CMU CS 10708 - Kalman Filters Gaussian MNs (22 pages)

Previewing pages 1, 2, 21, 22 of 22 page document View the full content.
View Full Document

Kalman Filters Gaussian MNs



Previewing pages 1, 2, 21, 22 of actual document.

View the full content.
View Full Document
View Full Document

Kalman Filters Gaussian MNs

98 views


Pages:
22
School:
Carnegie Mellon University
Course:
Cs 10708 - Probabilistic Graphical Models
Probabilistic Graphical Models Documents

Unformatted text preview:

Readings K F 6 1 6 2 6 3 14 1 14 2 14 3 14 4 Kalman Filters Gaussian MNs Graphical Models 10708 Carlos Guestrin Carnegie Mellon University December 1st 2008 1 Multivariate Gaussian Mean vector Covariance matrix 2 Conditioning a Gaussian Joint Gaussian p X Y N Conditional linear Gaussian p Y X N Y X 2Y X 3 Gaussian is a Linear Model Conditional linear Gaussian p Y X N 0 X 2 4 Conditioning a Gaussian Joint Gaussian p X Y N Conditional linear Gaussian p Y X N Y X YY X 5 Conditional Linear Gaussian CLG general case Conditional linear Gaussian p Y X N 0 X YY X 6 Understanding a linear Gaussian Variance increases over time the 2d case motion noise adds up Object doesn t necessarily move in a straight line 7 Tracking with a Gaussian 1 p X0 N 0 0 p Xi 1 Xi N Xi Xi 1 Xi 8 Tracking with Gaussians 2 Making observations We have p Xi Detector observes Oi oi Want to compute p Xi Oi oi Use Bayes rule Require a CLG observation model p Oi Xi N W Xi v Oi Xi 9 Operations in Kalman filter X1 O1 X2 O2 X3 O3 Compute Start with At each time step t X4 O4 X5 O5 Condition on observation Prediction Multiply transition model Roll up marginalize previous time step I ll describe one implementation of KF there are others Information filter 10 Exponential family representation of Gaussian Canonical Form 11 Canonical form Standard form and canonical forms are related Conditioning is easy in canonical form Marginalization easy in standard form 12 Conditioning in canonical form First multiply Then condition on value B y 13 Operations in Kalman filter X1 O1 X2 O2 X3 O3 Compute Start with At each time step t X4 O4 X5 O5 Condition on observation Prediction Multiply transition model Roll up marginalize previous time step 14 Prediction roll up in canonical form First multiply Then marginalize Xt 15 What if observations are not CLG Often observations are not CLG CLG if Oi Xi o Consider a motion detector Oi 1 if person is likely to be in the region Posterior is not Gaussian 16 Linearization incorporating



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Kalman Filters Gaussian MNs and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Kalman Filters Gaussian MNs and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?