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American Institute of Aeronautics and Astronautics

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    Course Outline

    Mathematical Introduction to Integrated Navigation Systems, with Applications


    Course Outline:

    I. Navigation Overview - From Dead-Reckoning to Inertial Navigation.
    A. Dead-Reckoning - early sensors
    1. Heading reference - magnetic needle, magnetic compass, …
    2. Speed/distance traveled - velocity log, air speed, odometer, …
    B. Inertial Navigation - current sensor technology
    1. Accelerometer - …, MEMS,
    2. Gyro - RLG, Fiber Optic,…, MEMS.
    C. Integrated Navigation Systems
    1. Kalman Filtering - recursive estimator,
    2. Navigation Aides - Doppler, GPS, Line-of-Sight, …

    II. Coordinate Systems - How we relate information so that others can use it.
    A. Earth-Centered Earth-Fixed,
    B. Local Level - geographic, Wander Azimuth,
    C. Line-of-Sight - range, azimuth, elevation.

    III. Navigation Equations - Position, velocity and attitude data for onboard use.
    A. Terrestrial, Space Referenced Inertial, …
    B. Linearization for Kalman filter implementation - importance of error model*.

    IV. Navigation Aides - Redundant information to correct navigation data.
    A. Doppler - Radar, acoustic, odometer, …, speed/distance traveled,
    B. GPS - orbital position, psuedo range, delta range, deterministic solution,
    C. Line-of-Sight - azimuth/elevation recursive least squares.

    V. Kalman Filtering - Optimal combination of navigation and aiding data.
    A. Recursive Weighted Least Squares Estimator - starting from least-squares,
    B. Minimum Variance - starting with and assumed linear estimator form,
    C. U-D Factored Form - enhanced numerical precision,
    D. Combination of Two (or more) Kalman Filters' Estimates - multiple systems.

    VI. Applications - calibration, alignment, INS/GPS, …
    A. Laboratory Sensor Calibration*,
    B. Alignment/Initialization - ground*, in-motion, …
    C. Integrated Navigation: INS/GPS*, Attitude Determination/ Estimation*,…

    *MATLAB/Simulink examples.