Overview of Message Passing Algorithms for Cooperative ......Message passing Algorithm for Sensor...

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

pag. 2University of Ghent - May 2011


Motivation


GPS may be:• unreliable (multipath, indoor)• unsufficient (3m accuracy)• too expensive (hardware + battery!)


What do we need for Localization?• Reference nodes (anchors)• Range or angle measurements

Motivation



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



Localization – An example network


AnchorMobile agent (true location)

Range measurements with 30cm standard deviationRadio range 20m


Localization - without cooperation


AnchorMobile agent (true location)Mobile agent (Estimated location)



Localization - with cooperation (MDS)








Outline



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



Example Factor Graph3 reference nodes2 mobile nodes5 measurements

Message Passing – example Factor Graph



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



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



Localization – An example network


AnchorMobile agent (true location)

Range measurements with 30cm standard deviationRadio range 20m


Localization – EP iteration 1







Outline



Standard deviation of range measurements: 10cmRadio range: 20m

Results – CDF SPAWN



Convergence after 30 iterationsis the standard deviation of the range measurements in meter

Results – CDF gaussian MF


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.


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



Thank you for your attention!Any questions?


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



Belief Propagation

1. (V to F): multiply incoming messages

2. (F to V): multiply incoming messages with factor + marginalize

Message Passing - BP



Belief Propagation

Multiply all incoming messages for the marginal

This is true for all Message Passing Algorithms→ Allows for distributed localization !

Message Passing - BP


Overview of Message Passing Algorithms for Cooperative ......Message passing Algorithm for Sensor...

Documents

Transcript of Overview of Message Passing Algorithms for Cooperative ......Message passing Algorithm for Sensor...