Sensor/Actuator Network Calibration

1. Sensor/Actuator Network Calibration Kamin Whitehouse Nest Retreat, June 17 2002

2. Introduction • Previous sensor systems: • “multi”-sensor = “5” sensor • Specialized, high-accuracy devices • Sensor networks: • Scores of assembly-line sensors • Non-adjustable, uncalibrated devices

3. Talk Outline • Calamari Overview • General Framework • Noisy environment • Least squares • Partially-unobservable, noisy environment • Joint calibration • Completely unobservable environment • Constraint-based calibration

4. Calamari Overview • Simultaneously send sound and RF signal • Time stamp both • Subtract • Multiply by speed of sound Filter the readings (one more multiply)

5. Calamari Parameterization • Bias – startup time for mic/sounder oscillation • Gain – Volume and sensitivity affect PLL • Frequency -- |FT-FR| is scaling factor • Orientation – f(OT,OR)is scaling factor • Calibration Function: r*= BT + BR + GT*r + GR*r + |FT-FR|*r + f(OT,OR)*r

6. No Calibration: 74.6% Error

7. General Calibration Framework • All calibration is sensor/actuator pairs • Iterative Calibration: use single calibrated node to calibrate all other sensors/actuators • All sensor/actuator signals are multi-dimensional • Observed signals • Unobserved signals • Absolute Calibration: choose standard absolute coordinate scale • Relative Calibration: choose single node as standard coordinate scale

8. Calibration Function • r – measured readings • r* – desired readings • ß – parameters r* = f(r, ß)

9. General Calibration Framework • Four classes of calibration • Known environment • Noisy environment or devices • Partially observable environments • Unobservable environments

10. Known Environment • All signals are known • observed • unobserved • Implies use of “perfect” calibrating device • Can be used to calibrate all other devices • If devices are uniform: r* = Ar + B • If devices have idiosyncrasies: r* = Air + Bi

11. Noisy Environment • Some input signals are noisy • I.e. no “perfect” calibrating device • Use multiple readings/calibrating devices • Assumes noise due to variations has Gaussian distribution • If devices are uniform: r* = Ar + B • If devices have idiosyncrasies: r* = Air + Bi

12. Uniform Calibration: 21% Error

13. Noisy Environment: 16%

14. Partially unobservable • Solve for transmitter and receiver parameters simultaneously • Assumes noise due to unobserved signal has gaussian distribution • If devices are uniform: r* = ATr + ARr + BT + BR • If devices have idiosyncrasies: r* = Atr + Arr + Bt + Br

15. Joint Calibration: 10.1%

16. Auto Calibration • No known input signals • ....!?

17. Constraint-based Calibration • All distances in the network must follow the triangle inequality • Let dij =BT + BR + GT*r + GR*r • For all connected nodes i, j, k: dij + djk - dik >=0

18. Consistency-based Calibration • All transmitter/receiver pairs are also receiver/transmitter pairs • These symmetric edges should be equal • Let dij =BT + BR + GT*r + GR*r • For all transmitter/receiver pairs i, j: dik = dki

19. Quadratic Program • Let dij =BT + BR + GT*r + GR*r • Choose parameters to 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: dij + djk - dik >=0 ; for all triangleijk

20. Unobservable Environment: ??%

21. Future Work • Non-gaussian variations of the above algorithms • Expectation\maximization • MCMC

22. Conclusions • New calibration problems with sensor networks • We can exploit the network itself to solve the problem • Computation on each sensor/actuator • Networking ability • Distributed processing • Feedback control