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

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

3. Talk Outline Calamari Overview General Framework Noisy environment Least squares Least squares Partially-unobservable, noisy environment Joint calibration Joint calibration Completely unobservable environment Constraint-based calibration 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 -- |F T -F R | is scaling factor Orientation – f(O T,O R ) is scaling factor Calibration Function: r*= B T + B R + G T *r + G R *r + |F T -F R |*r + f(O T,O R )*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 Observed signals Unobserved 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 Known environment Noisy environment or devices Noisy environment or devices Partially observable environments Partially observable environments Unobservable environments Unobservable environments

10. Known Environment All signals are known observed observed unobserved 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* = A i r + B i

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

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* = A T r + A R r + B T + B R If devices have idiosyncrasies: r* = A t r + A r r + B t + B r

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 d ij = B T + B R + G T *r + G R *r For all connected nodes i, j, k: d ij + d j k - d ik >=0

18. Consistency-based Calibration All transmitter/receiver pairs are also receiver/transmitter pairs These symmetric edges should be equal Let d ij = B T + B R + G T *r + G R *r For all transmitter/receiver pairs i, j: d ik = d ki

19. Quadratic Program Let d ij = B T + B R + G T *r + G R *r Choose parameters to maximize consistency while satisfying all constraints A quadratic program arises Minimize: Σ ik (d ik – d ki ) 2 + Σ T (G T – 1) 2 + Σ R (G R – 1) 2 Subject to: d ij + d j k - d ik >=0 ; for all triangle ij k

20. Unobservable Environment: ??%

21. Future Work Non-gaussian variations of the above algorithms Expectation\maximizationMCMC

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