Particle Filter

Contents Brief Introduction Concept on Particle Filter Details about errors

Uses

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

Characteristic

Monte Carlo Method Not restricted to Kinematics

The gist: filter particles by feedback evaluation

Example System

Movable robot

Rotation Translation

Particle Filter Method Prediction Phase Update Phase Prerequisites: Particles

Sample

Particles

lyinterative

Prediction Phase Take an actually move (interval)

New Pose

Forward change to all Particles Apply the change to all particles

EyxXX

yxXki

ki

ki

ki

ki

ki

,,

,,1

Error

Update Phase To update the weights of all particles Measurement

Measurement

Update Phase

Compute Measurement of Each particle

Use the measurement to decide weight

Update Phase

iw

The effect of ρ,θ,Φ

Eliminate particles with minor weights Keep and propagate the particles with large weights The significance of keep copies of large weight

particles:

Resampling

EyxXX

yxXki

ki

ki

ki

ki

ki

,,

,,1

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.

Select with Replacement

NN rrrrrr 2121 ],,[NT

Sway a little bit when rotate

Prediction Error: Rotation

The more the robot rotates the more deviation the error would be

May not follow a rigorous straight line Choppy Periodical emulation

Prediction Error: Translation

Prediction Error: Translation

: Length of each sub segment

The end

Thank you!