lla2flat - Estimate flat Earth position from geodetic latitude, longitude, and altitude

Syntax

Description

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 llo, psio, and href define.

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.

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.

Input Arguments

lla	m-by-3 array of geodetic coordinates (latitude, longitude, and altitude), in [degrees, degrees, meters].
llo	Reference location, in degrees, of latitude and longitude, for the origin of the estimation and the origin of the flat Earth coordinate system.
psio	Angular direction of flat Earth x-axis (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.
href	Reference height from the surface of the Earth to the flat Earth frame with regard to the flat Earth frame, in meters.
ellipsoidModel	String that specifies the specific ellipsoid planet model. This function supports only 'WGS84'. Default: WGS84
flattening	Custom ellipsoid planet defined by flattening.
equatorialRadius	Planetary equatorial radius, in meters.

Output Arguments

flatearth_pos

Flat Earth position coordinates, in meters.

Examples

Estimate coordinates at latitude, longitude, and altitude:

p = lla2flat( [ 0.1 44.95 1000 ], [0 45], 5, -100 )

p =

  1.0e+004 *

    1.0530   -0.6509   -0.0900

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

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

p =

  1.0e+004 *

    1.0530   -0.6509   -0.0900
   -0.2597    3.3751   -0.1900

Estimate coordinates at multiple latitudes, longitudes, and altitudes, specifying 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+004 *

    0.5588   -0.3465   -0.0900
   -0.1373    1.7975   -0.1900

Algorithms

The estimation begins by finding the small changes in latitude and longitude from the output latitude and longitude minus the initial latitude and longitude.

To convert geodetic latitude and longitude to the North and East coordinates, the estimation uses the radius of curvature in the prime vertical (R_N) and the radius of curvature in the meridian (R_M). R_N and R_M are defined by the following relationships:

where (R) is the equatorial radius of the planet and 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

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

where

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 (h_ref).

References

Etkin, B., Dynamics of Atmospheric Flight. NewYork: John Wiley & Sons, 1972.

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, 2nd ed. New York: John Wiley & Sons, 2003.

See Also

flat2lla

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