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American Institute of Aeronautics and Astronautics

    Course Outline

     Fundamentals of Kalman Filtering - A Practical Approach


     Course Outline:

    I. Numerical Techniques

    II. Presentation of required background for working with Kalman filters
    A. Method of Least Squares

    III. How to build a batch processing least squares filter
    A. Recursive Least Squares Filtering

    IV. How to make batch processing least squares filter recursive
    A. Polynomial Kalman Filters

    V. How to apply Kalman filtering and Riccati equations and relationship to recursive least squares filter
    A. Kalman Filters in a Non Polynomial World

    VI. How polynomial Kalman filters perform when they are mismatched to real world
    A. Continuous Polynomial Kalman Filter

    VII. Using transfer functions to represent and understand Kalman filters
    A. Extended Kalman Filtering
    VIII. How to apply extended filtering and Riccati equations to a practical example
    A. Drag and Falling Object

    IX. Designing two different extended filters for this problem and importance of process noise
    A. Cannon Launched Projectile Tracking Problem

    X. Developing extended and linear filters in the Cartesian and polar coordinate systems
    A. Tracking a Sine Wave

    XI. Developing three different filter formulations and comparing results
    A. Satellite Navigation (Simplified GPS Examples)

    XII. Extended Kalman filtering and a step by step approach to determining receiver location based on range measurements to several satellites
    A. Biases

    XIII. Various filtering techniques for estimating biases in a satellite navigation problem
    A. Linearized Kalman Filtering

    XIV. Comparing performances and robustness of linearized and extended Kalman filters
    A. Miscellaneous Topics
    B. Filter divergence in the real world and a practical illustration of inertial aiding

    XV. Filter Banks
    A. How filter banks can be used to improve estimation quality