A Distributed Algorithm for Managing MultiTarget Identities in Wireless Adhoc Sensor Network

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A Distributed Algorithm for Managing Multi-Target
Identities in Wireless Ad-hoc Sensor Network
Jaewon Shin, Leonidas Guibas and Feng Zhao
Stanford University, PARC
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Motivation

• Multi-target Tracking(MTT)
• Basic application of Sensor Net.
• Data Association problem (COHU) ? Target Swapping
• Want to re-lable the state estimates

?
?
COLU
COLU
COHU
COHU(COLU) Configuration Of High(Low) Uncertainty

• Multi-target Identity Management
• Manage additional quantity called target
  identity
• Simplified version of MTT Position estimates are
  given
• Can be extended to MTT or augment MTT

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Easy problem first Centralized Formulation
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Exact Approach
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Identity Mass Flow (IMF) Representation
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Details on IMF (1) Belief Matrix
Identity 1 Identity N
1st Obj Nth Obj
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Details on IMF (2) Mixing Matrix
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Facts about B(k) and M(k)
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Exploit Local Evidence (Probability Normalization)
A
Mixing 2/3

A
B
2/3
1/3
2
B
Doubly stochaticity guarantees the consistency
among the distributions.
This sensor tells that (2) is more likely to be
(A).
HOWEVER, this is the only case that we have
unique renormalization
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Many Solutions in General !
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How to find a single meaningful solution given
local evidence?
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Bayesian Normalization
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Sinkhorn Iteration for Normalization
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Sinkhorn Iteration Example
1st Obj 2nd Obj 3rd Obj 4th Obj
ID 1 ID 2 ID 3 ID 4
Local Evidence The correct ID is 4 !
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Sinkhorn Iteration Example
1st Obj 2nd Obj 3rd Obj 4th Obj
ID 1 ID 2 ID 3 ID 4
Apply Sinkhorn Iteration to this submatrix!
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Sinkhorn Iteration Example
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Sinkhorn Iteration Example
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Sinkhorn Iteration Example
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Sinkhorn Iteration Example
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Sinkhorn Iteration Example
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Sinkhorn Iteration Example
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Issues on Distributed Algorithm

• Q) Which node stores and/or compute what
  information?
• How to distribute B(k)?
• How to distribute/compute M(k)?
• How to implement the probabilistic
  normalization?
• What is required at the communication/network
  layer to make the above happen?

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Distributed Management of B(k)
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Distributed Management of B(k)
Local Mixing !
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Distributed Management of B(k)
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Distributed Management of B(k)
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Distributed Management of B(k)
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Distributed Management of B(k)
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Group Management Protocol

• When a leader initiate the probability
  normalization based on local evidence, it has to
  know where are the other leaders that have
  non-zero mass on the evidence ID.
• Group Management Protocol Maintains the group
  membership based on the ID probability mass.
• Subject of future work.

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Simulation

• Event-driven simulation of the distributed
  algorithm
• Simplified assumption on the network
• Group Management Protocol
• Scenario
• 4 targets 1 tank and 3 dots
• 4 IDs 1, 2, 3, 4
• 4 leaders red, blue, green, pink

The ID belief distribution of what the pink
leader is tracking
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Conclusion

• Summary
• Identity Mass Flow (IMF) representation of
  targets identity B(k) allows the efficient
  update and management in a distributed fashion.
• Use distributed Sinkhorn iteration to solve the
  target swapping problem.
• Future Work
• Group Management Protocol
• Extension to MTT
• Target Addition/Deletion