3d tracking : chapter2-2 kalman filter

Monocular Model-Based 3D Tracking of Rigid Ob-jects: A Survey

2008. 12. 11.백운혁

Chapter 2. Mathematical Tools (Bayesian Tracking)

2.6 Kalman FilteringThe kalman filter is the best possible (optimal) estima-tor for a large class of problems and a very effective and useful estimator for an even larger class

2.6.1. Kalman Filtering

Time Up-date

(“Predict”)

Measurement Update

(“Correct”)

Discrete kalman filter time update equations

project the state and covariance estimates for-ward from time step to step .

2.6.1. Kalman Filtering

QAAPP Tkk

1

kkk BuxAx

1ˆˆ

Q uncertainty

1k k

A state transi-tion

ix̂ actual state

ix̂ estimate

stateiu noise

iP posteriori estimate error co-variance

iP priori estimate error co-

variance

New state is modeled as a linear combination of both the previous state and som noise

Measurements are derived from the in-ternal state

Discrete kalman filter measurement update equations

the next step is to actually measure the process to obtain ,and then to generate an a posteriori state esti-mate.

2.6.1. Kalman Filtering

kZ

1)( RHHPHPK Tk

Tkk

)ˆ(ˆˆ kkki xHzKxx

KKk PHKIP )(

kz the actual measure-ment

K gain or blending factor

H measurement matrix

kxHˆ predicted measure-

ment

2.6.1. Kalman Filtering

Time Update (“Predict”)

Measurement Update (“Cor-rect”)

QAAPP Tkk

1

kkk BuxAx

1ˆˆ(1) Project the state ahead

(2) Project the error covariance ahead

1)( RHHPHPK Tk

Tkk

)ˆ(ˆˆ kkki xHzKxx

KKk PHKIP )(

(1) Compute the kalman gain

(2) Update estimate with mea-surement

(3) Update the error covariance

Initialize1ˆ kxInitial estimates for and

1kP

2.6.1. Kalman Filtering

2D Position-Velocity (PV Model)

2.6.1. Kalman Filtering

2D Position-Velocity (PV Model)

2.6.1. Extended Kalman Filtering

2.6 Particle Filters

2.6.2. Particle Filters

general representation by a set of weighted hypotheses, or particles

do not require the linearization of the relation between the state and the measurements

gives increased robustness

but few papers on particle based 3D pose es-timation

2.6.2. Particle Filters

2.6.2. Particle Filters

2.6.2. Particle Filters

Thanks for your attention