Distributed Information and Signal Processing in Sensor Network

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Distributed Information and Signal Processing in
Sensor Network

• CS213
• Winter 2003
• Hanbiao Wang

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Outline

• Information-based sensor selection
• Fundamental question about collaboration
• Who should be in the team?
• Two contradicting factors
• Utility of a sensors data
• Cost of getting a sensors data
• Beamforming
• Processing of synchronized data from multiple
  sensors

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Collaborative Sensing

• CS213
• Winter 2003
• Hanbiao Wang

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A tracking scenario
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Formulation of IDSQ

• Notation
• x target state zi sensor data
• p(xz1, .., zj-1) current belief state of target
  based on data z1, .., zj-1
• p(xz1, .., zj- , zj) new belief state of
  target with additional data zj
• IDSQ selects such zj that maximizes weighted
  difference between utility gain and cost

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A special case

• Sensors measure distance to target
• A leader node requests data from a sensor to
  improve belief state about stationary target
  location.
• Mahalanobis distance as information metrics,
  Euclidean distance as energy cost

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IDSQ example
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Challenge of sensor selection

• Selection decision has to be made without
  explicit knowledge of the measurement residing at
  sensors to be selected
• Decision has to be made solely based upon sensor
  characteristics and current belief state.

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Sensor selection example
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Information utility

• From now on, lets focus on information utility,
  and ignore communication cost.
• Requirements of information utility
• The bigger the utility, the more useful the data
  to sensing application.
• Utility of a piece of non-local data can be
  predicted before obtaining the data solely based
  on current belief state and sensor
  characteristics.

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Information theoretic measure entropy

• Entropy measures randomness of a random variable,
  e.g. target location
• Infor. utility measure of a belief state

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Back to Mahalanobis distance measure

• Entropy-based utility is difficult to compute in
  practice.
• Mahalanobis distance for special case
• Belief states distribution is Gaussian or very
  elongated
• Sensors are range sensors

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Ideal belief update

• where
• , current belief state given a
  history of measurement up to time t.
• , next belief state with
  additional data zj(t1) from sensor j.
• p(x(t1)x(t)), dynamic model, determines next
  target state based on current target state.
• p(zJ(t1)x(t1)) , predicts measurement on
  sensor j given next belief state.

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Approximation of belief state

• Belief state is represented by probability
  distribution on a discrete set of cells
• Integral changes into summation

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Approximation of observation likelihood function

• Expected likelihood function as approximation

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Belief state and expected likelihood function
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Expected posterior belief

• As approximation of the true next belief
• Its information utility can be measured
• Choose sensor i to maximize information utility

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Localize a stationary target by selecting nearest
neighbor
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Localize a stationary target by selecting
neighbor with min Mahalanobis distance
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Tracking a moving target
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Tracking error
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Tracking error
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Conclusion

• Information-driven approach balances information
  gain and communication cost
• Many remaining issues
• Efficient belief state representation
• Practically feasible information utility
  measurement