3 x 3 Rotation Matrices in Air Traffic Control (UMAP)

This module shows how orthogonal matrices are used to translate into local coordinates the airplane coordinate sent by radar sites to air traffic control centers in a system designed for West Germany by Raytheon Company in 1978. Students compute specific 3 x 3 matrices and use them in real-world coordinate transformation problems.

Table of Contents:

1. AN AIR TRAFFIC CONTROL RADAR SYSTEM
1.1 Airplane Positions
1.2 Radar Site Positions

2. THE COORDINATE TRANSFORMATION PROBLEM

3. A SOLUTION TO THE COORDINATE TRANSFORMATION PROBLEM
3.1 Analysis of the Problem
3.2 Computation of the Rotation Matrix
3.3 The Coordinate Transformation Equation

4. ORTHOGONAL MATRICES AND THEIR INVERSES

5. PRACTICAL ASPECTS OF THE COORDINATE TRANSFORMATION PROBLEM
5.1 Geodetic Latitude vs. Conformal Latitude
5.2 Constrained Stereographic Projection Onto a Plane
5.3 Speed and Accuracy of Calculations

6. REFERENCES

7. ANSWERS TO EXERCISES