Direction Cosine Matrix ECI to ECEF

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

• Library:

• 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 Universal Coordinated Time (UTC), for the specified time and geophysical data.

Ports

Input

ΔUT1 — Difference between UTC and Universal Time

scalar

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

ΔAT — Difference between International Atomic Time and UTC

scalar

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

[xp,yp] — Polar displacement of Earth

1-by-2 array

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

Port_5 — Adjustment based on reduction method

1-by-2 array

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 International Earth Rotation and Reference Systems Service.

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

Dependencies

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

Data Types: double

Port_6 — Time increment source

scalar

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 Value	Port 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

DCMfi — Direction cosine matrix

3-by-3 matrix

Direction cosine matrix ECI to ECEF.

Data Types: double

Parameters

Reduction — Reduction method

IAU-76/FK5 (default) | IAU-2000/2006

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 — Year

2013 (default) | double, whole number, greater than 1

Year to calculate the Universal Coordinated 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 — Month

January (default) | February | March | April | May | June | July | August | September | October | November | December

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 — Day

1 (default) | 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

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 — Hour

0 (default) | double, whole number, in the range of 0 and 24

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 — Minutes

0 (default) | double, whole number, in the range of 0 and 60

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 — Seconds

0 (default) | double, whole number, in the range of 0 and 60

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 — Time increment

Day (default) | Hour | Min | Sec | None

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'

Action for out-of-range input — Action

Error (default) | Warning | None

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

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

Programmatic Use

Block Parameter: errorflag

Type: character vector

Values: 'None' | 'Warning' | 'Error'

Default: 'Error'

Higher accuracy parameters — Enable higher accuracy parameters

on (default) | off

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™.