ned2ecef

Transform local north-east-down coordinates to geocentric Earth-centered Earth-fixed

Description

example

[X,Y,Z] = ned2ecef(xNorth,yEast,zDown,lat0,lon0,h0,spheroid) transforms the local north-east-down (NED) Cartesian coordinates specified by xNorth, yEast, and zDown to the geocentric Earth-centered Earth-fixed (ECEF) Cartesian coordinates specified by X, Y, and Z. 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.

[___] = ned2ecef(___,angleUnit) specifies the units for latitude and longitude. Specify angleUnit as 'degrees' (the default) or 'radians'.

Examples

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

wgs84 = wgs84Ellipsoid('kilometer');

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

lat0 = 44.532;
lon0 = -72.782;
h0 = 1.699;

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

xNorth = 1.3343;
yEast = -2.5444;
zDown = 0.3600;

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

[x,y,z] = ned2ecef(xNorth,yEast,zDown,lat0,lon0,h0,wgs84)
x = 1.3457e+03
y = -4.3509e+03
z = 4.4523e+03

Reverse the transformation using the ecef2ned function.

[xNorth,yEast,zDown] = ecef2ned(x,y,z,lat0,lon0,h0,wgs84)
xNorth = 1.3343
yEast = -2.5444
zDown = 0.3600

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'.

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 Reference Spheroids.

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

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

Data Types: char | string

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'.

Tips

To transform vectors instead of coordinate locations, use the ned2ecefv function.

Introduced in R2012b