LLA to ECEF Position

Calculate Earth-centered Earth-fixed (ECEF) position from geodetic latitude, longitude, and altitude above planetary ellipsoid

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Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The LLA to ECEF Position block converts geodetic latitude $$\left(\overline{\mu }\right)$$, longitude $$\left(\overline{\iota }\right)$$, and altitude $$\left(\overline{h}\right)$$ above the planetary ellipsoid into a 3-by-1 vector of ECEF position $$\left(\overline{p}\right)$$. 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. For more information the ECEF position calculation, see Algorithms.

Examples

Gravity Models with Precessing Reference Frame

Implement various gravity models with precessing reference frames using Aerospace Blockset™ blocks.

• Open Live Script

Limitations

• The planet is assumed to be ellipsoidal. To use a spherical planet, set the Flattening parameter to zero.

• The implementation of the ECEF coordinate system assumes that the origin is at the center of the planet, the x-axis intersects the Greenwich meridian and the equator, the z-axis is the mean spin axis of the planet, positive to the north, and the y-axis completes the right-handed system.

Ports

Input

μ l — Geodetic latitude and longitude

2-by-1 vector

Geodetic latitude and longitude, specified as a 2-by-1 vector, in degrees.

Data Types: double

h — Altitude

scalar

Altitude above the planetary ellipsoid, specified as a scalar.

Data Types: double

Output

X_f — Position

3-by-1 vector

Position in ECEF frame, returned as a 3-by-1 vector, in the same units as the input at the h port.

Data Types: double

Parameters

Units — Units

Metric (MKS) (default) | English

Parameter and output units:

Units	Radius from CG to Center of Planet	Equatorial Radius
Metric (MKS)	Meters	Meters
English	Feet	Feet

Dependencies

To enable this, set Planet model to Earth (WGS84).

Programmatic Use

Block Parameter: units

Type: character vector

Values: 'Metric (MKS)' | 'English'

Default: 'Metric (MKS)'

Planet model — Planet model

Earth (WGS84) (default) | Custom

Planet model to use, Custom or Earth (WGS84).

Programmatic Use

Block Parameter: ptype

Type: character vector

Values: 'Earth (WGS84)' | 'Custom'

Default: 'Earth (WGS84)'

Flattening — Flattening of planet

1/298.257223563 (default) | scalar

Flattening of the planet, specified as a double scalar.

Dependencies

To enable this parameter, set Planet model to Custom.

Programmatic Use

Block Parameter: F

Type: character vector

Values: double scalar

Default: 1/298.257223563

Equatorial radius of planet — Radius of planet at equator

6378137 (default) | scalar

Radius of the planet at its equator, in the same units as the desired units for ECEF position.

Dependencies

To enable this parameter, set Planet model to Custom.

Programmatic Use

Block Parameter: R

Type: character vector

Values: double scalar

Default: 6378137

Algorithms

The ECEF position is calculated from the geocentric latitude at mean sea-level (λ_s) and longitude using:

$$\overline{p}=\left[\begin{array}{c}{\overline{p}}_x\\ {\overline{p}}_y\\ {\overline{p}}_z\end{array}\right]=\left[\begin{array}{c}{r}_s\cos {\lambda }_s\cos \iota +h\cos \mu \cos \iota \\ r_s\cos {\lambda }_s\sin \iota +h\cos \mu \sin \iota \\ r_s\sin {\lambda }_s+h\sin \mu \end{array}\right],$$

where geocentric latitude at mean sea-level and the radius at a surface point (r_s) are defined by flattening $$\left(\overline{f}\right)$$, and equatorial radius $$\left(\overline{R}\right)$$ in the following relationships:

$$\begin{array}{l}{\lambda }_s=\text{atan}\left({(1-f)}^2\tan \mu \right)\\ \\ r_s=\sqrt{\frac{R^2}{1+\left(1/{(1-f)}^2-1\right){\sin }^2{\lambda }_s}}\end{array}$$

References

[1] Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation, Hoboken, NJ: John Wiley & Sons, 1992.

[2] Zipfel, Peter H., Modeling and Simulation of Aerospace Vehicle Dynamics. Second Edition. Reston, VA: AIAA Education Series, 2000.

[3] Recommended Practice for Atmospheric and Space Flight Vehicle Coordinate Systems, R-004-1992, ANSI/AIAA, February 1992.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a