Direction Cosine Matrix ECI to ECEF

Convert Earth-centered inertial (ECI) to Earth-centered Earth-fixed (ECEF) coordinates

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix ECI to ECEF block calculates the position direction cosine matrix (ECI to ECEF), based on the specified reduction method and Universal Coordinated Time (UTC), for the specified time and geophysical data.

Dialog Box

Reduction

Reduction method to calculate the direction cosine matrix. Method can be one of the following:

• `IAU-76/FK5`

Reduce the calculation using the International Astronomical Union (IAU)-76/Fifth Fundamental Catalogue (FK5) (IAU-76/FK5) reference system. Choose this reduction method if the reference coordinate system for the conversion is FK5.

 Note:   This method uses the IAU 1976 precession model and the IAU 1980 theory of nutation to reduce the calculation. This model and theory are no longer current, but the software provides this reduction method for existing implementations. Because of the polar motion approximation that this reduction method uses, the block calculates the transformation matrix rather than the direction cosine matrix.
• `IAU-2000/2006`

Reduce the calculation using the International Astronomical Union (IAU)-2000/2006 reference system. Choose this reduction method if the reference coordinate system for the conversion is IAU-2000. This reduction method uses the P03 precession model to reduce the calculation.

Year

Specify the year used to calculate the Universal Coordinated Time (UTC) date. Enter a double value that is a whole number greater than 1, such as `2013`.

Month

Specify the month used to calculate the UTC date. From the list, select the month from `January` to `December`.

Day

Specify the day used to calculate the UTC date. From the list, select the day from `1` to `31`.

Hour

Specify the hour used to calculate the UTC date. Enter a double value that is a whole number, from `0` to `24`.

Minutes

Specify the minutes used to calculate the UTC date. Enter a double value that is a whole number, from `0` to `60`.

Seconds

Specify the seconds used to calculate the UTC date. Enter a double value that is a whole number, from `0` to `60`.

Time Increment

Specify the time increment between the specified date and the desired model simulation time. The block adjusts the calculated direction cosine matrix to take into account the time increment from model simulation. For example, selecting `Day` and connecting a simulation timer to the port means that each time increment unit is one day and the block adjusts its calculation based on that simulation time.

This parameter corresponds to the fifth block input, the clock source.

Possible values are `Day`, `Hour`, `Min`, `Sec`, and `None`. If you select `None`, the calculated Julian date does not take into account the model simulation time. Selecting this option removes the fifth block input.

Action for out of range input

Specify the block behavior when the block inputs are out of range.

ActionDescription
`None`No action.
`Warning`Warning in the MATLAB® Command Window, model simulation continues.
`Error` (default)MATLAB returns an exception, model simulation stops.

Higher accuracy parameters

Select this check box to enable the following inputs. These inputs let you better control the conversion result. See Inputs and Outputs for a description.

 ΔUT1 ΔAT [xp,yp] [Δδψ, Δδε] or [dX,dY]

Inputs and Outputs

InputDimension TypeDescription

First (Optional)

Scalar

ΔUT1, difference between UTC and Universal Time (UT1) in seconds, for which the function calculates the direction cosine or transformation matrix, for example, `0.234`.

Second (Optional)

Scalar

ΔAT, difference between International Atomic Time (IAT) and UTC in seconds, for which the function calculates the direction cosine or transformation matrix, for example, `32`.

Third (Optional)

1-by-2 array

[xp,yp], polar displacement of the Earth, in radians, from the motion of the Earth crust, along the x- and y-axes, for example, `[-0.0682e-5 0.1616e-5]`

Fourth (Optional)

1-by-2 array

• If reduction method is `IAU-2000/2006`, this input is the adjustment to the location of the Celestial Intermediate Pole (CIP), specified in radians. This location ([dX,dY]) is along the x- and y-axis, for example, `[-0.2530e-6 -0.0188e-6]`.

• If reduction method is `IAU-76/FK5`, this input is the adjustment to the longitude ([Δδψ, Δδε]), specified in radians, for example, ```[-0.2530e-6 -0.0188e-6]```.

For historical values, see the International Earth Rotation and Reference Systems Service Web site (`http://www.iers.org`) and navigate to the Earth Orientation Data Data/Products page.

Fifth (Optional)

Scalar

Time increment, for example the Clock block.

If the Higher accuracy parameters check box is cleared and the Time Increment parameter is a value other than `None`, the block has no input.

OutputDimension TypeDescription

First

3-by-3 array

Direction cosine or transformation matrix.