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 GTr GRr FT-FRr f(OT,OR)r

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No Calibration 74.6 Error
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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

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Calibration Function

• r measured readings
• r desired readings
• ß parameters
• r f(r, ß)

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General Calibration Framework

• Four classes of calibration
• Known environment
• Noisy environment or devices
• Partially observable environments
• Unobservable environments

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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

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Uniform Calibration 21 Error
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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

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Joint Calibration 10.1
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Auto Calibration

• No known input signals
• ....!?

17
Constraint-based Calibration

• All distances in the network must follow the
  triangle inequality
• Let dij BT BR GTr GRr
• For all connected nodes i, j, k
• dij djk - dik gt0

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Consistency-based Calibration

• All transmitter/receiver pairs are also
  receiver/transmitter pairs
• These symmetric edges should be equal
• Let dij BT BR GTr GRr
• For all transmitter/receiver pairs i, j
• dik dki

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Quadratic Program

• Let dij BT BR GTr GRr
• Choose parameters to 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 dij djk - dik gt0 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