4_23_09_KalmanFiltering

4_23_09_KalmanFiltering - Optimal Probabilistic Adaptation...

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Optimal Probabilistic Adaptation
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
When flying from the outside of a canyon into. ..
Background image of page 4
… the corridors of the canyon…
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
… the statistics of the environment change.
Background image of page 6
Optimal Probabilistic Adaptation
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Kalman- filtering Adaptation
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The goal is to update the estimate of the environment Λ k at time k to have the prior probability distribution P( I | Λ k ) of inputs I . For this, we use responses measured in the past Ř k = { R k , R k-1 , … , R 0 }. Responses are with adaptation states Ă k = { A k , A k-1 , … , A 0 }, where P( R | I , A k ) is the likelihood function.
Background image of page 10
Present Environment History of Response P Λ k R k , A k ( ) = We want to estimate History of Adaptation
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Neural Response ( r ) Sensory Input (s) a b c Bayes Theorem P s | r ( ) = P ( r | s ) P s ( ) P r ( ) b a + b = b b + c b + c a + b + c a + b a + b + c P r ( ) = a + b a + b + c P s ( ) = b + c a + b + c P r | s ( ) = b b + c b a + b P s | r ( ) =
Background image of page 12
Neural Response 1 (R1) Sensory Input (I) a b c Generalization of Bayes Theorem P I | R 1 , R 2 ( ) = P ( R 1 | I , R 2 ) P I | R 2 ( ) P R 1 | R 2 ( ) Neural Response 2 (R2) d A B C
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Present Environment History of Response P Λ k R k , A k ( ) = We want to estimate History of Adaptation KP R k , A k Λ k , R k -1 , A k 1 ( ) P Λ k R k -1 , A k 1 ( ) Measurement Term Prediction
Background image of page 14
Kalman Adaptation Early Measurements Estimated Environment Predicted Environment New Measurements New Estimation: Clean Measurements New Estimation: Noisy Measurements
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
How do we estimate this function?
Background image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 44

4_23_09_KalmanFiltering - Optimal Probabilistic Adaptation...

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online