes each device
Global maximum
Optimizes system

22. Future Work Non-linear parameter estimation Other sensor domainsEM
MCMC
Other sensor domains
Auto-calibration
Post-deployment
Unknown distances

23. Auto-calibration f(tik, Ti, Rk) = f(tki, Tk, Ri) dik = dki Tk Rk Rk Tk
TOF Rk Tk
TOF

24. Auto Calibration dik <= dhk + dhk dik <= dkh + dhk dik dhk dkh

25. Auto-calibration
Choose parameters that maximize consistency while satisfying all constraints
A quadratic program arises
Minimize: Σik |dik – dki|
Subject to: dih + djk - dhk >= for all trianglehik

26. Joint Calibration Revisited
d12 = f(t12, T1, R2)
2n parameters
d13 = f(t13, T1, R3)
n2 equations
d14 = f(t14, T1, R4)
Up to n2-2n
distances can
be unknown …
d21 = f(t21, T2, R1)
d23 = f(t23, T1, R2)