In Situ Calibration

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In Situ Calibration

• Miodrag Potkonjak
• Computer Science Dept, University of California,
  Los Angeles
• NSF Center for Embedded Networked Sensing, UCLA

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Why Calibration ?

• Process of mapping from measured to correct(ed)
  values s.t. application yield more accurate
  conclusions

• Calibration as a special case of model
  construction predicting difficult to measure
  variable for one that is easy to measure

• Off-line Golden standard and/or controlled
  experiment are available

• On-line Only measurements and outcomes of
  applications are available

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In Situ Calibration Pair-wise Consistency

• No golden standard
• Idea Consistency is necessary and sufficient for
  correct conclusion

• Consistency definition
• x1 lt x2 gt f(x1) f(x2)
• x1 gt x2 gt f(x1) f(x2)

• Recipe
• Solve a problem by maximizing consistency
• Use obtained solution to build model
• Evaluate model for consistency

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Location Discovery

• The Problem
• In a wireless ad-hoc sensor network (WASN),
  usually a (small) subset of sensor nodes
  (beacons) have a-priori information of their
  locations.
• Seeks to determine the relative and/or absolute
  positions of each unknown node using the measured
  distances between pairs of communicating nodes.

• NLP formulation

for all other communicating pairs kl

• Location error vs. edge consistency

Obj Min Sum
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Model Construction Novel Properties

• Accuracy of prediction

• Simple is beautiful MLD principle

• Monotonicity

• Consistency

• Symmetry yf(x) xg(y) gt yf(g(y))

• Transitivity yf(x) zg(y) zh(x) gt
  f(x)z(h(x))

• Compact representation

• Low computational cost

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Recipe of Model Construction

• Translate continuous problem into discrete problem

• Pose problem as Graph Theoretic Problem
• Define edges
• Define cost
• Define path
• Identify path

• of data points

• Inconsistency cost count

• Transformation of a graph

Courtesy to Lewis Girod for providing acoustic
distance measurements
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Beyond Regression Curves

• Derivatives and slope m f(x) M

• Low complexity

• Robustness

• Multivariate

• Density estimation

• Classification

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Density Estimation Deriving PDF
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Consistency and Sensor Fusion (Location Discovery)

• Hide Beacons

• Hide Edges

• Hiding 8/16 beacons

• Hide Nodes

• Split nodes

• Predictability given different of hidden beacons

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Applications of Calibration and Model
Construction

• Compression

• Adaptive sampling

• Missing information recovery

• Faults detection

• Obstacle detection

• Misinformation detection