Wireless Distributed Sensor Tracking: Computation and Communication

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Wireless Distributed Sensor Tracking Computation
and Communication

• Bart Selman, Carla Gomes, Scott Kirkpatrick,
• Ramon Bejar, Bhaskar Krishnamachari,
• Johannes Schneider
• Intelligent Information Systems Institute,
  Cornell University Hebrew University
• Autonomous Negotiating Teams
  Principal Investigators'
  Meeting, Dec. 17, 2001

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Outline

• Overview of our approaches
• Ants - Challenge Problem (Sensor Array)
• Exact methods
• Determination of the phase diagram
• Results from physical model (annealing)
• Distributed CSP model
• Dynamic Bayesian networks
• Conclusions Steps to application

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Overview of Approaches

• We develop heuristics more powerful than greedy,
  not compromising speed
• Exact methods tuned for domain structure
• Overall theme --- Identification of domain
  structural features
• tractable vs. intractable subclasses
• phase transition phenomena
• backbone
• Goal
• Principled, controlled, hardness-aware systems

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ANTs Challenge Problem
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• Multiple doppler radar sensors track moving
• targets
• Energy limited sensors
• Communication
• constraints
• Distributed computation
• Dynamic system

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Models
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• Start with a simple graph model
• Refine in stages to approximate the real
  situation
• Static weakly-constrained model
• Add communication, target range constraints
• Physical model allows full range of real
  constraints, incorporate target acquisition
• Distributed constraint satisfaction model
• Goals
• Algorithms that scale for this problem
• Understand the sources of complexity

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Initial Assumptions
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• Each sensor can only track one target at a time
• 3 sensors are required to track a target

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Initial Graph Model

• The initial model presented is a bipartite
  graph, and this problem can be solved using a
  maximum flow algorithm in polynomial time
• Results incorporated into framework developed
  by Milind Tambes group at ISI, USC
• Joint work in progress

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Constrained Graph Model
sensors
targets
communication links
possible solution
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Description of Experiments
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• Limit cases

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Phase Transition w.r.t. Communication Range
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Experiments with a configuration of 9 sensors and
3 targets such that there is a communication
channel between two sensors with probability p
Insights into the design and operation of sensor
networks w.r.t. communication range
Probability( all targets tracked )
Special case all targets are visible to all
sensors
Communication edge probability p
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Phase Transition w.r.t. Radar Detection Range
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Experiments with a configuration of 9 sensors and
3 targets such that each sensor is able to detect
targets within a range R
Insights into the design and operation of sensor
networks w.r.t. radar detection range
Probability( all targets tracked )
Special case all nodes can communicate
Normalized Radar Range R
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Communication vs. Radar Range vs. Performance

• The full picture

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Performance and Phase Boundaries

• Natural units sensors/target, sensors within
  range of a target, sensors communicating with a
  sensor

19 sensors, 5 targets
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Phase diagram for the sensor array

• 3D phase diagram is bounded by
• 3 sensors/target
• 3 sensors within range of each target
• 2 one-hop neighbors for each sensor

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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
• Potential 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.
• Our results on the unconstrained problem validate
  the objective function, converge with as few as
  three iterations per sensor.

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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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Moving Targets -- Movies

• Conventions
• Targets
• Target range
• Sensors
• Sector active
• Target Clusters
• Coverage

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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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Examples of physical model solutions

• See www.cs.huji.ac.il/jsch/beautifulmovies/movies
  .html
• (these are 12-20MB animated gif files, so I will
  run my examples from local copies)
• Three lattices (hex, square, triangular)
• Target detection range 1.5, 2, 3, 4x nngbr
  dist.
• Avg. of neighboring sensors from 4.5 (hex) to 7
  (triangular)examples

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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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Results with moving targets

• Target visibility range and targets/sensor bounds
  seen

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Distributed Computational Model
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• In a Distributed Constraint Satisfaction
• Problem (DCSP), variables and constraints
• are distributed among multiple agents. It
• consists of
• A set of agents 1, 2, n
• A set of CSPs P1, P2, Pn , one for each agent
• There are intra-agent constraints and
  inter-agent constraints

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DCSP Models
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• With the DCSP models, we study both per-node
  computational costs as well as inter-node
  communication costs
• DCSP algorithms DIBT (Hamadi et al.) and ABT
  (Yokoo et al.)

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Communication vs. Radar Range vs. Computation
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• Computational Complexity total
• computation cost for all agents
• Communication Complexity total
• number of messages sent by all agents
• Communication range / Sensor (radar) range
• provides 3rd dimension.
• These measures can vary for the same
• problem when using different DCSP models

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Average Complexity (target-centered)
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Mean computational cost
Probability of Tracking

• 5 targets and 17 sensors

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Average Complexity (target-centered)
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Probability of Tracking
Mean communication cost

• 5 targets and 17 sensors

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• Next Steps

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Physical Model

• Increased realism in the objective function
• Energy costs of excessive coverage handoff
  policy
• Sector switching delay and energy costs
• Geometrical constraints for accurate tracking
• Continuous asynchronous tracking
• More accurate model of target acquisition
• Optimize to reduce communication costs
• Realistic criterion for successful tracking
• Specialize to a plausible, full-scale deployed
  system

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Dynamic Bayesian Model

• Joint work with Matt Thomas, AFRL
• Create dynamic Bayes network (with probabilistic
  information about domain state) within
  traditional influence diagram.
• Use this approach to handle turning off sensors
  as much as possible for energy conservation.

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Dynamic DCSP Model
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• Further refinement of the model
• incorporate target mobility
• The graph topology changes with time
• What are the complexity issues when
• online distributed algorithms are
• used?

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• Summary

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Summary
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• Graph-based and physical models capture
• the ANTs challenge domain
• Results on the tradeoffs between
• Computation, Communication, Radar range,
• and Performance are captured in phase
  diagram.
• Results enable a more principled and
• efficient design of distributed sensor
  networks.
• Techniques handle realistic constraints, fast
  enough for use in real distributed system.

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Collaborations / Interactions

• ISI Analytic Tools to Evaluate Negotiation
• Difficulty
• Design and evaluation of SAT encodings for
  CAMERAs scheduling task.
• ISI DYNAMITE
• Formal complexity analysis DCSP model (e.g.,
  characterization of tractable subclasses).
• UMASS Scalable RT Negotiating Toolkit
• Analysis of complexity of negotiation protocols.

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The End
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