Wireless Distributed Sensor Challenge Problem: Demo of Physical Modelling Approach

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Wireless Distributed Sensor Challenge Problem
Demo of Physical Modelling Approach

• Bart Selman, Carla Gomes, Scott Kirkpatrick,
• Ramon Bejar, Bhaskar Krishnamachari,
• Johannes Schneider
• Intelligent Information Systems Institute,
  Cornell University Hebrew University
• Autonomous Negotiating Teams
  CD Meeting, June 27, 2002
• Vanderbilt University, Nashville TN

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Outline

• Overview of our approach
• Movie conventions
• Computational cost (can be small)
• Phase diagram
• Connections with distributed agents
• We demonstrate results of varying amounts of
  renegotiation
• Enhancements and restrictions
• Reduce sector changes
• Scale to larger sensor arrays

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Overview of Approach

• We develop heuristics more powerful than greedy,
  not compromising speed
• Goal
• Principled, controlled, hardness-aware systems

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ANTs Challenge Problem
IISI, Cornell University

• Multiple doppler radar sensors track moving
• targets
• Energy limited sensors
• Constrained, fallible
• communications
• Distributed computation
• Real time requirements

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Physical model (and annealing)

• Represent acquisition and tracking goals in terms
  of a system objective function
• Define such that each sensor, with info from its
  1-hop neighbors, can determine which target to
  track
• Energy per target depends on of sensors
  tracking

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More on annealing

• Target Cluster (TC) is gt2 1-hop sensors tracking
  the same target enough to triangulate and reach
  a decision on response.
• Classic technique Metropolis method simulates
  asynchronous sensor decision, thermal annealing
  allows broader search (with uphill moves) than
  greedy, under control of annealing schedule.

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Moving targets, tracking and acquisition

• 100 sensors, t targets (t5-30) incident on the
  array, curving at random. Movies of 100 frames
  for each of several values of (sensors in
  range)/target and (1-hop neighbors)/sensor.
  Sensors on a regular lattice, with small
  irregularities. Between each frame a bounce,
  or partial anneal using only a low temperature,
  is performed to preserve features of the previous
  solution as targets move.

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Physical Model as Distributed Agents

• To compare with agent-based approaches
• Our sensors are independent agents
• At each time step, each chooses a target to
  track, based on the energy function, and informs
  its neighbors.
• At T0, sensors optimize locally
• Tgt0 is like renegotiation with reduced
  constraints, except that uphill moves may occur
  at any point in the search, not only when stuck.
  
• As targets move, sensor re-allocation is done
  using heat bumps low T is restricted
  renegotiation, higher T allows more extensive
  search for alternatives.

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Moving Targets -- Movies

• Conventions
• Targets
• (blue pts)
• Target range (green circles)
• Sensors (crosses)
• Sectors active in a TC are shown
• Target Clusters (red lines)
• Fraction of targets covered (thermometer)

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Introduce reduced connectivity
2.8 ngbrs/sensor
6.16 ngbrs/sensor
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Analysis of physical model results

• When t targets arrive at once, perfect tracking
  can take time to be achieved.
• Target is considered tracked when a TC of 3
  sensors keeps it in view continuously.
• We analyze each movie for longest continuous
  period of coverage of each target, report minimum
  and average over all targets.

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Analyzing the movies

• Summary frames
• easy case (10 targets)
  hard case (30 targets)
• color code red (1 TC), green (2 TCs), blue (3
  TCs), purple (4TCs) ,

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Additional summary information
Total time tracked, max continuous time tracked
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Computation can be speeded up gt100x without loss
of quality
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Determine Phase Boundary
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Results with moving targets

• Target visibility range and targets/sensor bounds
  seen

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Movies to show

• Results of pure agent, agents with renegotiation,
  and annealing operating points
• CR10 4 ngbrs on average
• 15 targets incident on the array
• Cases T0, T0.3, T3.0

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15 targets, no renegotiation
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15 targets, T0.3 in iterations
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15 Targets, T3.0 in iterations
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15 targets, no renegotiation
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15 targets, T 0.3 renegotiation
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15 targets, T 3.0
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Results of renegotiation
Harder cases see bigger improvement, but effect
of small amounts hard to control.
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Control of sector assignment

• Previous movies allowed sensor to sample all
  sectors while choosing target. Now we make that
  choice only at the outset of time step.
• Problem is harder. We lose about 8 average
  coverage, hold same continuous coverage. An
  intermediate approach is desireable.
• Phase boundary (or threshold of dif ficulty)
  moves in.

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Finding the phase boundary
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Finding the phase boundary
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Comparing coverage, 10 targets, CR10
Sectors fixed
Sectors varying
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Comparing coverage, 10 targets, CR10
Varying sectors
Fixed sectors
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How much can search be speeded up?
Conservative setting (100x) uses lt10
msec/sensor/time step (850 MHz Pentium) Further
10-100x reductions possible except near phase
bndry.
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As the problems get bigger

• Physical model effort, in principle, scales
  linearly, not exponentially, as number of sensors
  managed grows.
• In our model, biggest cost is the communications
  cost of keeping cluster information (TCs)
  current in a well-connected model with few
  targets present. As the problem gets uglier,
  this cost decreases because TCs get smaller!
• Example series of simulations with 400 sensors,
  40-120 targets incoming. One movie can be seen
  at http//www.cs.huji.ac.il/kirk/darpa/film.gif
  .

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How often must sectors change?
Note that varying sectors change less often, and
give better solution.
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Fraction of sensors covering targets
Once targets spread, nearly all sensors
contribute.
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Fraction of sensors covering targets
Fixing sectors reduces available sensors 12.
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Average of TCs per target tracked

Not wasteful, gt1 TCs helps handoff as targets
move.
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Average of sensors tracking a target
Excessive coverage of some targets. Can sensors
be freed up to improve detection, save power?
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Ways to further improve big array performance

• Explore restricted of sector changes in a time
  step.
• Reallocate sensors from overtracked targets, e.g.
  by tuning the potential for high densities.
• Introduce target-identity memory to reduce need
  for continuous tracking. Create a derived MRF
  object, like edge detection in image processing.

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Summary
IISI, Cornell University

• Graph-based physical models capture
• the ANTs challenge domain
• Results on the tradeoffs between
• Computation, Communication, Radar range,
• and Performance are captured in phase
  diagram.
• Techniques handle realistic constraints, fast
  enough for use in real distributed system.

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The End
IISI, Cornell University