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Consensus-based Distributed Estimation in Camera Networks
- A. T. Kamal, J. A. Farrell, A. K. Roy-ChowdhuryUniversity of California, Riverside
ICIP 2012
Contents
• Problem Statement
• Motivation for using Distributed Schemes
• Challenges in Distributed Estimation in Camera
Networks
• Our solution
• Results
Problem Statement
Our goal is to estimate the state of the targets using the observations from all the cameras in a distributed manner.
C1C5
C3C2 C4
T1
T4
T3
T5
T2
Motivation for using Distributed Schemes
Issues using centralized or fully connected architectures:• High communication & processing power
requirements.• Intolerant of node failure.• Complicated to install.
Centralized
Partially connectedFully connected
Network architectures for multi-camera fusion
• Distributed schemes are scalable for any given connected network
Sensing Model
𝑥 𝑗,
𝐶 𝑖
𝒛 𝑖𝑗=𝑯𝑖
𝑗 𝒙 𝑗+𝝂𝑖𝑗
Sending Model:
Parameter Vector:
can be position, pose, appearance feature etc. of a target
1
2
3
4
5
4 1.5
3.5
3.5
2.5
… 3
… 3
… 3
… 3
... 3
Average Consensus: Review
Average Consensus Algorithm
Example of Average Consensus
𝑧1=¿
𝑧 2=¿
𝑧 3=¿𝑧 4=¿
𝑧5=¿
𝑧𝑖 (𝑘+1 )=𝑧𝑖 (𝑘 )+𝜖 ∑𝑗∈𝒩𝑖
(𝑧 𝑗 (𝑘 )−𝑧𝑖 (𝑘))
lim𝑘→∞
𝑧 𝑖(𝑘)=∑𝑗=1
𝑁
𝑧 𝑗 (0)
𝑁
Each nodes converges to the global average
R. Olfati-saber, J. A. Fax, and R. J. Murray, “Consensus and cooperation in networked multi-agent systems,” in Proceedings of the IEEE, 2007
𝑓𝑜𝑟 𝑘=0 :∞
𝑒𝑛𝑑
Challenges in Distributed Estimation in Camera Networks
C1C5
C3C2C4
T1
Challenges:• Each node may not observe the target
(i.e. difference between vision graph and comm. graph)
• The quality (noise variance) of measurementsat different nodes may be different.
• Network sparsity makes the above challenges severe.
We propose a distributed estimation framework which:• Does not require the knowledge of the vision
graph.• Weights measurements by noise variances.• Network sparsity does not affect the estimate it
converges to.
Distributed Maximum Likelihood Estimation (DMLE)
𝑥 (𝑘)𝑧𝑖 ,𝑅 𝑖
𝐶𝑖
𝑦 𝑖(0) ,𝑊 𝑖 (0)
𝑦 𝑛(0) ,𝑊𝑛 (0)
𝑦𝑚(0) ,𝑊𝑚(0)�̂�𝑖
❑ ,𝐶𝑜𝑣 ( �̂� 𝑖❑)
𝐶𝑚
𝐶𝑛
Information Matrix
Weighted Measurement
𝑦 𝑖(1) ,𝑊 𝑖(1)
How is does DMLE solve the challenges?
• Weighted-average consensus
• Converges to the optimal ML estimate
(not affected by network sparsity.)
• Presence/absence and quality of measurement is captured in .(, for no node measurement)
Experimental Evaluation
C1C5
C3C2 C4
Error Statistics
Ground Truth
Observations
Avg. Consensus
DMLE
Legend:
**
Conclusion
This work was partially supported by ONR award N00014091066 titledDistributed Dynamic Scene Analysis in a Self-Configuring Multimodal Sensor Network.
• We have proposed a distributed parameter estimation method generalized for• Limited observability of nodes• Variable quality of measurements and• Network sparsity
that approaches the performance of the optimal centralized MLE.
• Future Work: Dynamic State Estimation (Distributed Kalman Filtering)
Incorporation of prior information and state dynamics (“Information Weighted Consensus - IEEE Decision and Control Conference, Dec 2012”)
Thank you
http://www.ee.ucr.edu/~akamal/
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