Kalman Filtering Tutorial

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Validation Gate Recall the measurement prediction covariance: S( k + 1) = H( k + 1) P( k + 1| k) H( k + 1)' + R( k + 1) and the measurement prediction: z$( k + 1| k ) = H( k ) x$( k + 1| k ) and measurement residual: v( k + 1) = z( k + 1) − z$( k + 1| k ) A validation gate can be set up around measurements as follows: −1 e = v( k + 1) S ( k + 1) v'( k + 1) ≤ g 2 2 where g 2 is chosen to for a confidence level. Normalised error e 2 varies as a Chi-Squared distribution with number of measurements degrees of freedom. 26 measurement update
Sequential Measurement Processing If the measurement noise vector components are uncorrelated then state update can be carried out one measurement at a time. Thus matrix inversions are replaced by scalar inversions. Procedure: state prediction as before scalar measurements are processed sequentially (in any order) using scalar measurement equations. 27
Page 1 and 2: Understanding and Applying Kalman F
Page 3 and 4: What is a Kalman Filter and What Ca
Page 5 and 6: Word examples: • Determination of
Page 7 and 8: The covariance of a column vector x
Page 9 and 10: Error Ellipses corresponding to 50
Page 11 and 12: Formulating a Kalman Filter Problem
Page 13 and 14: FALLING BODY EXAMPLE Consider an ob
Page 15 and 16: ⎡1 1⎤ ⎡0.5⎤ x(k +1) = ⎢ x
Page 17 and 18: State Estimation 0. Known are x$( k
Page 19 and 20: Page 219 Bar-Shalom ANATOMY OF KALM
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: Kalman Filter Extensions • Valida
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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