Kalman Filtering Tutorial

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State Covariance Estimation 1. State prediction covariance: P( k + 1| k ) = F( k) P( k| k ) F( k )' + Q( k ) 2. Measurement prediction covariance: S( k + 1) = H( k + 1) P( k + 1| k) H( k + 1)' + R( k + 1) 3. Filter Gain W( k + ) = P( k + | k) H( k + )' S( k + ) − 1 1 1 1 4. Updated state covariance P( k + 1| k + 1) = P( k + 1| k ) − W( k + 1) S( k + 1) W( k + 1)' 18 1
Page 219 Bar-Shalom ANATOMY OF KALMAN FILTER State at tk x(k) 19
Page 1 and 2: Understanding and Applying Kalman F
Page 3 and 4: What is a Kalman Filter and What Ca
Page 5 and 6: Word examples: • Determination of
Page 7 and 8: The covariance of a column vector x
Page 9 and 10: Error Ellipses corresponding to 50
Page 11 and 12: Formulating a Kalman Filter Problem
Page 13 and 14: FALLING BODY EXAMPLE Consider an ob
Page 15 and 16: ⎡1 1⎤ ⎡0.5⎤ x(k +1) = ⎢ x
Page 17: State Estimation 0. Known are x$( k
Page 21 and 22: {F, H} is completely observable if
Page 23 and 24: 101 99 97 95 93 91 89 87 True posit
Page 25 and 26: Kalman Filter Extensions • Valida
Page 27 and 28: Sequential Measurement Processing I
Page 29 and 30: Extended Kalman Filter (EKF) Many p
Page 31 and 32: Iterated Extended Kalman Filter (IE
Page 33 and 34: Kalman filtering classes, for defin
Page 35 and 36: Odometry Error Covariance Estimatio
Page 37: Scanned Monocular Sonar Sensing Sma

Kalman Filtering Tutorial

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