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# ned2geodetic

Transform local north-east-down coordinates to geodetic

## Syntax

``````[lat,lon,h] = ned2geodetic(xNorth,yEast,zDown,lat0,lon0,h0,spheroid)``````
``[___] = ned2geodetic(___,angleUnit)``

## Description

example

``````[lat,lon,h] = ned2geodetic(xNorth,yEast,zDown,lat0,lon0,h0,spheroid)``` transforms the local north-east-down (NED) Cartesian coordinates specified by `xNorth`, `yEast`, and `zDown` to the geodetic coordinates specified by `lat`, `lon`, and `h`. Specify the origin of the local NED 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. ```
````[___] = ned2geodetic(___,angleUnit)` specifies the units for latitude and longitude. Specify `angleUnit` as `'degrees'` (the default) or `'radians'`.```

## Examples

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Find the geodetic coordinates of Mount Mansfield with respect to a nearby aircraft, using the NED coordinates of Mount Mansfield with respect to the geodetic coordinates of the aircraft.

First, specify the reference spheroid as WGS84. For more information about WGS84, see Comparison of Reference Spheroids. The units for ellipsoidal height and NED coordinates must match the units specified by the `LengthUnit` property of the reference spheroid. The default length unit for the reference spheroid created by `wgs84Ellipsoid` is `'meter'`.

`wgs84 = wgs84Ellipsoid;`

Specify the geodetic coordinates of the local origin. In this example, the local origin is the aircraft. Specify `h0` as ellipsoidal height in meters.

```lat0 = 44.532; lon0 = -72.782; h0 = 1699;```

Specify the NED coordinates of the point of interest. In this example, the point of interest is Mount Mansfield.

```xNorth = 1334.3; yEast = -2543.6; zDown = 359.65;```

Then, calculate the geodetic coordinates of Mount Mansfield. The result `h` is the ellipsoidal height of the mountain in meters. To view the results in standard notation, specify the display format as `shortG`.

```format shortG [lat,lon,h] = ned2geodetic(xNorth,yEast,zDown,lat0,lon0,h0,wgs84)```
```lat = 44.544 ```
```lon = -72.814 ```
```h = 1340 ```

Reverse the transformation using the `geodetic2ned` function.

`[xNorth,yEast,zDown] = geodetic2ned(lat,lon,h,lat0,lon0,h0,wgs84)`
```xNorth = 1334.3 ```
```yEast = -2543.6 ```
```zDown = 359.65 ```

## Input Arguments

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NED x-coordinates of one or more points in the local NED system, specified as a scalar, vector, matrix, or N-D array. 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`

NED y-coordinates of one or more points in the local NED system, specified as a scalar, vector, matrix, or N-D array. 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`

NED z-coordinates of one or more points in the local NED system, specified as a scalar, vector, matrix, or N-D array. 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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Geodetic latitude of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified in degrees within the interval `[-90 90]`. To use values in radians, specify the `angleUnit` argument as `'radians'`.

Geodetic longitude of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified in degrees within the interval ```[-180 180]```. To use values in radians, specify the `angleUnit` argument as `'radians'`.

Ellipsoidal height of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified 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.

## Version History

Introduced in R2012b

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