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lla2flat

Convert from geodetic latitude, longitude, and altitude to flat Earth position

Description

example

flatearth_pos = lla2flat(lla,llo,psio,href) estimates an array of flat Earth coordinates, flatearth_pos, from an array of geodetic coordinates, lla. This function estimates the flatearth_pos value with respect to a reference location that you define with llo, psio, and href.

flatearth_pos = lla2flat(lla,llo,psio,href,ellipsoidModel) estimates the coordinates for a specific ellipsoid planet.

flatearth_pos = lla2flat(lla,llo,psio,href,flattening,equatorialRadius) estimates the coordinates for a custom ellipsoid planet defined by flattening and equatorialRadius.

Examples

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Estimate the coordinates at a latitude, longitude, and altitude:

p = lla2flat( [ 0.1 44.95 1000 ], [0 45], 5, -100 )
p =
   1.0e+04 *

    1.0530   -0.6509   -0.0900

Estimate coordinates at multiple latitudes, longitudes, and altitudes with the WGS84 ellipsoid model:

p = lla2flat( [ 0.1 44.95 1000; -0.05 45.3 2000 ], [0 45], 5, -100, 'WGS84' )
p =
   1.0e+04 *

    1.0530   -0.6509   -0.0900
   -0.2597    3.3751   -0.1900

Estimate coordinates at multiple latitudes, longitudes, and altitudes using a custom ellipsoid model:

f = 1/196.877360;
Re = 3397000;
p = lla2flat( [ 0.1 44.95 1000; -0.05 45.3 2000 ], [0 45], 5, -100,  f, Re )
p =
   1.0e+04 *

    0.5588   -0.3465   -0.0900
   -0.1373    1.7975   -0.1900

Input Arguments

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Geodetic coordinates (latitude, longitude, and altitude), specified as an m-by-3 array in [degrees degrees meters]. Latitude and longitude values can be any value. However, latitude values of +90 and -90 may return unexpected values because of singularity at the poles.

Data Types: double

Reference location of latitude and longitude, specified as an m-by-2 array, in degrees, for the origin of the estimation and the origin of the flat Earth coordinate system.

Data Types: double

Angular direction of the flat Earth x-axis, specified as a scalar. The angular direction is the degrees clockwise from north, which is the angle in degrees used for converting flat Earth x and y coordinates to the north and east coordinates.

Data Types: double

Reference height from the surface of the Earth to the flat Earth frame with regard to the flat Earth frame, specified as a scalar, in meters.

Data Types: double

Ellipsoid planet model, specified as 'WGS84'.

Data Types: char | string

Flattening at each pole, specified as a scalar.

Data Types: double

Planetary equatorial radius, specified as a scalar, in meters.

Data Types: double

Output Arguments

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Flat Earth position coordinates, specified as 3-element vector, in meters.

Tips

  • This function assumes that the flight path and bank angle are zero.

  • This function assumes that the flat Earth z-axis is normal to the Earth only at the initial geodetic latitude and longitude. This function has higher accuracy over small distances from the initial geodetic latitude and longitude. It also has higher accuracy at distances closer to the equator. The function calculates a longitude with higher accuracy when the variations in latitude are smaller. Additionally, longitude is singular at the poles.

Algorithms

The function begins by finding the small changes in latitude and longitude from the output latitude and longitude minus the initial latitude and longitude:

dμ=μμ0dι=ιι0.

To convert geodetic latitude and longitude to the north and east coordinates, the function uses the radius of curvature in the prime vertical (RN) and the radius of curvature in the meridian (RM). RN and RM are defined by the following relationships:

RN=R1(2ff2)sin2μ0,

where (R) is the equatorial radius of the planet and f is the flattening of the planet.

Small changes in the north (dN) and east (dE) positions are approximated from small changes in the north and east positions by

dN=dμatan(1RM),

and

dE=dιatan(1RNcosμ0).

With the conversion of the North and East coordinates to the flat Earth x and y coordinates, the transformation has the form of

[pxpy]=[cosψsinψsinψcosψ][NE],

where

(ψ)

is the angle in degrees clockwise between the x-axis and north.

The flat Earth z-axis value is the negative altitude minus the reference height (href):

pz=hhref.

References

[1] Etkin, B., Dynamics of Atmospheric Flight. New York: John Wiley & Sons, 1972.

See Also

Topics

Introduced in R2011a