Bayesian Filtering- From Kalman Filters to Particle Filters and Beyond
Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE...
-
Upload
sheila-ward -
Category
Documents
-
view
213 -
download
0
Transcript of Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE...
![Page 1: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/1.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 1
Infi
neo
nA FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS
CSNDSP 2006
Michael Lunglmayr, Martin Krueger, Mario Huemer
![Page 2: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/2.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 2
Contents
Introduction
Simulation Model
Particle Filters
Particle Filters for Equalization
Simulation Results
![Page 3: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/3.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 3
Introduction
Particle Filters popular in e.g. image recognition, positioning,...
Aim of this work: Equalization with particle filters
Symbol estimation for GSM/EDGE in a multipath propagation environment
![Page 4: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/4.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 4
Simulation Model
![Page 5: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/5.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 5
Simulation Model
![Page 6: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/6.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 6
Particle Filters
Connection to Equalization: Estimate p(xk|yk) and choose those state with the highest probability
Straight Forward Method: calculate p(xk|yk) for every state
Effort to high for practical systems
![Page 7: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/7.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 7
Particle Filters
Connection to Equalization: Estimate p(xk|yk) and choose those state with the highest probability
Straight Forward Method: calculate p(xk|yk) for every state
Effort to high for practical systems
Importance Sampling:Principle: If p(xk|yk) would be known, it could be sampled:
Particles:
then for N:
![Page 8: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/8.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 8
Particle Filters
Bad News: p(xk|yk) is not known because it is to be estimated!
But: If we can sample a different probability function:q(xk|xk-1,yk) (importance sampling function) and weight the particles with an importance weight:
![Page 9: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/9.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 9
Particle Filters
Bad News: p(xk|yk) is not known because it is to be estimated!
But: If we can sample a different probability function:q(xk|xk-1,yk) (importance sampling function) and weight the particles with an importance weight:
Example: q(xk|xk-1,yk) = p(xk|xk-1)
![Page 10: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/10.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 10
PF for Equalization
Probability functions for GSM/EDGE
![Page 11: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/11.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 11
PF for Equalization
Probability functions for GSM/EDGE
Until now: Sequential Importance Sampling (SIS)But not very efficient yet!
![Page 12: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/12.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 12
Resampling
![Page 13: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/13.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 13
Particle Filter Algorithm
![Page 14: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/14.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 14
Implementation
![Page 15: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/15.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 15
Simulation ResultsGMSK
![Page 16: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/16.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 16
Simulation Results
![Page 17: Michael Lunglmayr Particle Filters for Equalization Page 1 Infineon A FEASIBILITY STUDY: PARTICLE FILTERS FOR MOBILE STATION RECEIVERS CSNDSP 2006 Michael.](https://reader036.fdocuments.in/reader036/viewer/2022062802/56649ef15503460f94c0229a/html5/thumbnails/17.jpg)
Michael LunglmayrParticle Filters for EqualizationPage 17
Conclusion
Particle Filters can outperform existing algorithms
Disadvantage: computational complexity
But: complexity depends only linearly on channel length e.g. Promising use in extremely broadband communication systems with long impulse responses