LLA to Flat Earth
Conversion of geodesic coordinates to local tangent plane coordinates.
blockType: SubSystem
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Path in the library: |
Description
The LLA to Flat Earth block converts geodetic coordinates - latitude ( ), longitude ( ), and elevation ( ) - into a 3-by-1 vector of positions in a planar coordinate system ( ). Latitude and longitude can take any values, but latitude values +90° and −90° (poles) may return incorrect results due to peculiarities of calculations.
Algorithms
The local tangent plane coordinate system assumes a positive downward direction of the Z axis. The calculation begins by defining small changes in latitude and longitude as the difference between the final and initial values of latitude and longitude.
The algorithm uses to convert geodetic latitude and longitude to north/east coordinates:
where
-
- is the equatorial radius of the planet;
-
- the compression of the planet.
Small changes of coordinates in the north ( ) and east ( ) are approximated through small changes of latitude and longitude by the formulas:
When converting north/east coordinates to and coordinates of a plane coordinate system, a transformation of the form is used:
where is the clockwise angle (in degrees) between the axis and the north direction.
The value of coordinate in the local tangent plane coordinate system is calculated as:
Ports
Input
#
μ l (deg)
—
geodetic latitude and longitude
`vector 2 by 1
Details
Geodetic latitude and longitude given as a vector, in degrees.
| Data types |
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| Complex numbers support |
No |
#
h (m)
—
altitude above sea level
scalar
Details
The height above the input reference height given by a scalar quantity.
| Data types |
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| Complex numbers support |
No |
#
href (m)
—
reference height
scalar
Details
The reference height from the Earth’s surface to the coordinate system of the local tangent plane.
| Data types |
|
| Complex numbers support |
No |
Output
#
Xe (m)
—
position in the coordinate system of the local tangent plane
`vector 3 by 1
Details
The position in the coordinate system of the local tangent plane, returned as a vector.
| Data types |
|
| Complex numbers support |
No |
Parameters
Parameters
#
Planet model —
planet
Earth (WGS84) | Custom
Details
The planet model used.
| Values |
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| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Flattening — planetary contraction
Details
The compression of the planet defined as a scalar.
Dependencies
To use this parameter, set the parameter Planet model to Custom.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Equatorial radius of planet — equatorial radius of the planet
Details
The equatorial radius of the planet, given as a scalar.
Dependencies
To use this parameter, set the parameter Planet model to Custom.
| Default value |
|
| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Reference geodetic latitude and longitude [deg] — initial geodetic latitude and longitude (deg)
Details
Initial geodetic latitude and longitude (in degrees) given as a vector.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Direction of flat Earth x-axis (degrees clockwise from north — direction of the local tangent plane along the axis (in degrees clockwise from north)
Details
Angle to convert the local tangent plane coordinates and to north and east (geodetic) coordinates, specified as a scalar, in degrees.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |