Aerospace Blockset™

Flat Earth to LLA

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

Library

Utilities/Axes Transformations

Description

The Flat Earth to LLA block converts a 3-by-1 vector of Flat Earth position into geodetic latitude , longitude , and altitude . 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 and the radius of curvature in the meridian are used. and are defined by the following relationships:

where 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 .

Dialog Box

Units

Specifies the parameter and output units:

Units	Position	Equatorial Radius	Altitude
Metric (MKS)	Meters	Meters	Meters
English	Feet	Feet	Feet

This option is only available when Planet model is set to Earth (WGS84).

Planet model

Specifies the planet model to use: Custom or Earth (WGS84).

Flattening

Specifies the flattening of the planet. This option is only available with Planet model Custom.

Equatorial radius of planet

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.

Initial geodetic latitude and longitude

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.

Direction of flat Earth x-axis (degrees clockwise from north)

Specifies angle used for converting flat Earth x and y coordinates to North and East coordinates.

Inputs and Outputs

Assumptions and Limitations

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.

Example

See the asbhl20 demo for an example of this block.

References

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.

See Also

Direction Cosine Matrix ECEF to NED

Direction Cosine Matrix ECEF to NED to Latitude and Longitude

ECEF Position to LLA

Geocentric to Geodetic Latitude

LLA to ECEF Position

Radius at Geocentric Latitude

Estimate Inertia Tensor

FlightGear Preconfigured 6DoF Animation