Particle Filter

1. Particle Filter

2. Contents • Brief Introduction • Concept on Particle Filter • Details about errors

3. Uses • Track a variable of interest in the system • Example in the paper: localization • Noise, • Variable: Position

4. Characteristic • Monte Carlo Method • Not restricted to Kinematics • The gist: filter particles by feedback evaluation

5. Example System • Movable robot Rotation Translation

6. Particle Filter Method • Prediction Phase • Update Phase • Prerequisites: Particles Particles Sample

7. Prediction Phase • Take an actually move (interval) New Pose

8. Forward change to all Particles • Apply the change to all particles Error

9. Update Phase • To update the weights of all particles • Measurement

10. Update Phase • Measurement

11. Update Phase • Compute Measurement of Each particle • Use the measurement to decide weight

12. The effect of ρ,θ,Φ

13. Resampling • Eliminate particles with minor weights • Keep and propagate the particles with large weights • The significance of keep copies of large weight particles:

14. Select with Replacement • Object: eliminate minor weight particles, but leave large ones • 1. Compute cumulative sum: • Sample N random numbers and sort them: • If Ti < Qj, then choose particle j, otherwise drop particle j • If particle J is chosen, then i++, if Ti+1 still < Qj then chose particle J another time and likewise.

15. Prediction Error: Rotation • Sway a little bit when rotate The more the robot rotates the more deviation the error would be

16. Prediction Error: Translation • May not follow a rigorous straight line • Choppy • Periodical emulation

17. Prediction Error: Translation : Length of each sub segment

19. The end Thank you!