overview of message passing algorithms for cooperative ......message passing algorithm for sensor...
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University of Ghent - May 2011
Overview of Message Passing Algorithms for Cooperative Localization in UWB wireless
networks
pag. 1
Samuel Van de [email protected]
Promotor: Heidi Steendam Co-promotor Marc Moeneclaey, Henk Wymeersch
Department of Telecommunications and Information Processing TELIN/UGent
Universiteit Gent – September 2007
1. Motivation2. Factor Graphs3. Message Passing Algorithms
1. Belief Propagation (BP)2. Mean Field (MF)3. Expectation Propagation (EP)
4. Results5. Future work
Outline
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Universiteit Gent – September 2007
Motivation
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GPS may be:• unreliable (multipath, indoor)• unsufficient (3m accuracy)• too expensive (hardware + battery!)
Universiteit Gent – September 2007
What do we need for Localization?• Reference nodes (anchors)• Range or angle measurements
Motivation
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Universiteit Gent – September 2007
How to solve?• Optimization
find point estimates: given e.g. Least Squares, MDS, ..→ Centralized algorithms or they need good initial estimates
• Baysian Inferencefind posterior distribution:e.g. Message Passing→ Distributed, iterative
Problem formulation
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Universiteit Gent – September 2007
Localization – An example network
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AnchorMobile agent (true location)
Range measurements with 30cm standard deviationRadio range 20m
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Localization - without cooperation
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AnchorMobile agent (true location)Mobile agent (Estimated location)
AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization - with cooperation (MDS)
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AnchorMobile agent (true location)Mobile agent (Estimated location)
AnchorMobile agent (true location)Mobile agent (Estimated location)
Universiteit Gent – September 2007
1. Motivation2. Factor Graphs3. Message Passing Algorithms
1. Belief Propagation (BP)2. Mean Field (MF)3. Expectation Propagation (EP)
4. Results5. Future work
Outline
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Universiteit Gent – September 2007
Factorize the posterior:
Create the Factor Graph1. Each variable becomes a round node2. Each factor becomes a square node3. Connect the factors with their variables
Message Passing – Factor Graphs
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Universiteit Gent – September 2007
Example Factor Graph3 reference nodes2 mobile nodes5 measurements
Message Passing – example Factor Graph
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Universiteit Gent – September 2007
Message Passing Algorithms:• Belief Propagation (BP = SPA), • Mean Field (MF = VMP), • Expectation Propagation (EP)• Many more..
All try to find:
Given the constraint:
By approximating the factors of the posterior:
Message Passing Algorithms
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Universiteit Gent – September 2007
BP Gaussian MF EPlocally
minimizes inclusive exclusive inclusive
Constraint on message
No restrictionCircular symmetric
gaussianGaussian family
PRO •High accuracy •Simple messages•High accuracy•Simple messages
CON•Messages are full distributions•Complexity
•A lot of iterations•Low accuracy
•breaks down at UWB due to tight loops
convergence 4-5 iterations +/- 30 iterations 6-7 iterations
reference [SPAWN] [Claus] [SLEEP]
Message Passing Algorithms
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Universiteit Gent – September 2007
Localization – An example network
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AnchorMobile agent (true location)
Range measurements with 30cm standard deviationRadio range 20m
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Localization – EP iteration 1
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AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization – EP iteration 2
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AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization – EP iteration 3
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AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization – EP iteration 4
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AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization – EP iteration 5
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AnchorMobile agent (true location)Mobile agent (Estimated location)
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Localization – EP iteration 6
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AnchorMobile agent (true location)Mobile agent (Estimated location)
Universiteit Gent – September 2007
1. Motivation2. Factor Graphs3. Message Passing Algorithms
1. Belief Propagation (BP)2. Mean Field (MF)3. Expectation Propagation (EP)
4. Results5. Future work
Outline
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Universiteit Gent – September 2007
Standard deviation of range measurements: 10cmRadio range: 20m
Results – CDF SPAWN
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Convergence after 30 iterationsis the standard deviation of the range measurements in meter
Results – CDF gaussian MF
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Accuracy 10x lower than SPAWN
Source: C. Pedersen, T Pederson, B. H. Fleury, “A Variational Message passing Algorithm for Sensor Self-Localization in Wireless Networks”, ISIT 2011.
Universiteit Gent – September 2007
Future work• Find the ultimate Message passing algorithm• Make EP work for UWB• Sensor fusion (IMU, GPS, ...)• Integrating floor plan information• Effect of link attenuation and network protocol• Practical experiments
Future work
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Thank you for your attention!Any questions?
Universiteit Gent – September 2007
References
[SPAWN] H. Wymeersch, J. Lien, and M.Z. Win, “Cooperative Localization in Wireless Networks,” Proceedings of the IEEE, vol. 97, Feb. 2009, pp. 427-450.
[Claus] C. Pedersen, T Pederson, B. H. Fleury, “A Variational Message passing Algorithm for Sensor Self-Localization in Wireless Networks”, ISIT 2011.
[SLEEP] M. Welling and J.J. Lim, “A Distributed Message Passing Algorithm for Sensor Localization,” 2007, pp. 1-10.
References
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Belief Propagation
1. (V to F): multiply incoming messages
2. (F to V): multiply incoming messages with factor + marginalize
Message Passing - BP
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Universiteit Gent – September 2007
Belief Propagation
Multiply all incoming messages for the marginal
This is true for all Message Passing Algorithms→ Allows for distributed localization !
Message Passing - BP
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