Aerospace Blockset™

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 into a vector in north-east-down (NED) axes . The order of the axis rotations required to bring this about is:

1. A rotation about oz₀ through the longitude to axes

2. A rotation about oy₁ through the geodetic latitude to axes

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

Assumptions and Limitations

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

See Also

Direction Cosine Matrix ECEF to NED

Direction Cosine Matrix to Rotation Angles

Direction Cosine Matrix to Wind Angles

ECEF Position to LLA

Rotation Angles to Direction Cosine Matrix

LLA to ECEF Position

Wind Angles to Direction Cosine Matrix

Direction Cosine Matrix ECEF to NED

Direction Cosine Matrix to Quaternions