# aer2ecef

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

## Syntax

``````[X,Y,Z] = aer2ecef(az,elev,slantRange,lat0,lon0,h0,spheroid)``````
``[___] = aer2ecef(___,angleUnit)``

## 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'`.

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.

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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