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ECEF Position to LLA

Calculate geodetic latitude, longitude, and altitude above planetary ellipsoid from Earth-centered Earth-fixed (ECEF) position


Utilities/Axes Transformations


The ECEF Position to LLA block converts a 3-by-1 vector of ECEF position into geodetic latitude , longitude , and altitude above the planetary ellipsoid.

The ECEF position is defined as

Longitude is calculated from the ECEF position by

Geodetic latitude is calculated from the ECEF position using Bowring's method, which typically converges after two or three iterations. The method begins with an initial guess for geodetic latitude and reduced latitude . An initial guess takes the form:

where R is the equatorial radius, f the flattening of the planet, e2 = 1−(1−f )2, the square of first eccentricity, and

After the initial guesses are calculated, the reduced latitude is recalculated using

and geodetic latitude is reevaluated. This last step is repeated until converges.

The altitude above the planetary ellipsoid is calculated with

where the radius of curvature in the vertical prime is given by

Dialog Box


Specifies the parameter and output units:



Equatorial Radius


Metric (MKS)








This option is only available when Planet model is set to Earth (WGS84).

Planet model

Specifies the planet model to use, Custom or Earth (WGS84).


Specifies the flattening of the planet.

This option is available only with Planet model set to Custom.

Equatorial radius of planet

Specifies the radius of the planet at its equator. The equatorial radius units should be the same as the desired units for ECEF position.

This option is available only with Planet model set to Custom.

Inputs and Outputs

InputDimension TypeDescription


3-by-1 vector Contains the position in ECEF frame.

OutputDimension TypeDescription


2-by-1 vectorContains the geodetic latitude and longitude, in degrees.


ScalarContains the altitude above the planetary ellipsoid, in the same units as the ECEF position.

Assumptions and Limitations

This implementation generates a geodetic latitude that lies between ±90 degrees, and longitude that lies between ±180 degrees. The planet is assumed to be ellipsoidal. By setting the flattening to 0, you model a spherical planet.

The implementation of the ECEF coordinate system assumes that its origin lies at the center of the planet, the x-axis intersects the prime (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-handed system.


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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