Monocular Model-Based 3D Tracking of Rigid Objects: A Survey 2008. 12. 11. 백백백 Chapter 2. Mathematical Tools (Bayesian Tracking)
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