MultipleTarget Tracking Using Binary Proximity Sensors

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Multiple-Target Tracking Using Binary Proximity
Sensors
Jaspreet Singh Wireless Comm. and Sensornets Lab
ECE Dept, UC Santa Barbara
Joint work with Prof. U. Madhow, ECE Dept,
UCSB R. Kumar and Prof. S. Suri, CS Dept, UCSB R.
Cagley, Toyon Research Corp
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The Problem of Tracking

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The Binary Proximity Model

• Tracking with binary proximity sensors
• Fundamental limits Shrivastava et al, Sensys
  2006 localization accuracy
  1/(sensor densitysensing range)
• Mechitov et al, Cooperative tracking with
  binary-detection sensor networks, ENSS 2003
• Kim et al, On target tracking with binary
  proximity sensors, IPSN 2005.
• What if we consider multiple targets?
• - Oh et al, Instrumenting wireless sensor
  networks for real time surveillance, ICRA 2006.

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Quick Preview

• 1. Snapshot based (counting) inferences

2. Tracking across snapshots
3. Experiment with PIR sensors
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What can we say with a snapshot ?

• Define two sensors to be positively independent
  if we can guarantee that they are on due to
  different targets

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Fundamental Counting Resolution

• number of targets gt number of (pairwise)
  positively independent sensors

• In 1-D, minimal description is consistent with
  this lower bound
• Implication Irrespective of sensor density, we
  can only hope to achieve a resolution of one
  target per distance 2R
• Payoff for higher density deployment
• improved localization
• resolving two closely spaced targets

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Tracking across snapshots

• How do we piece together the snapshots?
• Exploit the smoothness of trajectories using
  particle filter

true trajectories estimated trajectories
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If there is only one target
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Particle Filter for tracking a single target

• Maintain a set of K candidate trajectories
  (particles) at each time instant n
• Extend each of these K to time n1 by picking m
  samples from F(n1)
• Prune this set of mK trajectories to get the K
  surviving trajectories at time n1

T3
T2
T1
T4
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Pruning of trajectories
Cost Function
xn
vn-1
vn
xn-1
xn1
Additive cost function
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A cluster of trajectories
A cluster of good trajectories around the
best one
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Clustering effect with multiple targets

• Identify Clusters of trajectories, and pick one
  representative from each cluster
• Potential Problem All trajectories maybe
  monopolized by one cluster
• Solution Rather than looking for clusters at
  the end, monitor their formation throughout the
  tracking process, and limit the number of
  trajectories per cluster

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Clustering of trajectories
yn
yn-1
yn1
xn
xn-1
xn1
Distance metric accumulated difference between
the trajectories
Cluster X and Y together if
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Simulation set-up

• One-dimensional system 30 sensors placed
  uniformly along a line (X-axis)

• 5 targets, and trajectories of 20 time instants
  were generated for each target.
• Velocity at each time instant was picked
  randomly within 20 (on either side) of some mean
  value.
• Each of the plots depicted next is a x-t plot
  (location along X-axis against time)

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Simulation results
Analytical rules of thumb needed for deciding the
threshold sequence Do(N)
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Constant acceleration motion
Velocities vary appreciably, but still smoothly
Multiple simulation runs Variable (gt5) number
of trajectories obtained, but 5 of them always
provide good approximations for true paths
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Handling non-ideal sensing
Non-ideal sensing with PIR sensor
A simple model
Feasible target space intersection of outer
intervals with complements of
inner intervals
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Simulation results with non-ideal sensing
Same set up as before, with Ri 30 units, Ro
50 units for each sensor
Number of trajectories obtained varies between 5
and 7 For this simulation run, the cost
associated with the 7 trajectories are 31.5
38.1 41.7 54.5 57.4 80.5 95.9 units

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Lab-scale experimental set-up

• Small testbed with 5 PIR sensors
• Each sensor transmits to base station when it
  changes state
• Data gets time-stamped at the PC
  (interfaced to the base station)

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Results

• Non-ideal behavior evident noisy readings
• One sensor completely missed a target
• Respectable tracking performance still achieved

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Conclusions and Future Directions

• Snapshot based inferences
• Limits of target counting in 1-D
• Extension to higher dimensions ?
• Particle filter tracking algorithm
• Exploits temporal correlations well
• Robust to non-ideal sensing
• Distributed realizations ?
• Higher layer of more capable sensors (e.g.,
  cameras) to enhance performance ?

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• jsingh_at_ece.ucsb.edu
• Thank you !
• Questions ?

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Clustering effect with multiple targets

• Identify Clusters of trajectories, and pick one
  representative from each cluster
• Potential Problem All trajectories maybe
  monopolized by one cluster
• Solution Rather than looking for clusters at
  the end, monitor their formation throughout the
  tracking process, and limit the number of
  trajectories per cluster

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Clustering effect with multiple targets

• Identify Clusters of trajectories, and pick one
  representative from each cluster
• Potential Problem All trajectories maybe
  monopolized by one cluster
• Solution Rather than looking for clusters at
  the end, monitor their formation throughout the
  tracking process, and limit the number of
  trajectories per cluster

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Pruning and Clustering of Trajectories
Cost Function
yn
yn-1
yn1
xn
vn-1
vn
xn-1
xn1
Additive cost function
Clustering
Distance metric accumulated difference between
the trajectories
Cluster X and Y together if
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