Overview of Message Passing Algorithms for Cooperative Localization in UWB wireless networks. Samuel Van de Velde

Transcription

1 Overview of Message Passing Algorithms for Cooperative Localization in UWB wireless networks Samuel Van de Velde Promotor: Heidi Steendam Co-promotor Marc Moeneclaey, Henk Wymeersch Department of Telecommunications and Information Processing TELIN/UGent University of Ghent - May 2011 pag. 1

2 Outline 1. Motivation 2. Factor Graphs 3. Message Passing Algorithms 1. Belief Propagation (BP) 2. Mean Field (MF) 3. Expectation Propagation (EP) 4. Results 5. Future work pag. 2

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

4 Motivation What do we need for Localization? Reference nodes (anchors) Range or angle measurements pag. 4

5 Problem formulation How to solve? Optimization find point estimates: given e.g. Least Squares, MDS,.. Centralized algorithms or they need good initial estimates Baysian Inference find posterior distribution: e.g. Message Passing Distributed, iterative pag. 5

6 Localization An example network Anchor Mobile agent (true location) Range measurements with 30cm standard deviation Radio range 20m pag. 6

7 Localization - without cooperation Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 7

8 Localization - with cooperation (MDS) Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 8

9 Outline 1. Motivation 2. Factor Graphs 3. Message Passing Algorithms 1. Belief Propagation (BP) 2. Mean Field (MF) 3. Expectation Propagation (EP) 4. Results 5. Future work pag. 9

10 Message Passing Factor Graphs Factorize the posterior: Create the Factor Graph 1. Each variable becomes a round node 2. Each factor becomes a square node 3. Connect the factors with their variables pag. 10

11 Message Passing example Factor Graph Example Factor Graph 3 reference nodes 2 mobile nodes 5 measurements pag. 11

12 Message Passing Algorithms 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: pag. 12

13 Message Passing Algorithms BP Gaussian MF EP locally minimizes inclusive exclusive inclusive Constraint on message No restriction Circular symmetric gaussian Gaussian 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] pag. 13

14 Localization An example network Anchor Mobile agent (true location) Range measurements with 30cm standard deviation Radio range 20m pag. 14

15 Localization EP iteration 1 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 15

16 Localization EP iteration 2 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 16

17 Localization EP iteration 3 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 17

18 Localization EP iteration 4 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 18

19 Localization EP iteration 5 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 19

20 Localization EP iteration 6 Anchor Mobile agent (true location) Mobile agent (Estimated location) pag. 20

21 Outline 1. Motivation 2. Factor Graphs 3. Message Passing Algorithms 1. Belief Propagation (BP) 2. Mean Field (MF) 3. Expectation Propagation (EP) 4. Results 5. Future work pag. 21

22 Results CDF SPAWN Standard deviation of range measurements: 10cm Radio range: 20m pag. 22

23 Results CDF gaussian MF Source: C. Pedersen, T Pederson, B. H. Fleury, A Variational Message passing Algorithm for Sensor Self- Localization in Wireless Networks, ISIT Accuracy 10x lower than SPAWN Convergence after 30 iterations is the standard deviation of the range measurements in meter pag. 23

24 Future work 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 pag. 24

25 Thank you for your attention! Any questions? University of Ghent - May 2011 pag. 25

26 References References [SPAWN] H. Wymeersch, J. Lien, and M.Z. Win, Cooperative Localization in Wireless Networks, Proceedings of the IEEE, vol. 97, Feb. 2009, pp [Claus] C. Pedersen, T Pederson, B. H. Fleury, A Variational Message passing Algorithm for Sensor Self-Localization in Wireless Networks, ISIT [SLEEP] M. Welling and J.J. Lim, A Distributed Message Passing Algorithm for Sensor Localization, 2007, pp pag. 26

27 Message Passing - BP Belief Propagation 1. (V to F): multiply incoming messages 2. (F to V): multiply incoming messages with factor + marginalize pag. 27

28 Message Passing - BP Belief Propagation Multiply all incoming messages for the marginal This is true for all Message Passing Algorithms Allows for distributed localization! pag. 28