Direction Cosine Matrix ECEF to NED
Convert geodetic latitude and longitude to direction cosine matrix
Aerospace Blockset / Utilities / Axes Transformations
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 into a vector in north-east-down (NED) axes. For more information on the direction cosine matrix, seeAlgorithms.
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. For more information, see About Aerospace Coordinate Systems.
μl — Geodetic latitude and longitude
Geodetic latitude and longitude, specified as a 2-by-1 vector, 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.
DCMef — Direction cosine matrix
DCM to perform coordinate transform of a vector in ECEF axes into a vector in NED axes, returned as a 3-by-3 matrix.
The DCM matrix performs the coordinate transformation of a vector in ECEF axes, (ox0, oy0, oz0), into a vector in 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.
 Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation, Hoboken, NJ: John Wiley & Sons, 1992.
 Zipfel, Peter H., Modeling and Simulation of Aerospace Vehicle Dynamics. Second Edition. Reston, VA: AIAA Education Series, 2000.
 Recommended Practice for Atmospheric and Space Flight Vehicle Coordinate Systems, R-004-1992, ANSI/AIAA, February 1992.
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Direction Cosine Matrix ECEF to NED to Latitude and Longitude | Direction Cosine Matrix to Rotation Angles | Direction Cosine Matrix to Wind Angles | ECEF Position to LLA | LLA to ECEF Position | Rotation Angles to Direction Cosine Matrix | Wind Angles to Direction Cosine Matrix