# aer2geodetic

Local spherical AER to geodetic

## Syntax

• ```[lat,lon,h] = aer2geodetic(az,elev,slantRange,lat0,lon0,h0,spheroid)``` example
• `[___] = aer2geodetic(___,angleUnit)`

## Description

example

``````[lat,lon,h] = aer2geodetic(az,elev,slantRange,lat0,lon0,h0,spheroid)```) returns geodetic coordinates corresponding to coordinates `az`, `elev`, `slantRange` in a local spherical system. Any of the first six numeric input arguments can be scalar, even when the others are nonscalar; but all nonscalar numeric arguments must match in size. ```
````[___] = aer2geodetic(___,angleUnit)` adds `angleUnit` which specifies the units of inputs `az`, `elev`, `lat0`, `lon0`, and outputs `lat`, `lon`.```

## Examples

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### Zermatt to the Matterhorn

Compute the latitude, longitude and orthometric height of the summit of the Matterhorn (Monte Cervino) from its azimuth, elevation and (slant) range relative to Zermatt, Switzerland. All distances and lengths are in meters.

Origin (reference point): Zermatt.

```fmt = get(0,'Format'); format short g lat0 = dm2degrees([46 1]) % convert degree-minutes to degrees lon0 = dm2degrees([ 7 45]) hOrthometric0 = 1620; hGeoid = 53; h0 = hOrthometric0 + hGeoid```
```lat0 = 46.017 lon0 = 7.75 h0 = 1673```

Azimuth, elevation, and slant range to Matterhorn summit.

```az = 237.8; elev = 18.755; slantRange = 8871.7;```

Latitude, longitude, and ellipsoidal height of summit.

```[lat, lon, hEllipsoidal] = aer2geodetic( ... az, elev, slantRange, lat0, lon0, h0, wgs84Ellipsoid) ```
```lat = 45.976 lon = 7.6583 hEllipsoidal = 4531```

Orthometric height of summit.

```hGeoid = 53; hOrthometric = hEllipsoidal - hGeoid format(fmt)```
```hOrthometric = 4478```

## Input Arguments

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### `az` — Azimuth angles scalar value | vector | matrix | N-D array

Azimuth angles in the local spherical system, specified as a scalar, vector, matrix, or N-D array. Azimuths are measured clockwise from north. Values must be in units that match the input argument `angleUnit`, if supplied, and in degrees, otherwise.

Data Types: `single` | `double`

### `elev` — Elevation angles scalar value | vector | matrix | N-D array

Elevation angles in the local spherical system, specified as a scalar, vector, matrix, or N-D array. Elevations are with respect to a plane perpendicular to the spheroid surface normal. Values must be in units that match the input argument `angleUnit`, if supplied, and in degrees, otherwise.

Data Types: `single` | `double`

### `slantRange` — Distances from local originscalar value | vector | matrix | N-D array

Distances from origin in the local spherical system, returned as a scalar, vector, matrix, or N-D array. The straight-line, 3-D Cartesian distance is used. Units are determined by the `LengthUnit` property of the `spheroid` input.

Data Types: `single` | `double`

### `lat0` — Geodetic latitude of local originscalar value | vector | matrix | N-D array

Geodetic latitude of local origin (reference) point(s), specified as a scalar value, vector, matrix, or N-D array. In many cases there is one origin (reference) point, and the value of `lat0` is scalar, but it need not be. (It may refer to a moving platform, for example). Values must be in units that match the input argument `angleUnit`, if supplied, and in degrees, otherwise.

Data Types: `single` | `double`

### `lon0` — Longitude of local originscalar value | vector | matrix | N-D array

Longitude of local origin (reference) point(s), specified as a scalar value, vector, matrix, or N-D array. In many cases there is one origin (reference) point, and the value of `lon0` is scalar, but it need not be. (It may refer to a moving platform, for example). Values must be in units that match the input argument `angleUnit`, if supplied, and in degrees, otherwise.

Data Types: `single` | `double`

### `h0` — Ellipsoidal height of local originscalar value | vector | matrix | N-D array

Ellipsoidal height of local origin (reference) point(s), specified as a scalar value, vector, matrix, or N-D array. In many cases there is one origin (reference) point, and the value of `h0` is scalar, but it need not be. (It may refer to a moving platform, for example). Units are determined by the `LengthUnit` property of the spheroid input.

Data Types: `single` | `double`

### `spheroid` — Reference spheroidreferenceEllipsoid | oblateSpheroid | referenceSphere

Reference spheroid, specified as a referenceEllipsoid, oblateSpheroid, or referenceSphere object. Use the constructor for one of these three classes, or the `wgs84Ellipsoid` function, to construct a Mapping Toolbox spheroid object. You can not directly pass in a string that names your spheroid. Instead, pass that string to `referenceEllipsoid` or `referenceSphere` and use the resulting object.

### `angleUnit` — Units of angles`'degrees'` (default) | `'radians'`

Units of angles, specified as ‘degrees' (default), or 'radians'.

Data Types: `char`

## Output Arguments

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### `lat` — Geodetic latitudesscalar value | vector | matrix | N-D array

Geodetic latitudes of one or more points, returned as a scalar value, vector, matrix, or N-D array. Units are determined by the input argument `angleUnit`, if supplied; values are in degrees, otherwise. When in degrees, they lie in the closed interval [-90 90].

### `lon` — Longitudesscalar value | vector | matrix | N-D array

Longitudes of one or more points, returned as a scalar value, vector, matrix, or N-D array. Units are determined by the input argument `angleUnit`, if supplied; values are in degrees, otherwise. When in degrees, they lie in the interval [-180 180].

### `h` — Ellipsoidal heightsscalar value | vector | matrix | N-D array

Ellipsoidal heights of one or more points, returned as a scalar value, vector, matrix, or N-D array. Units are determined by the `LengthUnit` property of the `spheroid` object