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Direction Cosine Matrix ECI to ECEF

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

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  • Direction Cosine Matrix ECI to ECEF block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

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

Ports

Input

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Difference between UTC and Universal Time (UT1) in seconds, specified as a scalar, for which the function calculates the direction cosine or transformation matrix.

Example: 0.234

Dependencies

To enable this port, select the Higher accuracy parameters check box.

Data Types: double

Difference between International Atomic Time (IAT) and UTC, specified as a scalar, in seconds, for which the function calculates the direction cosine or transformation matrix.

Example: 32

Dependencies

To enable this port, select the Higher accuracy parameters check box.

Data Types: double

Polar displacement of Earth, specified as a 1-by-2 array, in radians, from the motion of the Earth crust, along the x-axis and y-axis.

Example: [-0.0682e-5 0.1616e-5]

Dependencies

To enable this port, select the Higher accuracy parameters check box.

Data Types: double

Adjustment based on reduction method, specified as 1-by-2 array. The name of the port depends on the setting of the Reduction parameter:

  • If the 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-axis and y-axis.

  • If the reduction method is IAU-76/FK5, this input is the adjustment to the longitude ([Δδψ, Δδε]), specified in radians.

For historical values, see the International Earth Rotation and Reference Systems Service website (https://www.iers.org).

Example: [-0.2530e-6 -0.0188e-6]

Dependencies

To enable this port, select the Higher accuracy parameters check box.

Data Types: double

Time increment source, specified as a scalar, such as the Clock block.

Dependencies

  • The port name and time increment depend on the Time Increment parameter.

    Time Increment ValuePort Name

    Day

    day

    Hour

    hour

    Min

    min

    Sec

    sec

    None

    No port

  • To disable this port, set the Time Increment parameter to None.

Data Types: double

Output

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Direction cosine matrix ECI to ECEF.

Data Types: double

Parameters

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

  • IAU-76/FK5

    Reduce the calculation using the IAU-76/Fifth Fundamental Catalogue (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.

Programmatic Use

Block Parameter: red
Type: character vector
Values: 'IAU-2000/2006' | 'IAU-76/FK5'
Default: 'IAU-2000/2006'

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

Programmatic Use

Block Parameter: year
Type: character vector
Values: double, whole number, greater than 1
Default: '2013'

Month to calculate the UTC date.

Programmatic Use

Block Parameter: month
Type: character vector
Values: 'January' | 'February' | 'March' | 'April' | 'May' | 'June' | 'July' | 'August' | 'September' | 'October' | 'November' | 'December'
Default: 'January'

Day to calculate the UTC date.

Programmatic Use

Block Parameter: day
Type: character vector
Values: '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' | '10' | '11' | '12' | '13' | '14' | '15' | '16' | '17' | '18' | '19' | '20' | '21' | '22' | '23' | '24' | '25' | '26' | '27' | '28' | '29' | '30' | '31'
Default: '1'

Hour to calculate the UTC date. Enter a double value that is a whole number, from 0 to 24.

Programmatic Use

Block Parameter: hour
Type: character vector
Values: double, whole number, 0 to 24
Default: '0'

Minutes to calculate the UTC date. Enter a double value that is a whole number, from 0 to 60.

Programmatic Use

Block Parameter: min
Type: character vector
Values: double, whole number, 0 to 60
Default: '0'

Seconds to calculate the UTC date. Enter a double value that is a whole number, from 0 to 60.

Programmatic Use

Block Parameter: sec
Type: character vector
Values: double, whole number, 0 to 60
Default: '0'

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 time increment input, the clock source.

If you select None, the calculated Julian date does not take into account the model simulation time.

Programmatic Use

Block Parameter: deltaT
Type: character vector
Values: 'None' | 'Day' | 'Hour' | 'Min' | 'Sec'
Default: 'Day'

Out-of-range block behavior, specified as follows.

ActionDescription

None

No action.

Warning

Warning in the Diagnostic Viewer, model simulation continues.

Error (default)

Error in the Diagnostic Viewer, model simulation stops.

Programmatic Use

Block Parameter: errorflag
Type: character vector
Values: 'None' | 'Warning' | 'Error'
Default: 'Error'

Select this check box to enable these inputs. These inputs let you better control the conversion result. See Input for a description.

  • Δ UT1

  • Δ AT

  • [ xp , yp ]

  • [Δδψ, Δδε] or [d X, d Y ]

Programmatic Use

Block Parameter: extraparamflag
Type: character vector
Values: 'on' | 'off'
Default: 'on'

Extended Capabilities

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

Version History

Introduced in R2013b

See Also

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