Direction Cosine Matrix ECEF to NED to Latitude and Longitude - Convert direction cosine matrix to geodetic latitude and longitude

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix ECEF to NED to Latitude and Longitude block converts a 3-by-3 direction cosine matrix (DCM) into geodetic latitude and longitude. The DCM matrix performs the coordinate transformation of a vector in Earth-centered Earth-fixed (ECEF) axes (ox₀, oy₀, oz₀) into a vector in north-east-down (NED) axes (ox₂, oy₂, oz₂). The order of the axis rotations required to bring this about is:

A rotation about oz₀ through the longitude (ι) to axes (ox₁, oy₁, oz₁)
A rotation about oy₁ through the geodetic latitude (μ) to axes (ox₂, oy₂, oz₂)

Combining the two axis transformation matrices defines the following DCM.

To determine geodetic latitude and longitude from the DCM, the following equations are used:

Dialog Box

Inputs and Outputs

Input	Dimension Type	Description
First	3-by-3 direction cosine matrix	Transforms ECEF vectors to NED vectors.

Output	Dimension Type	Description
First	2-by-1 vector	Contains the geodetic latitude and longitude, in degrees.

Assumptions and Limitations

This implementation generates a geodetic latitude that lies between ±90 degrees, and longitude that lies between ±180 degrees.

The implementation of the ECEF coordinate system assumes that the origin is at the center of the planet, the x-axis intersects the Greenwich meridian and the equator, the z-axis is the mean spin axis of the planet, positive to the north, and the y-axis completes the right-hand system.

References

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.

Zipfel, P. H., Modeling and Simulation of Aerospace Vehicle Dynamics, AIAA Education Series, Reston, Virginia, 2000.

"Atmospheric and Space Flight Vehicle Coordinate Systems," ANSI/AIAA R-004-1992.