Kalman Filtering Tutorial

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. y( k + 1) = y( k) + y( k) − the height y(k+1) depends on the previous velocity and height at time k. We can define the state as . x(k) ≡ [y(k) y(k)]' and then the state equation becomes 14 g 2
⎡1 1⎤ ⎡0.5⎤ x(k +1) = ⎢ x(k) + ⎣0 1 ⎥ ⎢ ⎥ ⎦ ⎣ ⎦ F x G u − ( g) 1 = ( k) + Assuming we observe or measure the height of the ball directly. The measurement equation is: z(k) = [1 0] x(k) + w(k) = H x( k) + w( k) The variance of w(k) needs to be known for implementing a <strong>Kalman</strong> filter. Given the initial state and covariance, we have sufficient information to find the optimal state estimate using the <strong>Kalman</strong> filter equations. 15
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: FALLING BODY EXAMPLE Consider an ob
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 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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