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

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, *e*^{2} =
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

**Units**Specifies the parameter and output units:

Units

Position

Equatorial Radius

Altitude

`Metric (MKS)`Meters

Meters

Meters

`English`Feet

Feet

Feet

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)`.**Flattening**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`.

Input | Dimension Type | Description |
---|---|---|

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

Output | Dimension Type | Description |
---|---|---|

First | 2-by-1 vector | Contains the geodetic latitude and longitude, in degrees. |

Second | Scalar | Contains the altitude above the planetary ellipsoid, in the same units as the ECEF position. |

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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