# aer2ecef

Transform local spherical coordinates to geocentric Earth-centered Earth-fixed

## Description

example

[X,Y,Z] = aer2ecef(az,elev,slantRange,lat0,lon0,h0,spheroid) transforms the local azimuth-elevation-range (AER) spherical coordinates specified by az, elev, and slantRange to the geocentric Earth-centered Earth-fixed (ECEF) Cartesian coordinates specified by X, Y, and Z. Specify the origin of the local AER system with the geodetic coordinates lat0, lon0, and h0. Each coordinate input argument must match the others in size or be scalar. Specify spheroid as the reference spheroid for the geodetic coordinates.

[___] = aer2ecef(___,angleUnit) specifies the units for azimuth, elevation, latitude, and longitude. Specify angleUnit as 'degrees' (the default) or 'radians'.

## Examples

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Find the ECEF coordinates of a satellite, using the AER coordinates of the satellite relative to the geodetic coordinates of a satellite dish.

First, specify the reference spheroid as WGS84 with length units measured in kilometers. For more information about WGS84, see Comparison of Reference Spheroids. The units for the ellipsoidal height, slant range, and ECEF coordinates must match the units specified by the LengthUnit property of the reference spheroid.

wgs84 = wgs84Ellipsoid('kilometers');

Specify the geodetic coordinates of the local origin. In this example, the local origin is the satellite dish. Specify h0 as ellipsoidal height in kilometers.

lat0 = 42.3221;
lon0 = -71.3576;
h0 = 0.0847;

Specify the AER coordinates of the point of interest. In this example, the point of interest is the satellite. Specify the slant range in kilometers.

az = 24.8012;
elev = 14.6185;
slantRange = 36271.6327;

Then, calculate the ECEF coordinates of the satellite. In this example, the results display in scientific notation.

[x,y,z] = aer2ecef(az,elev,slantRange,lat0,lon0,h0,wgs84)
x = 1.0766e+04
y = 1.4144e+04
z = 3.3992e+04

Reverse the transformation using the ecef2aer function. In this example, slantRange displays in scientific notation.

[az,elev,slantRange] = ecef2aer(x,y,z,lat0,lon0,h0,wgs84)
az = 24.8012
elev = 14.6185
slantRange = 3.6272e+04

## Input Arguments

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Azimuth angles of one or more points in the local AER system, specified as a scalar, vector, matrix, or N-D array. Azimuths are measured clockwise from north. Specify values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Elevation angles of one or more points in the local AER system, specified as a scalar, vector, matrix, or N-D array. Specify elevations with respect to a plane that is perpendicular to the normal of the spheroid surface. If the local origin is on the surface of the spheroid (h0 = 0), then the plane is tangent to the spheroid.

Specify values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Distances from the local origin, specified as a scalar, vector, matrix, or N-D array. Specify each distance as along a straight, 3-D, Cartesian line. Specify values in units that match the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

Data Types: single | double

Geodetic latitude of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify the values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Geodetic longitude of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify the values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Ellipsoidal height of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify values in units that match the LengthUnit property of the spheroid object. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

For more information about ellipsoidal height, see Find Ellipsoidal Height from Orthometric Height.

Data Types: single | double

Reference spheroid, specified as a referenceEllipsoid object, oblateSpheroid object, or referenceSphere object. The term reference spheroid is used synonymously with reference ellipsoid. To create a reference spheroid, use the creation function for the object. To specify the reference ellipsoid for WGS84, use the wgs84Ellipsoid function.

For more information about reference spheroids, see Comparison of Reference Spheroids.

Example: spheroid = referenceEllipsoid('GRS 80');

Angle units, specified as 'degrees' (the default) or 'radians'.

## Output Arguments

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ECEF x-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

ECEF y-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

ECEF z-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

## Version History

Introduced in R2012b

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