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# Mathematical Introduction to Integrated Navigation Systems, with Applications

#### Course Outline:

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.
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*.

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*,…