Lecture-17.ppt - Lecture-17 Kalman Filter Main Points •...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture-17 Kalman Filter Main Points • Very useful tool. • It produces an optimal estimate of the state vector based on the noisy measurements (observations). • For the state vector it also provides confidence (certainty) measure in terms of a covariance matrix . • It integrates estimate of state over time. • It is a sequential state estimator. State-Space Model ) ( ) 1 ( ) 1 , ( ) ( k k k k k w z z + − − Φ = ) ( ) ( ) ( ) ( k k k k v z H y + = State-transition equation Measurement (observation) equation State Vector Measurement Vector State model error With covariance Q(k) Observation Noise with covariance R(k) Kalman Filter Equations ) 1 ( ˆ ) 1 , ( ) ( ˆ − − Φ = k k k k a b z z ) ( ) 1 , ( ) 1 ( ) 1 , ( ) ( k k k k k k k T a b Q P P + − Φ − − Φ = 1 )) ( ) ( ) ( ) ( )( ( ) ( ) ( − + = k k k k k k k T b T b R H P H H P K )] ( ˆ ) ( ) ( )[ ( ) ( ˆ ) ( ˆ k k k k k k b b a z H y K z z − + = ) ( ) ( ) ( ) ( ) ( k k k k k b b a P H K P P − = State Prediction Covariance Prediction Kalman Gain State-update Covariance-update Two Special Cases R R H H Q Q = = = Φ = − Φ ) ( ) ( ) ( ) 1 , ( k k k k k ) ( ) 1 , ( = = − Φ k k k Q I • Steady State • Recursive least squares Comments • In some cases, state transition equation and the observation equation both may be non- linear. • We need to linearize these equation using Taylor series. Extended Kalman Filter ) ( )) 1 ( ( ) ( k k k w z f z + − = ) ( )) ( ( ) ( k k k v z h y + = )) 1 ( ˆ- 1)- k ( ( ) 1 ( )) 1 ( ( ))...
View Full Document

This note was uploaded on 06/12/2011 for the course CAP 6411 taught by Professor Shah during the Spring '09 term at University of Central Florida.

Page1 / 15

Lecture-17.ppt - Lecture-17 Kalman Filter Main Points •...

This preview shows document pages 1 - 5. Sign up to view the full document.

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