Kalman Filtering Tutorial

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Introduction Objectives: 1. Provide a basic understanding of Kalman Filtering and assumptions behind its implementation. 2. Limit (but cannot avoid) mathematical treatment to broaden appeal. 3. Provide some practicalities and examples of implementation. 4. Provide C++ software overview. 2
What is a Kalman Filter and What Can It Do? A Kalman filter is an optimal estimator - ie infers parameters of interest from indirect, inaccurate and uncertain observations. It is recursive so that new measurements can be processed as they arrive. (cf batch processing where all data must be present). Optimal in what sense? If all noise is Gaussian, the Kalman filter minimises the mean square error of the estimated parameters. 3
Page 1: Understanding and Applying Kalman F
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 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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