Estimate geodetic latitude, longitude, and altitude from flat Earth position
The Flat Earth to LLA block converts a 3-by-1 vector of Flat Earth position into geodetic latitude , longitude , and altitude (h). The flat Earth coordinate system assumes the z-axis is downward positive. The estimation begins by transforming the flat Earth x and y coordinates to North and East coordinates. The transformation has the form of
where is the angle in degrees clockwise between the x-axis and north.
To convert the North and East coordinates to geodetic latitude and longitude, the radius of curvature in the prime vertical (RN) and the radius of curvature in the meridian (RM) are used. (RN) and (RM) 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 in latitude and longitude are approximated from small changes in the North and East positions by
The output latitude and longitude are simply the initial latitude and longitude plus the small changes in latitude and longitude.
The altitude is the negative flat Earth z-axis value minus the reference height (href).
Specifies the parameter and output units:
This option is only available when Planet
model is set to
Specifies the planet model to use:
Specifies the flattening of the planet. This option is only available with Planet model Custom.
Specifies the radius of the planet at its equator. The units of the equatorial radius parameter should be the same as the units for flat Earth position. This option is only available with Planet model Custom.
Specifies the reference location, in degrees of latitude and longitude, for the origin of the estimation and the origin of the flat Earth coordinate system.
Specifies angle used for converting flat Earth x and y coordinates to North and East coordinates.
|3-by-1 vector||Contains the position in flat Earth frame.|
|Scalar||Contains the reference height from surface of Earth to flat Earth frame with regard to Earth frame, in same units as flat Earth position.|
|2-by-1 vector||Contains the geodetic latitude and longitude, in degrees.|
|Scalar||Contains the altitude above the input reference altitude, in same units as flat Earth position.|
This estimation method assumes the flight path and bank angle are zero.
This estimation method assumes the flat Earth z-axis is normal to the Earth at the initial geodetic latitude and longitude only. This method has higher accuracy over small distances from the initial geodetic latitude and longitude, and nearer to the equator. The longitude will have higher accuracy the smaller the variations in latitude. Additionally, longitude is singular at the poles.
Etkin, B., Dynamics of Atmospheric Flight, John Wiley & Sons, New York, 1972.
Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, Second Edition, John Wiley & Sons, New York, 2003.