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Direction Cosine Matrix ECEF to NED

Convert geodetic latitude and longitude to direction cosine matrix

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix ECEF to NED block converts geodetic latitude and longitude into a 3-by-3 direction cosine matrix (DCM). 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:

  1. A rotation about oz0 through the longitude (ι) to axes (ox1, oy1, oz1)

  2. A rotation about oy1 through the geodetic latitude (μ) to axes (ox2, oy2, oz2)

Combining the two axis transformation matrices defines the following DCM.

Dialog Box

Inputs and Outputs

InputDimension TypeDescription

First

2-by-1 vectorContains the geodetic latitude and longitude, in degrees. Latitude and longitude values can be any value. However, latitude values of +90 and -90 may return unexpected values because of singularity at the poles.

OutputDimension TypeDescription

First

3-by-3 direction cosine matrixTransforms ECEF vectors to NED vectors.

Assumptions

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.

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